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Rep. Pmg Phys. 55 (1992) 1165-1240. Pliuted in the UK

Scanning tunnelling microscopy

L E C van de Leemput and H van Kempen Rerearch Institute for Materials, Univelaity of Nljmegm, lbzmoaiveld, 652.5 ED Nipegen, The Netherlands

Abstract

A scanning tunnelling microscope can image surfaces down to the atomic scale. Its very high resolution is caused by its local probing mechanism: a tunnel current which Rows through the outermost atom of a scanning tip to the sample. Its invention, about ten years ago, was based on an ingenious blend of pantum physics: mechanical design and electronic control. Since then, it has proved to be a very versatile instrument Its applications range from the characterization of surface roughness to atomic reconstructions, and from doped semiconductors to cell membranes. It can operate in ultra high vacuum, in air, in reactive gases, in corrosive solutions or at cryogenic temperatures.

This paper reviews the evolution of scanning tunnelling microscopy in the first decade after its invention. Attention is focused on the basics of STM. tunnelling theory, mechanical design and modes of operation. Representative examples of applications in various fields of research are discussed.

This review was received in March 1991.

W34-4885/92/081165+76$18.W @J 1992 IOP Publishing Ltd 1165

1166 L E C van de Leemput and H van Kempen

Contents

1. General aspects of scanning tunnelling miaOSWpY 1.1. Introduction 1.2. Principle of operation 1.3. Fundamental aspects of a local hmneUing probe 1.4. The STM as a research tool 1.5. STM related techniques

2.1. General formalism 2.2. "ieiling, a distance probe 2.3. The barrier shape 2.4. Elastic tunnelling SpeCUOSWpY 2.5. Inelastic tunnewg specvoswpy 2.6. Resonant tunnelling, surface states and Gundlach oscillations 2.7. lhnneiling at bigher voltages 2.8. The tunnel time 2.9. Single electron effects

3.1. lbpograpbical imaging 3.2 Spectroscopical imaging

4. Building a scanning tunnelling miaoscope 4.1. Mechanical design 4.2. Ditferent environments 4.3. Electronics and data processing

5. Operating modes of an STM 5.1. lbpography 5.2 Spectrascopy 5.3. Work function measurement 5.4. Potentiometry

6. Other scanning tip miamcopes 6.1. The atomic force miaoscope 6.2. Scanning thermal profiler 6.3. Scanning noise microswp? 6.4. Non-linear alternating current tunnelling miaoscopy 6.5. Scanning ion conductance. microswpe 6.6. Detection of secondary particles 6.7. Ballistic electron emission microscopy

7.1. Graphite 7.2 Silicon(ll1) 7 x 7 7.3. Metals 7.4. Non-regular structures 7.5. Adsorbate wvered surfaces

2. The physics of tu~elling

3. The imaging prosess

7. Surface science with STM

page 1167 1167 1167 1167 1168 1169 1169 1169 1171 1171 1173 1174 1176 1177 1178

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m a

Scanning funnelling microscofl

8. Solid state physics 8.1. Charge density waves 8.2. Superconductors 8.3. Conduction in inhomogeneous materials 8.4. Phonon detection 8.5. Spin polarized tunnelling

9. Exotic applications in physics 9.1. Displacement sensors 9.2. Detectors and mixers 9.3, Quantum point contacts 9.4. Electron spin resonance

10. Biology and organic chemistry 10.1. Introduction 10.2. Preparation methods and examples

11. Electrochemistry 12. Technological applications of STM

12.1. lkibology: wear and friction 12.2. Nanomachining and nanolithography

13. Conelusions Acknowledgments Referenm

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I. General asps& oi scanniw tunnelling miemscopy

1.1. Introduction A wnning tunnelliig microscope (sm) is a microscope which has a resolution of a few hgstr6m in lateral directions and less than one hgstrom in the direction perpendiculae to the surface. It consists of a scanning tip which images the surface by means of a tunnel current Therefore, the sample has to be conducting An S m provides not only three-dimensional information on the topography of the sample, but it also yields information about spectroscopic properties and local variations of the work functions. These unprecedented possibilities make the sm an extremely valuable research tool.

The s m was developed by G Bmnig and H Rohrer in the early 1980s (Bmnig et a1 1982a,b) and experienced a revolutionary expansion in many research areas. As it is a relatively young technique, the interpretation of the measurements is not yet clear in all circumstances. Therefore, the STM itself is still an interesting topic.

1.2. PrrncipIe of operatian

Consider two conducting electrodes separated by some isolator which forms a barrier for the electrons inside the electrodes. If the barrier is thin enough, electrons can tsavei inrough it by a quantum-mecnanisai mechanism caiiea tunneiimg. in an sm, the barrier is a vacuum gap of approximately one nanometre. The tunnelling electrons constitute a current that depends exponentially on the distance between the electrodes. It is this sensitivity that gives an sm its unique resolution: a few hgstriim extra separation leads to a decrease in the tunnel current by a factor ten. One of the electrodes of the sm is shaped into a sharp tip and acts as a probe which investigates the surface properties of the opposite electrode (figure 1). In order to control the barrier width and the lateral position of the tip, it is mounted onto an actuator consisting of piezoelectric ceramic elements. A constant voltage (a few millivolts up to a few volts) is applied to the junction. A control unit regulates the z-piezodrive in such a way that a preset Current (several hundred picoamperes up to several nanoamperes) is established and maintained. Any change in current will be corrected hy a feedback signal to the piezodrive, which will position the tip at a constant-current level above the surface. By applying appropriate ramps to the 2- and y-piezodrives, the tip is scanned along the surface and will follow its contours. Given a liiear behaviour of the transducers, the feedback signal yields directly the topography of the surface. More information on this subject can be found in sections 4 and 5.

1.3. fii.'iamental nspecls of a local runnellingprobe

'hnneUimg of electrons has been studied for ahout forty years (Duke 1969, Burstein and Lundqvist 1969, Walmsley 1987). An STM contains a tunnel junction in which the barrier width can be tuned continuously, in which any kind of electrode material can be used, and in which any kind of materials can be adsorbed at the electrodes. Experiments using these unique properties of an STM can give new insights into the

Snme possibfities of s" in tunnelliig research are described in section 2.

Section 3 deals with the question: what does an STM 'see', and what is its resolution? A simple model indicates that a measured image represents a contour of

L E C van de Leemput and H van Kempen

tunnel pees iLse!f a!!c ! h e ;ntn !he opent;nr nf I" sT?;I. Td:fi&?g

Scanning tunnelling microscopy 1169

Figore 1. Schematic WAV of an SFM. With the help of the z and p pieurelements, a scanning mwement is made Meanwhile, the z piezo-element IS regulated by B feedback circuit which keeps the tunnel current ~ o ~ t a n t . A computer builds up an image of the surface by registering the movements of the lip. In this psture, the sample IS mounted on a plew walker which consists of a piem disk (1) with four metal feet (2). These feet are standing, separated by an mmulating layer (3), an slainle~s-steel blaeks (4). The walker can move by conmctrng and expanding whde electmtatically clamping its h n t and back legs alternativeiy. With this ’louse’ mnstruclion, the sample can be brought withm the range of the z piezo-element. Another way of obtairung approximate pumning is to use a differential scm.

wnstant charge density at a certain energy. However, extensions of ths model show that it is only a first-order approximation. Some of the uncertainties are due to an intrinsic problem: what is the geometrical shape and electronic structure of the tip? This problem is not only a theoretical one: tips differ from experiment to experiment and results can depend on the actual tip shape.

1.4. The sm as a research mol

An STM is an unprecedented surface science tool in that it provides information on a subnanometre scale in three dimensions in direct space. Conventional technique5 with subnanometre resolution (e.g. x-ray diffraction and electron d h c t i o n (LEED)) are restricted to periodic structures and give information in k-space which can be dillicult to interpret, especially in the case of wmplex structures. A major advantage of a local probe is that it enables defem, growth centres and other non-periodic structures to be imaged.

Furthermore, an STM can yield spectroscopic information. By operating at different voltages (up to a few volts), electron states at different energies are probed. In this way, it is possible to obtain images of a selective set of electron orbitals or bands.

However, STM also has some disadvantages. As mentioned in the previous section, the images obtained may depend on the shape of the scanning tip. Because of this and for some other reasons, the lateral resolution is limited to a few hstrOms (daaction techniques can be much more accurate). A severe limitation of STM is that the sample’s surface must be wnducting. Despite this drawback, STM has been used in a wide variety of fields, includmg surface science, solid state physics, electrochemistry, biology, organic chemistry and nano-machining. As a wmplete overview is impossible

1170

due to the rapidly expanding applications, the discussion in this review is limited to some examples of STM measuremeus. More examples can be found in Soethout and van Kempen (1990).

1.5. sm rekted techniques

lb enable measurement3 on non-conducting surfam, other probing techniques have been developed. By far the most promising method uses the attractive or repulsive force between a small tip and the surface: the atomic force microscope (m). The force bends a small lever on which the tip is mounted. The amount of bending is measured by laser techniques or by a tunnelling tip positioned above the lever. This apparatus can obtain ammic resoiuiion on some materiais. Yne &% iogeiber iviih some other STM related microscopes are presented in section 6.

L E C van de Leempur and H van Kempn

2. The physics of tunnelling

21. General fmal i sm

A conduction electron at the surface of a metal feels a potential step which keeps it inside the metal. The height of this step is the energy needed to remove the electron from the metal, a quantity known as the work function (generally written as 4). A typical value for the work function is a few electmnvolts.

Between two metal surfaces opposite each other, two such steps combine to make a potential barrier. Classically, electrons can be at either side of this barrier, but the barrier region is inaccessible. Quantum-mechanically, electrons are described by wavefunctions, which do not drop to zem abruptly at the surface but extend into the barrier with an exponentially decaying tail. When the tails of the wavefunctions from both metals overlap, electrons can cross the barrier, a process known as tunnelling.

the wavefunctions (states) on one side (11,) to those on the other side (11,) (figure 2). The tola1 current is a sum over all possible states:

np !,,np! p&ebzv PR" be y4aE&5eg $; :he -etz% e!ep*ec: AtP" -";-h m=p!pr

The 6-fundon means that the electron does not lose energy during tunnelling (elastic tunnelling). This is not necessarily the case, see section 2.5. The Fermi-Duac functions ( f ( E ) ) take into amunt the tact that tunnelling can only occur from a filled state into an empty state. The energy shift eV is the result of the bias voltage. Note that there are two contributions to the current one from electrons flowing from left to right and another from electrons flowing in the opposite direction. Unfess explicitly stated, we will only consider the low-temperature limit (eV K kT) where the Fermi-Dirac functions become step functions (0) and one of the two contributions drops out:

Scanning tunnelling mikroscopy 1171

PI@= 2. ?be tunnel barrier. lhe following quantities are invoh.ed: the barrier width 8 ,

the work functions 91, $2, the Fermi energies f i x , fm. and the applied voltage V. ?be pmbability that an elecvon tunnels f" a slate $,. to a state $" is given by M,.". lhe salid bani- is a tmpzmldal apprrmimation, a real one is mlraded and lowered by the image potential.

Bardeen (1%1) showed that the matrix elemem can be calculated via

where the integral has to be evaluated over any surface lying in between the two electrodes.

If the bias voltage is small (eV K 6 and eV < EFerm,), the number of states involved increases linearly with bias voltage while the matrix elements stay roughly constant. Because of these two properties the current is proportional to the bias voltage in this limit, which will be dicussed in section 22. Deviations from liearity that are primarily due to a change in the matrix element will be discussed in section 2.7. The section devoted to elastic tunnelling spectroscopy (2.4) will deal with the intluence of the distribution of the electron states among different energies.

The formalism described above is known as the independent electrode approximation. It implicitly assumes that the two electrodes can be described as independent systems, otherwise it would not make sense to talk about wavefunctions belonging to the left or right electrode. The tunnelling proms is described by a small coupling and it is assumed that this coupling does not perturb the wavefunctions significantly. That this assumption is far from valid in an STM will be shown in the section 'The bamer shape in 3D' (see also Sacks and Noguera (1988)). However, as this method makes it relatively straightforward to incorporate many-body effects such as band structure and surface states it is widely used.

Another approach, known as the scattering approach, is to solve the Schrodinger equation by matching an incoming wave with a reflected and a trdnsmitted wave. The current is obtained by adding the transmission probabilities of relevant incoming waves. This approach is very straigbtfonvard but the calculation of the transmission probability can be very difficult. It requires a solution of the Scbradinger equation of a system consisting of the two metals and a barrier. Simmons (1963) solved this

'Ib extend this to a real metal and a complex geometry like an STM is a tremendous task.

problem i!l one dimension; ming the wun app~oxitatinn and a free e!ectron mecl!;

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22. ~nnelling a distance probe

In the limit of low voltage, Simmons (1963) found the folloWing expression for the current density J in a planar tunnel junction:

L E C van de Leempur and H van Kempn

where V is the applied voltage, s is the barrier width and no is the decay constant of the wavefunction in the bamer (t2n32m = 4). Substituting the constants yields

with c, = 4.74 PA V-1 A-1 ev-lla, C, = 1.025 A-l ev-'/,. The main feature of this equation is the exponential decrease of the current if the separation between the two surfaces increases: an increase of 1 A yields a current reduction of a factor ten (4 = 5 ev). The physical basis underlying this exponential behaviour is the fact that the tunnel current depends on the overlap between the two wavefunctions which both decrease exponentially outside the ekarodes.

In three dimensions, the energy of the electmns can be. split into one contribution from motion parallel to the barrier (Ell = ( t k 1 1 ) 2 / ( 2 m ) ) and another from motion perpendicular to the barrier (EI = (hk1)a/(2m)) . The parallel wavevector is conserved during the tunnelling process and the decay length is only determined by the perpendicular energy. An electron moving at the Fermi level has a decay constant n = m. Thus an electron which moves perpendicularly towards the surface (small kll) has a relatively large Nnnel probability. This foeusing effect is amplified hy the fact that the barrier width is smallest if the barrier is traversed along the normal direction (see also section 3.1.2).

2.3. The barrier shape

'Ib calculate the tunnel current, one has to know the shape of the bamer. The simplest bamer is one of constant height: the rectangular barrier. Evidently, this is not a very realistic one. The fimt wrrection is the classical image potential. This potential is the result of the interaction between the tunnelling electron and the Opposing electrode at which a surface charge builds up. Its influence on the tunnel current was investigated in a free electron model by Simmons (1963)t. In the low- voltage range he re-obtained the results of a square barrier, but with reduced height and width. In tke typical case of gold (work function: 5.2 ev), the bamer width is reduced by 2.3 while the height reduction depends on the width s: 5% if s = 100 4 25% if s = 10 A and a total collapse of the barrier if s = 2.3 A As the width of the barrier in an sm (approximately 1 tun) is much smaller than in the usual planar junctions (approximately 10 nm), this effect is much more pronounced

A second wrrection is caused by the many-body nature of the problem. The electrons interact with other charge camem, both in the surface. layer and in the bulk

t Note that the expresion for the image potential which was used by Simmons ~6 a factor of twa IW

large.

:.. ".. 1-1 "1 a" YA,.I.


An emct calculation of such problem is imiossible due to the enormous amount of particles involved. A widely used approximation is the local density approximation: the interaction between the eiearons are summarized in an effective one-electron potential which is caIled the exchangeeonelation energy. Lang and Kohn (1970, see also Orosz (1988)) applied this scheme to the surface of a jellium metal (in which the positive ion cores are approximated by a homogeneous positive background charge) and calculated the one-electron potential Their results are correct close to the surface. At larger distances (typically > 10 A), the classical image potential should emerge. However, as the image potential is a typical non-lod effect, the model CaMOt reproduce this behaviour. Serena et a1 (1986) proposed an interpolation scheme for intermediate regions between the large distance and the small distance behaviour.

The model of Lang and Kohn applies to a single metallic surface. 'Eb make a barrier, two surfaces are needed. Ferrante and Smith (1979) calculated the one electron potential for two identical metal surfaces opposite to each other. As could be expected, there is a strong interaction between the surfaces if they are close together. In another work (1985), they considered two dgerent metals. In this situation a net surface charge exists because of the alignment of the Fermi energies.

A subtle aspect associated with the image potential is that it takes a finite time to build up an image charge. A way to take this into account is to describe the process as an interaction between surface plasmons and the tunnelling electron. The result of such an analysis is that the image charge can build up if the time associated with the tnnnel process is large mmpared with the inverse plasmon frequency and that it is reduced if the tunnel time is small (Jonson, 1980, see also section 2.8). Persson and Baratoff (1988) noted that the problem must be solved self-consistently: the tunnel time intluences the barrier shape via the image potential, but the barrier shape determines the tunnel time. They showed that the use of a classical expression for the image potential overestimates its effect by 20-30% compared with their dynamical results.

The calculations involved become more complicated if the chosen geometry is more realistic (and less symmetric). Several groups (Lucas er a1 1984, Bono and Good 1985, Miskovsky et a1 1980, Morawitz et a1 1987) calculated the image potential for different geometries.

At an atomic scale, correct calculations should take into account the underlying lattice of discrete ion cores. Using the techniqiies from band structure calculations, a self-consistent calculation of the charge density and electron energy can be performed.

Such calculations demand large amounts of computer time; there is the further disadvantage that the lack of symmetry fo rm the use of a rather large unit cell. Tb follow the standard practice of periodic boundary conditions, a periodic array of tips is used.

An example showing the complexity of such calculations is the model System studied by Batra and Ciraci (1988). It consists of a graphite lattice with a periodic array of tips. The tips are single carbon atoms and they are spaced only WO unit cells apart. These calculations, which do not take into account a tunnel current or a bias voltage, show that the barrier height decreases with the separation and a kind of bond is formed at low tip to sample distances. Despite the roughness of the model, it is very clear that the electrodes are not independent at small distances. The result of independent electrode approximations should therefore be treated with the utmost care.


These types of calculation can also be used to obtain the force between tip and sample by considering the change in total energy due to a small tip displacement (F = -VU). In this way, the atomic corrugation showing up in the AFM can be calculated. Abraham e.' a1 (19W) showed that tbe shape of the tip can !Lave a profound auence.

2.4. Etastic IunneIting speclmom

The expression for the tunnel current invokes a summation over electron states. By probing the tunnel current or its derivative as a function of voltage, information on the density of states can be obtained. h gah some insight, assume that the matrix elements depend only on the energy

and not on the direction of the waveveam. The double summation can then be U I m ~ u L l l l ~ llllU a "UYUIG luwplruru W"1W UuUylulGD L" e JUryG InrGgm, ""C tu L U G

Duac 6-function wbich is a consequence of the fact that energy is consewed during ._.. z-_^_I :_.- ~ A-..=*- >..*"-.:-.. -.I.:..l. ..:--,:e-" *^ " ":..A- A.." .- .x.- tunn&g.

I = [VdE D , ( E - e V ) D , ( E ) M ( E , V )

D, and D, are the density of states in the electrodes, the energies they a d on are defined relative to the Fermi energies. If the density of states of the tip (D,) and the matrix element are taken to be constant, aI/aV becomes proportional to the density of states of the sample (D,( E)).

Unfortunately, the matrix elements, far from being constant, cause an exponential increase in current with voltage: the dculat'on of aI/aV becomes compliited and spec& features due to the density of states drown in the exponential background. This can be partIy compensated for by dividing (aI/aV) by I because (aI/aV) and I show the same exponential background. For a metal, ( a I / a V ) / I diverges in the limit of zero voltage (Ohm's law!). Multiplying by V prevents this divergence.

( a I / a V ) / ( I / V ) is a useful, dimensionless quantity in discussing tunnelling spectroscopy. lb first order, (aI /aV) and I are also expected to depend in the same way on the tipsample separation 8, so any change in s is automatically corrected. This allows one to use the separation as a parameter to keep the different variables Within a measurabb range (see the section on spemosmpical operating modes).

At the edge of a band gap I / V drops to zero faster than (aI /aV) , causing a catastrophe in ( a I / a V ) / ( I / V ) (M8rtensson and Feenstra 1989). This can be prevented by averaging I / V over a large voltage range. The justification of th s experimental trick is that I!V B used as n_ nom.&&ca Lenr tc mmpe~rzte fer the matrix elements. As the matrix elements are not related to specific features in the density of states, I /V may be smoothed over a large voltage range.

Having compensated for many experimental inconveniences with some crude es- timates, it cannot be expected that an exact representation of the surface density of states will be measured Several theories try to calculate more rigorously what will be measured.

Chen (1988) uses a modiied version of the independent electrode approximation and concludes that a I / a V / ( I / V ) equals the normalized density of states multiplied by the matrix element plus a mnstanr Selloni et uI (1985) ccmidered the model introduced by lbrsoff and Hamann (see section 3.1.3) and anived at the expression:

Scanning tunnelling microscon 1175

aI/aV a p(r,,, V)T( V). p(ro, V) is the local density of states a: energy V evaluated at the centre of the tip (r,,). T ( V ) is a factor which compensates the behaviour of the matrix elements. There are no comparisons of this approximated result with some more exact results, so it is not possible to give a comment on its validity (see also Lang (1986h)). A better way to calculate the current is direct insertion of the wave funceions

in Bardeen's independent electrode formalism. Figure 3 shows the result of such a sriicuiaiion 6ue io iang (i986Dj. Eased on the modei of Tersoii ana i-iamann, iang proposed the folloanng simplied expresion to calculate the tunnel current:

A numerical evaluation of this formula yields results quite close to the more exact calculations (figure 3). It should be noted that both these calculations depend on Bardeen's independent electrode approximation, which is not necesarily correct under the conditions met in STM operation (Chen 1988).

25. Inelasric IunneUing spectrmco~

The concept 'inelastic tunnelling' refers to tunnel processes duriag which the electrons lose energy inside the barrier. A possible mechanism is the excitation of a vibrational mode of a molecule inside the barrier. This gives rise to increased tunnel conductivity because electrons can tunnel via an extra channel, parallel to the elastic channel. Of course, the energy of the electrons should be larger than the lowest vibrational excitation. The presence of this phenomenon was shown for the list t h e by Lambe and Jacklevic (1968). By now, inelastic tunnellig specuoscopy (IETS) has become a well established technique to probe the vibrational energy levels of adsorbed molecules (see Hansma (1982) for a review).

The junctions are prepared by evaporating a bottom electrode and an insulating layer, adsorbing the desired molecules and finally evaporating a second electrode. The derivative of the tunnelling conductance is measured while varying the applied voltage. The excitation energy shows up as a step in the conductance, thus as a peak in its derivative. A typid peak ~ d t h is 1 mV To avoid thermai smearing, experiments are performed at liquid helium temperatures (1-4 K).

The main limitation of this technique is the junction preparation. As not all materials are suited to be a separator between the two electrodes, the choice of substrate materials is limited. Second, as not all molecules stick to the possible substrates, the choice of molecules is also limited. Furthermore, the influence of the top electrode, which is in direct contact with the adsorbed molecules, is not Clear.

The use of an STM could reduce this influence and could greatly enhance the number of possible :iubstrates and adsorbates. As it measures the properks of a single adsorbed molecule, it could also elucidate the influence of different pOSible adsorption sites on the vibrational properties of the molecule. AlteInatively IETS could help STM to identify unknown adsorbed molecules (or contaminations) by their vibrational spectrum.

However, the inelastic tunnel current is very small. if the coup@ mechankm between the tunnelling electron and the molecule is a dipole interaction, the change in tunnel conductance at the threshold voltage is expected to be aboul 0.1% (Binig

emis le",

~-3, ~ m m p a l l ~ o n d thedemlyofstalesmtipandsamplewrth ( a I / a V ) / ( I / V ) ( Img 1986b). The lip is reprsented by a Na atom adsorbed on a jelhum metal, the sample by an adsorbed Ca atom. lbp: density of states of the Ca and the Na atom. The contribution of the jeUium metal has been subtmced, Note lhe d S m t dmtions of Ihe energy scales far the dlfierent awms Bottom: the full curve is a calculated curve of ( a I / a V ) / ( I / V ) ; L e dolled llae is the same quantity, evaluated wng the simple model r e p m t e d by equation.

et e! m 5 m , FSEsG9 ma I?eEI!!t!! 19E). sx*. 1 mz!! unrkirrl! rm &%!se he i&%ec by a change in tunnel barrier width of 5 x

So an STM should be very stable to obtaio a measurable result. In spite of a great optimiim in the early years of STM and the use of comparatively stable squeezable tunnel junctions (Hansma 1986), this l i t has not been reached up until now.

There have been reported two observations of peaks in a wnductance specmm which possibly correspond to a vibrational mode of a possible surface adsorbate (Smith et al 1987b, van de W e er ul 1987). The fact that the peaks show up in the first, instead of the second derivative, wuic be due to the fact that the state from which the electrons leave the tip has a sharply defined energy (E L Wolf, private c~mmunication). Persson and Baratoff (1987, see also Persson 1988) wnsider

A!


a different coupling mechanism, known as resonant coupling: the tunnelling electron enters a molecular orbital, stays there a while, and excites the vibration mode on leaving. A condition is the existence of an orbital with the proper energy. This mechanism could give rise to a decrease in conductance of a few percent, requiring a stability of ‘only’ 0.05 A An example of a suitable system should be 0, chemisorbed on Pt(ll1).

2.6. &“t tunnelling surface states and Gundlach oscillations

Sometimes, there exists a state inside the barriei ’win between a double barrier) at a sharply defined energy. If an electron state inside the electrode at that energy matches the wavefunction of that state, the tunnel probability can increase enormowly. This gives rise ta a peak iii :he tnnsmission a t that specific energy or, experimentally to a peak in aijGV piotied against V ai constant current. Tnese processes an Mown as resonant tunnelling (Duke 1969).

If the state in question is localized laterally, it will lead to a hill or a hole in a topographical STM picture (Sumetskii 1986).

A surface state is a state which is localized at the surface. Such states are forbidden in the bulk and hence tend to lie inside a band gap (Zangwill 1988). If it is degenerate to an extended (bulk) state, the two states can mix. The resulting bulk state has an abnormally large amplitude at the surface and is called a surface resonance. The large amplitude at the surface can easily lead to resonant tunnelling.

There is a subtlelty associated with states which are not connected to a bulk state: they have, in principle, an infinite lifetime. The electron will never leave the state and no current will flow, unless some leak is present. This leak can be a coupling via phonons or some other interaction between the surface state and a bulk state (Garcia et a1 1987, Tagliacozzo and Tbsatti 1988). The resulting behaviour is vety similar to the resonant case of inelastic tunnelling. Theory predicts that if the decay time from the surface state becomes large, this becomes the speed limiting step in the tunnel process and a saturation of the current occurs (Louis el a1 1986, Ihm 1988).

An image state is a special kind of surface state which lies outside the surface and is the result of the attractive image force exerted by a surface on a nearby electron combined with some repulsive mechanism from the surface. If there is a gap in the surface density of states at the energy of the surface state, the repulsion is evident: an electron with that energy is not allowed in the bulk. If there is no gap, electrons can still be reflected from the surface but are no longer confined: the image state becomes an image resonance in which the electrons are captured for some finite time.

Fig” 4. The eUecrs of a high bias voltage: (0) lhe 6Ned shies dose to the F m i energy cnnslitule the major pan of the cutrent; (b) pan of Ihe bamer is dasicaliy aeeersible and a dlserele spectrum of slates emerges inside the barrier. These slates are mupled dlreelly 10 stales inside lke lee electmde.


In an m, the attractive force is the image force plus a contribution of the applied voltage (see section 2.3). The final result is a V-shaped potential well in which a spectrum of states can be present. In the regime where the applied voltage is larger than the work function (the Fowler-Nordheim regime), pan of the barrier region becomes classically aocessible (figure 4(b)). The interference of transmitted and reflected elecnons causes a surface resonance h l i in the Crassically aCCeSSibk pzrr nf thp hamer (&ere resonances are aLo known as 'field emission resonances'!. Gundlach (1966) predicted conductance osdations in a tunnel junction which are the result of a resonant tunnel process via those resonances. As the energies of the resonances depend on the shape of the potential well, which depends on the barrier width, step& structures occur m a plot of the separation against the applied voltage at constant current. Such osdations have been ObSeNed with an STM on Au(ll0) (Becker er al 1985b) and Ni(100) (Bnnig et a1 19856) (figure 5).

ngare 5. Gundlach mdlauoas lhe right-hand pan of this figure shows the conductivily (arlav) &I B f u n c t ~ n of ~ i r a $ e bm ( s e c k n d 198%). me moductivity has a marmum f the bias energy wincides with a passible resonance in the elasJieally accessible part of the barrier. The lefl-hand pan of the picture s h m the wavefunetion UI the barrier. *Oh asnllztiun in the wnduclanee incorp.rata M widil i i l standing wave.

As the energy levels of these states are highIy sensitive to the shape of the potential, they may be used to probe the surface potential (Bono and Good 1987) and the vacuum gap width (Leavens and Aers 1986). Clinton et a1 (1987) show that the image states are also intluenced by the corrugation on the surface. Coombs and Gimzewski (1988) investigated field emission resonances up to very high voltages. They were able to measure up to 40 states, Their results showed beats and other kinds of fine structure which muld be explained by taking into a w u n t ditferent patches of the tip, located at diiferent separations from the sample and with slightly different work functions.

2.Z TunneIling at higher voItages Simmoas' fomuh for the tunnel current (4) was based on the assmption that the applied voltage is much smaller than the two other relevant energy scales: the Fermi energy and the work function. This enabled some mathematical and physical simpli- fications. Simmons also calculated the current without using these assumptions and showed that its dependence on the applied voltage is definitely not linear.


If the applied voltage becomes a significant fraction of the Fermi energy, the density of states will not be constant. The influence of changes in the density of states are discussed in section 2.4.

If the bias voltage becomes a significant fraction of the work function, the barrier can no longer be considered to be of the same height for all electrons (figure 4(0)). An electron a t the Fermi level of the negative electrode sees a lower barrier and hence has a larger tunnel probability than an electron at a lower energ. Most of the current is carried by electrons from states near the Fermi level. This has important implications for specmsmpical applications: by varying the applied voltage, different states to which electrons tunnel in the positive electrode can be probed, but the states from which the electrons leave the negative electrode remain the same. lhnslated to STM: we can probe the empty states of the sample, but probing the states below the Fermi level is more dillicult.

If the applied voltage is larger than the work function (the Fowler-Nordheim regime), image states occur. The effect of these states are discussed in section 26.

The high voltage limit as calculated by Simmons (1963) shows that an extrapolation of a plot of the tipample separation against the applied voltage at constant current crosses the origin. This would enable an absolute determination of the separation (Garcia et a1 1986). Aers and Leavens (1986, see also Bono and Good (1987)) show that this is an artefact caused by Simmons' assumption that the work function of both materials are the same. Numerical calculations made them propose that the extrapolation of the positive and negative voltage sides cut the V = 0 axis in two points separated by a voltage AV = 2A$/e (A.$ is the difference in work fun0 tions). This would still enable an absolute determination provided that the difference in work functiom is known.

A final remark on higher voltages concerns the area of the tip which contributes significantly to the tunnel current At low voltages, only the outermost atom@) contribute(s), that is why the sm has such a high resolution. Bono and Good (1987) suggest that at larger voltages the relative contribution of parts, which are only slightly further away from the surface, increases. This will lead to an increased tunnel area at higher voltages. These conclusions are confirmed experimentally by Caombs and Gimzewsky (1988).

2.8. The tunnel time

The concept of tunnel time is a very interesting subject. Attemps to define and calculate such a time have led to complex times, imaginary velocities and superluminal velocities, indicating that the process is still not fully understood. Apart from its philosophical implications, the tunnel time is relevant for a proper desmiption of the barrier which an electron sees. For example, an electron opposite to a metal surface will feel a force towards it because of the image force. However, such an induced charge takes a finite time to build up. So an electron which tunnels more quickly than the image charge can build up will feel a reduced image force.

Several times related to the tunnel process can be identitled The least contro- versial time is the dwell time, that is the average time spent in the barrier by an electron, regardless of whether it is reflected or transmitted. It can be calculated as the number of electrons inside the barrier divided by the incoming flux, or as a double integral (over time and barrier width) of the wavefunction of an evohing wave packet (Buttiker 1983, Leavens and Aers 1989).


The traversal time and the reflection time are defined as the mean time spent in the bamer by a transmitted (sespfxtively Tefleaed) electron. A problem with thi defition is that it is not possible to decide whether an electron will be reflected or transmitted if it is close to or within the barrier. (Intersting question: what is the probability of finding a reflected electron just a little behind the barrier ?) So it is questionable whether it is relevant to speak about those times.

Despite these difliculties, several methods have been proposed to Calculate a traversal time. In the parameter range which is of interest for STM, the different methods converge to the same time s (Cutler et a1 1987). F" a PIaCti- cal point of view, this is an advantage because it yields a usehrl value, but it is a disadvantage in the sense that it will not be easy to discriminate between different theories.

The different theories will not be discussed in detail. Leavem and Aers (19SSa, lW), and Hauge and Stameng (1989) compare several methods and discuss their conceptual difficulties.

(i) Phase delay. From basic considerations on the phase shift between incoming and outgoing waves, Wigner (1955) derived a delay time due to the barrier interaction which equals the energy derivative of the phase shift between the two waves. Hartman (1962) applied this concept to a rectangular bamer and obtained an expression which is known as the classical phase time. A problem with this time is that it becomes independent of barrier thickness in the limit of a thick barrier. This causes the 'velocity' of the tunnelling elemon to increase arbitrarily (even beyond the speed of light) if the bamer thickness is increased.

(ii) Modulated barrier. Buttiker and Landauer (1982) considered a bamer, the height of which is modulated in time. The electrons see a static barrier if the tunnel

a rapidly changing potendal. These different regimes result in different transmission probabilities. The characteristic time separating the fast and slow limits turns out to be: 7 = &mrerdx[Zm(V(z) - where V(x) is the local barrier height and E the electron energy). This time is different from the phase time mentioned earlier. If only part of the bamer is modulated, the same result is obtained for this part (Leavens and Aers 1987b, Kotler and Nitzan 1988).

(i) Iarmor clock This method considers the precession of electron spins in a magnetic field which is present inside the Barrier. The amount of precession is a measure for the time spend in the barrier by the electrons (Baz' 1967, Rpachenko 1967). Buttiker (1983) showed that the simple picture of prccessing spin is somewhat blurred because spin-up electrons tunnel more easily due to the Zeeman splitting in energy. He identiIied the resulting times with the modulated barrier traversal time. Huang et a1 (1988) use the same method but apply the magnetic field throughout the whole space. Their calculations yield the phase delay time! Leavens and Aers (1987a) extended the fomalism to arbitrary bamers. The same authors (1988b) used a magnetic field confined to a part of the barrier to obtain a local version of the Larmor clock time.

(iv) Wave packet. h u g e and St0vneng (1987) considered a single wave packet which evolved in a reflected and a transmitted part after passing the barrier. They extrapolated the linear motion of the centres of mass of the packets long before and after the bamer interaction to obtain a traversal time. This method is dangerous because it extrapolates to a region where strong interference mixes the reflected and

the B much shorter than the period ofthe "Iu&tion: In the oppmite ca3e9 they gee

Scanning tunnelling micrwojy 1181

transmitted waves. It should be noted that this time can become negative for a certain choice of the parameters. In the limit of a very narrow packet in k-space their result equals that of the phase delay. In contrast to these results, Cutler er a1 (1987) calculated numerically the evolution of a wave packet through a barrier. Using a similar extrapolation to that of Hauge er al (1987), they found a traversal time which agrees roughly with the modulated barrier time, but depends sensitively on the width of the wave packet in k-space.

(v) Dynamical image potential. Jonson (1980) calculated the image potential using a many-body formalism which yielded a result which depends on the surface plasmon frequency w,/2rr. The result coincides with the classical image potential if the quantity w.z/v is large ( z is the position in the barrier, ;muz = V - E, V is the barrier height, E is the electron energy, V > E). It can be understood from the reasoning in the introduction of this section that the quantity r / v can be identified with a tunnel time. This time coincides with the modulated barrier time.

(vi) Bansverse magnetic field. Gu6ret et a1 (1987) considered the effect of magnetic field on the electron paths in the barrier. A LOreIIQ force will bend the electron trajectory, thus elongating the tunnel barrier from the electron’s point of view. This will lead to decreased transmission probability, which can be measured as a decrease of the tunnel current if the magnetic field is increased. Their predictions are in good agreement with the experiments they performed on a heterostructure with a barrier dd th of 430 A (typical traversal time:

Cutler et a1 (1987) also measured a traversal time. They used a polarized laser beam to generate a high-frequency AC electric field across the tunnel barrier of an STM and argued that if half of the period of osfillation is larger than the traversal time, electrons will travel back and forth between the two electrodes. Due to an asymmetry in the I ( V ) curve of the STM (Lucas er al 1988b), this AC current generates a Dc voltage across the junction, a p r o m known as rectification. However, if the traversal time is larger than half of the period, electrons cannot tunnel any more and the DC voltage will disappear. In an experiment with infrared light (A = 1.06 p m -+ 7 = 1.77 x s), they varied the traversal time hy varying the distance between tip and surface. They measured a cut-off of the response at a distance of 2.5 nm, in agreement with the modulated barrier time.

which have been done and will be done may shed some light on the different models.

2.9. Single electron effecrs

2.9.1. Introduction. In the usual tunnelling theory it is assumed that macroscopic variables, such a5 voltage and charge, behave classically. However, the junction Of an STM is intrinsically small. Especially when tunnelling into mesoscopic systems, such as macro-molecules or metalli particles, the transfer of an integer charge e into the system leads to a shift in the energy levels due to the electrostatic Coulomb interaction. In principle, this means that these macrosmpic variables must be treated quantum mechanically. In a first-order approximation this can be achieved by including the macroscopic energies, such as the electrostatic Coulomb energy, into the microscopic tunnelling Hamiltonian.

From a purely scientific point of view, the sm o p e s up the possibility of studying physical phenomena at the crossroads between atomic or molecular physics and solid state physics. From a technical point of view, the quantum-mechanical behaviour

s).

ii ciear ihai fie subjeci of iurnei i&,e ij far fiar, exFeihT,eiia

1182

could be used for new electronic devices, where switching is achieved by single electrons.

29.2. The Coulomb blockade of tunnelling. A tunnel junction has a finite intrinsic capadtanw. The hias voltage induces a charge on the electrodes (Q = CV), and the capacitor will contain an electrostatic energ E = Q2/(2C). An electron which tunnels causes a discrete change in this charge and energy. A tunnelling event will onty o m r if the Enal state has a lower energy than the initial state. If I Q 1 < e/2, tunnelling will always increase the charging energy, and hence it will be prohibited (if the thermal Buctuations are smaller than the charging energy: k,T < e2/(2C)). This so called Coulomb blockade of tunnelling can therefore only be observed in junctions with extremely small capacitances at low enough temperatures (TC <

One very interesting consequence of this blockade occurs in a current-biased tunnel junction. Suppose the tunnel time is small compared with the charging time r, = e/I , the time needed to charge the junction with one electron. At t = 0, there is no charge on the junction. It takes a time r c / 2 to build up a charge e/2. No tunnelling is allowed until Q reaches e/Z. Some time after this threshold is reached, an electron will tunnel and the charge will change to about -e/2. Then the process

Measuring thh frequency muld provide a very accurate ament standard (Averin and Likharev 1986, MuMen et a1 1988).

In practice, the effective capacitance of a junction can only be small if the junction is properly decoupled from the stray capacitances of its environment, e.g. the current leads, which have a capacitance of a few pl? This can be done by incorporating the junction in an array of junctions or by connecting the junction m highly resistive leads. Modem nanofabrication technology is capable of making such systems in which all basic predictions of the single electron tunnelling theory have been verified (Fulton and Dolan 1987, KuVnin et 01 1989, Delsing et a1 199oa,b, Geerligs and Mooij 1988, Fulton et al 1989).

A series M3MectiOn between two junctions can be obtained with an STM by positioning the tip above a small isolated particle. In this geometiy, the junctions are demupled from stray capacitances in a very nanual way. The number of excess electrons on the particle is limited by the applied voltage. That number increases in discrete steps when the voltage is increased. Each extra electron that can be a o mmmodated on the particle state constituta an extra tunnel channel and canses a Stepwise increase of the current the Coulomb staircase.

Several groups (van Bentum et a1 198%. 1989, McGreer et al 1989, Wilkins er al 1989, Wan et a1 1990) have observed a very clear Coulomb staircase while tunnelling through single isolated particles.

There is an on-going discussion as to whether or not a Coulomb blockade is present in a single sTM junction (as reported by van Bentum er a1 (1988b), Smokers et a1 (1990)). The main issue is that the capacitance of an STM junction between two clean metals (Ramos et a1 1988) is by no means decoupled from the stray capacitances, and will therefore not show a Coulomb blockade (in agreement with recent theory (Nmrov el al 1989, GirVin et al 1990, Devoret et 01 1990)). Only in the case of some aCCidenta@ or intentionally present decouplhg mechanism a Coulomb blockade might be possible (wilkins et a1 1990, Smokers et a1 1990).

L E C van de Leemput and H van K e m p

K F).

i c m n m n t d T h m m=..lr i e II e n s x l t n n t h hnhn.'nmr nf the r h n r n m un'fh n f rpnxnnnnr r In '-y""...". .-"U. " ""....,"... .,....".."". ...- I.-Y. " -,-.


3. The imaging process

3.1. Topographical imaging

31.1. Innoduclion.' die insmtment finction. An sm produces an image of the sample's surface. The usual way to describe the performance of an imaging device is to formulate some transformation (e.g. a convolution) by which the original is converted io its image (Teuchhvang et ai iysg). in the case of a condutbn, the resolution of the instrument can be defined as the full-width at half-maximum of the convolutiou functiou

This scheme cannot be applied to sm directly, simply because the original does not exist: the electrons at the surface are desmied by wavefunctions and do not constitute a sharp boundary. AU surface science tools probe a surface layer with some finite thickness, depending on the penetration length of the probing particle. Only on a scale which is much larger than that thickness, can the physical surface region be idealized to a mathematical two-dimensional sheet.

In an STM, this limit is reached on the scale of a nanomerra In the range above a nanomeue, the imaging p r o m can be described by a transformation of an ideal picture to its image. In the sub-nanometre range, the original is no longer defined and a different approach is needed. TRi will be deseribed in the next sections.

Suriace S ~ N C ~ U I ~ E on a nanometre scaie or bigger can be interpreted as some geometric convolution of the tip and sample shapes. Several features are not influenced by the convolution and can be determined exactly: e.g. the height and directions of steps on the surface. The distance between two parallel and equal steps can be determined if both steps are associated either with an increase or a deerease in the surface height in a fixed direction. The width of a valley will always be measured as being too small. Other features like the shape of a step also suffer severely from the convolution. Deep troughs in the surface landscape are imaged as being much shallower than they are because the tip does not fit in. The reliability of the picture is determined by the aspect ratio and the roughness of the tip together with the roughness of the sample. Generally, the tip shape is unknown and some caution for spurious tip effecm is necessary.

Images which are the result of a convolution can be corrected by applying a aeconvoiution proceQure. Cicon et ai (i987) (see ais0 Aiieiian et ai (iggijj, ae- veloped a decouvolution algorithm for sm by assuming that the current flows along the shortest path between a spherical tip and the sample. Their algorithm works well on numerically simulated measurements but its application to real measurements is limited by the fact that the tip shape is generally not spherical while its radius is unknown. This method cannot be properly extended to the sub-nanometre scale because on this scale the current no longer leaves the tip at one point

3.1.2. The scattering qproach. Several theories calculate the actual current distribution. Garcia et a1 (1983) (also Garcia and Fldres (1984)) and StoM el a1 (1984) consider a surface witb a periodic height modulation. They use a periodic array of tips to be able to use periodic boundary conditions. Of course, the tips are chosen so far away from each other that their mutual influence can be neglected. Tips and sampie are separated by a barrier with constant height. ~n iddent eiectron wave is scattered by the barrier in various directions, described by the original wavevector plus a surface reciprocal-lattice vector. After properly matching the wavef'unction in

1184

the different regions (sample, barrier and tip). the transmission probabirity can be derived and the current density can be obtained via the current operator. A summation over relevant wavevectors yields the final result, which illustrates a number of relevant features connected with the distribution of the tunnel current

First of all, the major contribution to the tunnel current is not rowing in the direction normal to the surface and tip apex but at an angle of about 15O-ZOO. This can be understood as the result of two countemning mechanisms: if the angle between the surface normal and the tunnelliig direuion increases, the transmission probabdity decreases because the effective barrier width becomes larger. However, the number of electrons moving at an angle between 0 and 0 + d0 (which is proportional to the solid angle dS2 = 2n sin 0 de) increases with increasing angle. These two effects lead to an angular current distribution with a maximum in the indicated range.


Second, the total current is given by

where N( Er) is the density of states at the Fermi level. G is a geometricat function depending only on the effective radius Re. which is the harmonic mean of the local radius of the tip and the sample. In the range from 2.5 to 10 G(Re) can be approximated by a linear function with an OEset, so the current is more or less h e a r with the effective radius. Compared with the one-dimensional result (4) the factor two in the exponent is replaced by 2.14. This is the result of an increase in averaged barrier width, due to the effect mentioned in the previous paragraph.

Having calculated the current as a function of lateral and vertical position of the tip, an inversion of this equation is necessary to obtain the contours of constant current which are generally measured with an STM. The measured cormgation (h,) can be expresed as a function of the real corrugation (h,,), the tip radius (R), the separation between tip and sample (s), the period of the modulation (a) and the decay constant of the wavefunction in the bamer (no):

h,/h, % exp( -nZ(6 + R)/(Q'K,,)) . (9)

As can be seen, the measured corrugation decreases rapidly if the separation OT the tip radius is increased.

The previo~~ly mentioned approach uses a barrier of constant height. More realistic results are obtained when the contribution of the image potential is added to the barrier shape. Das and Mabanty (1987) include the image potential and use a WKB approximation to calculate the tunnel current from a spherical tip to a flat sample. The WKB approximation is a tricky concept in three dimensions. An incoming electron is followed along its classical path until it reaches the classical turning point (the point where its kinetic energy becomes zero). From that point, a trajectory is calculated in the barrier region and a transmission coefficient is derived. In one dimension, this works out quite well. In three dimensions, a particle which approaches the barrier along a non-normal direction will never have zero kinetic energy as the velocity component parallel to the barrier will not become zero. As a consequence, the particle will travel back into the electrode along a classical path and it does not contribute to the tunnel current So the results of a ~D-WKB approximation should be treated with care.


Better ways to attack the problem are presented by Lucas et al (1988s,c) and Laloyaux et al (1988). They consider a hemispherical protrnsion on a flat surface opposite another flat surface. The advantage of this geometry is that the image potential can be presented in closed form (Lucas et ol 1984). The cylindrical symmetry reduces the problem to two dimensions. Lucas et d solve the Schrildinger equation by a Green function method, Laloyaux et al solve the problem by a finite element

ten as a linear combination of four basis functions. The expansion coefficients are obtained by matching the wavefunction and its derivatives on each boundary. The results of both methods agree quite welI. The full-width at half-maximum of the current distribution ranges from 3 to 5 A depending on the tip radius. Louis and Flores (1987) include the contributions of the band structure of an unreconstructed Si(ll1) surface in a calculation of the tunnel current. The ultimate goal is to incorporate the geometry and electronic band structure of the sample and the tip, together with their mutual influence, in the calculation of tunnel current. Such a tremendous task is still far beyond present day computer power. An enormous simplification omrs if the electrodes are treated independently, neglecting the mutual iafluence. This wifl be the subject of the next section.

7 I I LA~..~..A~..+ mn-~~...n&r uamnnn t i o m i a s ~ rnniipa

the independent electrode approximation to the sm. They expand the (Bloch) wave-

vectors G

met!!d s p e b .I;v;ner! it! rmz!! scp?res, i!! ezc!! sqwe tke ...W!!.tin!! b &t-

d.1.J. "'c.CpC,-w.. Z.=L..-C Ypp~"*",.Y.'"r.. I I S I Y Y ".." I-.-".. \'/"d, I..-, "yr.'-"

* functions of the electrons outside the surface as a sum over surface reciprocal lattice

k, is a wavevector along the surface; it is the sum of G and the parallel component of the Bloch wavevector of the state +". The first exponent describes the exponential decay into the vacuum, the second one describes the wavefunction parallel to the surface. The tip is approximated by the asymptotic limit of the 1 = 0 spherical wavefunction (s-wave), centred at the tip position rt ( T ~ = s + R):

Substituting these wavefunctions in Bardeen's formula (3) yields

(12) e2 I (r , ) = 3 2 ~ s - V ~ 2 N t ( E r ) R Z e ( 2 h R ) p ( r t , Er) Ti

where Nt(Er) is the density of states at the Fermi level in the tip and p(r t ,Er) = E, l+v(rt)lz6(Ev - Er) is the electmn density evaluated at position rt . Since p ( r t , Er) exp[-2tco(R + s)], the current is proportional to exp(-2nos).

Apart from the prefactors, this formula states that the tunnel current is simply proportional M the density of states at the Fermi energy, evaluated at the centre of the tip. Note that the evaluation of + at the tip position is not a physicaliy meaningful operation; it is merely the result of the coincidental analytical pIOpertieS of the vial functions +" and +,. The major advantage of this result is that it enables a direct comparison of an STM image with an electronic structure calculation.

1186

In terms of ordinary imaging theory: the convolution is reduced to a multiplication by a constant factor. It is not possible to defme a performance in terms of some convolution function, the STM image is an exact contour of constant p( Er). The fact that a contour of constant current coincide better with a contour of consant densit) of states at the Fermi energy than with one of constant total charge is confirmed by Lang (1986a), who calculated the image of a sulphur atom adsorbed on a jellium

From these formulae, it can be easily seen bow the corrugation changes if the separation between tip and surface cbanges. The expansion of +v shows that those components with the smallest le, decay the most slowly. Thus, if the tip motes farther away, the higher Fourier components disappear. At large distances, only the lowest Fourier component is present, giving rise to a sinusoidal height profile. By comparing the experimental corrugation in images of the Au(l00) 2 x 1 surface with calculated contours of different charge density, it is possilble to determine the separation between tip and sample (lkrsoff and Hamann 1983). A typical result is 6 A

One important remark should be made (lkrsoff 1986). If p(Ef) contains a node, the current will drop to zero and the tip will be pushed into the sample by the feedback system. In practice, this mathematical catastrophe will be prevented by some mechanism (e.g. munibutions to the tmmel current due to I # 0 states in the

anomalously high measured corrugation. The relatively slow decay of this corrugation can lead to unexpectedly high resolution with respect to this component prsoff 1989). In a normal metal, a lot of different wavevectors contribute to p ( E f ) and nodes are not expected. Materials which show nodes are those in which only a few symmeuy related states at tbe mne edge of the surface Brillioun zone contribute to the p(E& Examples whicb have been studied with sTM are graphite, charge density waves and surface states in Si(ll1) 2 x 1 (Strascio et al 1988).

As the theory of lkrsoff and Hamann is widely used, it is worthwhile considering the applied approximations carefully (see also Feuchtwang and Cutler (1988) and Bukada and Shima (1987)). The coefficient in the expansion of the surface wavefunction (10) should be determined by a Fourier transformation of the parallel component of the wavefunctiou The basis set which is used forces the behaviour per-

at the Fermi energy and a square barrier, which daes not seem very sophisticated. In fact, calculations of the constant current contours of oxygen adsorbed on Ni(1W) show an indentation at small se aration (high currents), nothing (a flat surface) at intermediate separations (= 6.4!i) and a hill which-grows with incrwing distance at larger separation (Doyen et ul 1988, Martin-Rodero et al 1988, Kopatzki et al 1988). n\is certainly does not agree with contours of the density of states at the Fermi level. The disagreement is caused by the perturbation of the exponential decay of the wavefunction by the oxygen atom.

The assumption of the s-wave tip model (11) is considered by Chung et ul (1987). They calculate the energy levels of an isolated spherical tip and show that for low quantum numbers 2 and n, the energy levels Win be well separated if the tip radius is smdler than.20 A This confn'ms that only one level is involved in m. However,

diferent from d- or p-states because of the difemnce in symmetry. Finally, it should be remarked that a real tip is not only not spherical but also not isolated. Up till now, little attention has been given to the consequences of the latter fact on the energy

L E C van de Leemput and H VM Kempen

--I." metnl rmnnelt ---.._.I-" with 2 rndiiim mnm~

ep "r 9; .*y%z~"s =f +&e ~p atc'"" FAves I?@&)). *q"*rver, z0ce'-s *,$! !eat tc

nanAi,...lnr *- **- ...* e""- :-*,. " &.- -..I.:A. :" k"""* -- ~ .--.... ,.*.....--.. L.-d-- p"".vu.p. L" ".U .3u1_ Ill&" P .",ill lllllwl w "OCU "U LI l l G C G,GCUUII wa"G,Y"s"uII

EB~:'~G& ei ri: (EW, that a e cona-n from a shgie sievei a n be very


distribution and the shape of the tip wavefunctions Sacks el a1 (1987) apply the "off-Hamann result (12) to a surface model consist-

ing of a sharp boundaty of a free electron metal. In the perspective of the discussion at the beginning of this chapter, this is equivalent to re-entering the range in which a resolution can be defined. They showed that in the l i t of (s + R)K, > 1, the image can be described as the result of a two-dimensional convolution of the sur-

of 2[ln2(s i- R)/n,]llz. This mrresponds to a typical lateral resolution of a few hgsuiim. In their article, they discuss some intewting examples of different surface geometries l i e a step or a Gaussian hill.

They also find that the density of states at large distances is proportional to exp[-2rso(R+ s j l / ( R + s ) , yieldinga current:

_--- fire with 1 - Omdm --I"-._ mmvnlntinn fnnctinn _-..--.-_. whit-h has -- 1 - hill-wklth .._ -... st -_ ~ half-mmimam .-.-_..--..-I

This result may be the clue to a disagreement on the dependence of the tunnel current on the tip radius: Garcia et a1 (8) conclude a linear dependence from numerical calculations, Rrsd and Hamann (12) claim a quadratic dependence. This formula shows that in the limit of small separation (s R), the result of Garcia et at can be obtained f" the Ersoff-HamaM formula.

A big advantage of the model of l?xsoff and Hamann is that it is very simple and gives reasonable results. The charge density at the Fermi level can sometimes be approximated well by a sum of spherical charge distributiors centred at the atom positions. This enables a very simple calculation of sTM pictures (figure 6)

1188 L E C VM de Leempul and H van Kempen

If the wavefunctions of the sample and the tip are known, they can be used directly to calculate the tunnel current in the independent electrode approximation. In this way, Doyen and Drakova (1986) calculated the image of a mono-atomic step in the Ni(ll0) surface.

3.2 Speclmcopicol imoging The previous sections described different methods for calculating STM images. They all considered only a smaU band of electlon states close to the Fermi energy. If voltages are applied which are large compared with the Fermi energy (typical Fermi energy: a few ev), more electron states get involved and the resulting image may depend dramatically on the bias voltage. Section 2.4 discussed the complexity of the calculations of the tunnel current at different bias voltages. The evaluation of constant current contours d t several voltages i even more complicated as it also has to incorporate the spatial extend of the different electron states.

An extension of the Ersoff-Hamann result for the current at non-negligible voltage is

where p(rt . E) is the electron density of states at energy E evaluated at the centre of the tip (rt). This formula neglects the influence of the matrix elements and the Muence of the electric Eeld on the surface WavefunctionS. It enables, however, a direct comparison of band structure calculations with an STM picture and can be quite useful for distinguishing between different possible models of the surface.

Lang (1987a) calculated the expected height of an adsorbed atom on a jellium metal. Due to states of the adatom at specilic energies, the heieht varies considerable with bias voltage. Na and MO adsorbates are seen as a hill. The maximum height (about 3.3 A) occurs if the bias is tuned to the empty s-states on those atoms. A sulphur adatom has a very broad p band somewhat lower than the Fermi energy. It is imaged as a small hill (a few tenths of an Angstrcim) if probed below the Fermi level, but as a hole at about 3 eV above the Fermi energy (figure 7).

4 4 ' I I -2 - 1 0 1 2

BIAS lev1

Figom 7. Apparent height of an S atom adsorbed on a jellium metal at different bra= mng 1987a). Note lhal the height can be negative as well as paaitive: the atom appears as a hale or as a bump, depending on bias.

Scanning runnelling microscopy 1189

A special problem is caused by the fact that the independent electrode approximation is not obviously applicable at non-zero bias voltages. An extemion of this approximation by Chen (1988) deals with this problem and also addresses the e f f m of non-spherical tips.

4. Building a scanning tunnelling micruseope

4.1. Mechanical design

4.1.1. V77mtion isolarion. The mechanical stability of an STM has to be better than the desired resolution. If atoms have to be resolved, a resolution of 0.01 nm normal to the sample and 0.1 nm parallel to the sample is needed; a noise level of 10% corresponds to 1 pm. The behaviour of an sm as a result of external noise is the result of two factors: the amount of vibrations which reach the STM and the response of the STM to those vibrations.

An important source of vibrations are resonances of the building in which the STM - is located. p p i d fre$uencies which are jnvdved range from 1 to IW Hi; *ita! amplitudes are 0.5 to 150 nm. The simplest solution is to situate the STM in a quiet part of the laboratory and measure at quiet times. This is even more effective if the STM operates in a medium which transports sound waves. However, such a measure is not always desirable and almost never sufficient. A better way of reducing the external sources of vibrations is the insertion of some vibration isolation mechanism.

Three types of isolation for the STM have been employed. The fust STM used magnetic levitation of permanent magnets on a supermnducting lead bowl (Binnig et a1 1982a). At the moment this method is no longer used.

The second generation of STMS were suspended with coil springs. Tbese springs act as a low-pass filter: up to the cut-off frequency the STM follows the movement of the suspension of the coils. At frequencies much higher than the cut-off frequency, the response decreases logarithmically, approximately by a factor of 100 for each '.CyU"LLy UGUYG. b'C.lL,y, 'I w .luvarrtogwUa tu C"UUUG U,= CUL-Y l l ,,*yuG"cy as low as possible. The cut-off frequency U,, of a mass suspended by a spring is given by 2nuo = ( g / A l ) ' l 2 where A1 is the elongation of the spring from its unloaded length and g the gravitational acceleration. 'Ib obtain a cut-off frequency of 1 €4 Al must be 25 cm. So, in practice, the lower limit of the cut-off frequency is dictated by the size of the system.

Unfortunately, at the cut-off frequencies a resonance peak occurs. This peak should be suppressed by adding damping to the system. Another advantage of damping is that movemen@ of the sm stage die out faster. Without damping, vibrations near resonance can take up to half an hour to relax! A common method is eddy current damping: motions of a permanent magnet, connected to the STM, induce eddy currens in a metal block (attached to the outer world). These curren@ cause heating and in this way dissipate energy from the oscillating motion of the STM stage. A disadvantage of damping k that it reducts the performance of tne iiiter ai higher frequencies. So the amount of damping should be as low as possible. The performance of the system can be further improved by adding more stages to the spring systems. A very wmmon design consists of two stages mounted concentrimliy. OkanO et a1 (1987) conclude that the best performance is obtained if only the sewnd stage

_I^^^>^ Paa"-*.. :. 1" "_I ....-. ^_ .. 1- "Le"^^ 4.- ... -m *..a ..*"m. I,. I.- ," "C

1190

is damped. Park and Quate (1987a) derive some more detailed criteria to optimize the effect of a double vibration isolation.

A third method of vibration isolation consists of several metal plates, stacked on top of each other, separated by pie= of viton which act as springs and dampers (Gerber et al 1986). A fypical compression of the vitons is 1 mm, fflrrespwding to a c u t 4 frequency of about 16 Hz if the vitons are assumed to have harmonic behaviour. This-due is higher than what can be achieved by a mil spring system and, consequently, the latter perform better. Okano ef al(1987) made a thorough analysis of such a stack. The response of viton is veq non-linear and also depends, amongst other factors, on frequency. Clearly, the performance of a stack can be improved by suspending it with springs or rubber tubes. Another method is to replace a layer of viton by small springs. Both methods are aimed at achieving higher compression or expansion lengths and thus lowering the cut-off frequency.

The methods mentioned so far are based on isolating the SlM from its direct environment. A ditferent approach is to isolate the entire vacuum chamber, cryostat or table in or on wbich the STM is located. This can be done by suspending it from the ceiling with bungee fflrds, rubber tubes or springs, or by placing the set-up on a pile of sandbags, an ineated tube, tennis balls or industrial vibration dampers. It can be useful to an approximate determination of the available modes with which the entire set-up can wiggle. Some canting modes may exist, giving rise to lateral movements of several micrometres or more far away from the centre of rotation. The STM should be positioned as close as possible to this centre.

lb examine the response of an STM to Vibrations the following model can be used (figure 8, POhl(l986)). m e external vibrations are suppmed to couple with a base on which the sample is bed. The fflnstruction which suspends the tip above the sample is represented by a (stiff) spring; the tip is attached to a certain mass on top of the


spring.

a

Figure 8. (a) A model of ?E N to eremine I& fregueney rerponse to external Vibrations. (b) Ihe rerponse function of the ribmian isolation (I), the sm (2) and the mmbinalron of the two (3)

When discuss@ the vibration isolation, the absolute motion of the suspended mass was relevant and the result was a low-pass filter. In this case, we are interested in the motion af the tip relative to the samle. Exactly the opposite emerges: a high-pass Uter. Up to its cut-off frequency, the response increases (approximately by a factor of 100 for each frequency decade). At the cut-off frequency, a resonance occurs. At very high frequencies, all vibrations couple directly to the distance between tip and sample.

Scanning hrnneUing microscon 1191

It is advantageous to have a rigid STM with a very high cut-off frequency. There exist some general guidelines for designing a rigid STM. The lowest resonance frequency of a rectangular rod, clamped on both sides is given by (Pohl 1986):

U =

where h is the height of the rod, 1 is its length, c is a numerical constant: c = 3&~/16 % 1 and E (elasticity) and p spedfic mass) are material parameters. The material parameters range from s' E / p = 3.7 m kHz (concrete) to 5.1 m kHz (stainless steel and aluminium). From this formula, the following two design rules for an sm can be derived: small is beautiful (an overall scaling down hy some factor yields an increase of the resonance frequency by the same factor) and square is also very handsome. (The ratio h/12 is optimized when h = 1. If h > 1 the role of h and 1 interchange, different modes become the lowest in frequency). A small gain can he obtained via the numerical constant. For example, for a hollow tube, c = 9r/(16&) c 1.25.

The response of an STM together with vibration isolation is in the first approximation the pmdua of the low-pass action of the vibration isolation and the high-pass action of the STM itself. This combined action results in a constant plateau in between the cut-off frequencies (figure 8). This plateau is bounded by two resonance peaks. At the high- and low-frequency side of this plateau the response decreases. The response on the plateau can be estimated by (vz/ul)2. A comparison of the maximum allowed mechanical noise (1 pm) with the external amplitudes (100 nm) yields a required attenuation factor of lo5, corresponding to a difference between the cut-off frequencies of 2.5 decade.

Concluding: optimal viheation insensitivity is reached if the following is done:

(i) The cut-off frequencies of the sm and the vibration isolation stage should be as far away from each other as possible. This can be achieved by lowering the cut-off frequency of the isolation sm2e or by increasing the cut-off frequency of the scan unit. There is a tendency to focus on the latter possibility.

(U) Damping should he added until the resonance peaks are low enough. (e) As damping reduces the amount of low- and high-pass filtering and thus

increases the height of the plateau, damping should not be larger than necessary. (iv) Care should be taken that the eigenfrequencies of the supporting floor do

not coincide with the resonances of the system. This reduces the amount of damping needed.

4.1.2. The scan unil. 'lb obtain the maximum possihle immunity to extemal distur- bances, the scan unit should be as rigid as possible, that is its resonance frequency should be as high as possihle.

Resonance frequencies also limit the scan speed. 'Ib quantify this, it is necessary to distinguish between two different typa of resonance modes. The first type are modes which couple to motion parallel to the sample's surface. They should have higher resonance frequencies than the scan frequency. The other type couple to motion perpendicular to the surface. The movements of the tip in this direction are expected to contain higher frequency components, depending of the roughness of the

1192 L E C van de Leempur and H van Kempen

Figorr 9. S w d of scanheads: A, a tripad; B1, a tube; BZ, different electrode arrangements of B Lube. ?he left one h Symmelnc but requires more mmplicated eleevonics than the nght one. The lafler is aSy"e1nc and redulfs in tilted images if the tip is mounted eoncentrically.

surface. So these modes must have frequenaes which are orders of magnitude larger than the scan frequency.

The scan unit originally used by Binnig and Rohrer (Binnig and Rohrer 1982, Binnig et al 1982b) consisted of a tripod (figure SA): three mutually perpendicular piezo bars, connected together at one end and to a base on the other end. Applying a voltage across one of the bars moves the tip in the x, y or z direction. The resonance frequency of such systems ranges from 3 & (Demuth er nl 1986) up till 20 !&z (Kajimura er a1 1987). The crosstalk between two different directions is usually small (a few percent, e.g. Park and Quate (1987h) and Jericho et al (1987)) but values as high as 13% have been reported (Pashley er a/ 1988). Some attention and testing on this point may be useful. Vieira er a1 (1987) and Blackford er al (1987) used tubes or bimorphs respectively instead of fne piezo bars. Van de Walle er a/ (1985, also

would reduce drift. Gregory and Rogers (1988) improved that design and obtained a lowest resonance frequency above 30 &.

Au designs mentioned so far have a sensitivity for the piezo displacers of about 0.5 nm V-' and a scan range of the order of (250 r ~ m ) ~ , using voltages of a few hundred volt. These designs are suited to obtain atomic resolution, but if large scan areas are desired, other approaches have certain advantages. Matey et aI(1987) and Muralt er aI(1986c) used bimorphs to obtain a sensitivity of 0.3 p n V-' and a scan range of (120 Garcia Cantu et a/ (1987) used coils moving in a magnetic field to move the tip. The scan range is (100 the lowest resonance frequency is 300 Hz.

A very simple s m unit consists of a single piem tube (figure 9B1, B2, Binnig and Smith, 1986). An ingenious arrangement of electrodes makes it possible to bend the

axis ( z motion). The first advantage of this idea is the simplicity of its construction. A second advantage is the high stiffness of a tube. Resonance frequencies of 10 kHz parallel to the surface and 100 kHz perpendicular to the surface are easily obtained.

The easiest yay to operate %ch a tube scanner is to apply the I signal to the inner electrode and the x and y Signal to two of the four outer electrodes (figure 9B1, B2). The remaining outer electrodes are grounded. This scheme results in a large crossover from the x (Or Y) to the z motion which can be minimized by mounting the tip between the two grounded outer eleamdes. However, to minimize the thermal drift it is far more favourable to place the tip on the symmetry axis of the tube. A way of compensating for the resulting crossover is to subtract a tilted plane from a measurement (e.g. Bando e: al 1988). A better way is a symmetrical activation of the

Ueme. e: z! @")) rc2!ked 'hat 2 .?,y"ca! and !hP"! PnmpsctPrl dPSig!

h diiections perpendieuiar 10 iis (x, ani 10 eiongate it &ong iis

Scanning tunnelling micmscom 1193

tube: the two grounded electrodes are now connected to the negative voltage of the opposite electrode (figure 9(b)). This. is equivalent to grounding the inner electrode and applying -I - z, y - I, --I - z and -I - z to the outer electrodes. In this way the inner electrode can be used as an electrical shieldmg of the wire to the tip (Besocke 1987). A finite element analysis of tube motion which gives some insight in how piezo tubes bend and what sensitivity and crossover can be expected for different sues of the tube is given by Cam (1988). l'$picaI sensitivities reported in literature range from 1.65 nm V-l (Besenbacher et a1 1988) to 10 nm V-' (Snyder and de hzanne 1988).

A thermally compensated tube scanuer can be made of two concentric tubes, connected together at one side. At the other side, the outer tube is connected to the base while the tip is attached to the inner tube.

A totaUy different scan unit is used by Uommi et a1 (1988). It consists of two shear piem disics and a normai piem disk stacked on top of each other, so it is a soiid cube of piezo material. Such a construction is extremely rigid, the lowest resonance frequency is 200 kHz!

4.1.3. Piezo characteristics and calibrating. Piezoelectric ceramics are commonly used as actuators in an STM. They combine a suitable large scan range with a minimum displacement in the (sub)hgsmm range. A bad characteristic of piezoelectric ceramics is their hysteresis, which can be as large as 10% of the scanned range. Hysteresis can be minimized by the choice of the piezo materials (Nisbikawa et a1 1987) or by inserting a small capacitor in series with the piezo element (Kaizuka and Siu 1988). The latter solution is based on the fact that the hysteresis is due to the change in capacitance of the piezoactuator itself when it expands.

The sensitivity of the actuator depends on the size of the piezo and on the intrinsic properties of the piezo material. These propenies vary for different materials and depend heavily on temperature. This can be important for a low-temperature STM. An important parameter of piezo materials is the Curie temperature. Above this temperature, depolarization occurs, resulting in a reduced sensitivity. 'Ib avoid this, an u ~ v STM should be baked at not too high temperatures.

Calibration of the actuator is done by measuring the displacement which results from a certain change of applied voltage. Such small displacements can be measured by connecting the actuator to an electrode of a capacitor and measuring the change in capacitance Cyurke et a1 1986, Vieira 1986, Simpson and Wolfs 1987). This yields an accuracy of 0.1 to 0.01 A Less sensitive methods are based on laser interferometly (500 nm) or on a linear variable differential transformer (0.1 Wm, Locatelli and Lamboley 1988, Emch et a1 19888).

4.1.4. Coarsepositioning mechanisms. The aim of a coarse positioning mechanism is to bring the sample within the range of the scan unit and to keep it there as rigid as possible. Thii requires aceurate positioning (within a few hundred nanometres) and a sufficiently large range (several millimetres), combined with a very stiff constmction. At least one degree of freedom is needed to bring the tip close enough to the surface. Ib choose Werent parts of the sample, two or even three degrees of freedom are desirable. Notwithstanding the degrees of freedom of the sample, it should be connected to the scan unit as rigid as possible to minimize the influence of vibrations. Furthermore, a thermally compensated or symmetric design is advantageous because it yields lower thermal drift.


It can be useful to interconnect an automatic approach system with a Current detector. This will minimize the probability that the tip will hit the surfs= and it makes the approach less dependent on the amount of patience of the experimentalst.

The first clas of coarse positioning mechanisms uses a sample holder which is free to move on a baseplate, yielding two degrees of freedom. Motion of the sample holder can be accomplished in several ways. Binnig and Rohrer (198213) caued their sample holder a ‘louse’. It consists of a slice of piem material which rests on three 01 four feet. The louse can make steps by electrostatically clamping some of its feet while contracting the disk, and clamping some other while expanding it. The not-clamped feet slip over the underlying sm”ace. Step sizes range from 10 to 400 nm, a typical speed is 40 p m s-l (Bnnig and Rohrer 1982, Mamin et al 1985). A major problem with these types of louse is their sensitivity to dust and other effem which influence the sticking of their feet to the supporting base. An improvement is a double set of feet, each set being extended (retracted) when it is s u p p e d to stick (glide) (Binnig and Gerber 1980, Uommi e( al 1988). Another way to move the sample holder is by pulling or pushing it by an inch-worm (Hemen et al 1987). a stepping mom (Park and Quate 198%) or magnets and coils (the ‘maggot’ of Corb et al(1985), also Smith and Elrod (1985) and Kajimura et al (1987)). Pohl (1987) and Anders et al (1987) use a dynamic translator whose motion is caused by a sawtooth-lie periodic aceeleration of a piezo element During the very fast aeceleration in one direction the sample holder slips on the base plate while during the opposite aceeleration it sticks to the base because of friction f o m .

The same principle is used by Besocke (1987, see also Emch et al (1988a)): The sample lies upside down on three piezo tubs which act as pillars. One of the tubes can be lowered using a micrometer screw. A sawtooth bending movement of the tubes can transport the sample hteTaUy. The tip is mounted on a fourth tube in between the other three. This design is thermally compensated, small and veny simple. An even more ingenious extension uses a ramped sample holder. Appropriate movement of the piUars causes a rotation which is converted in a motion of the tip towards the sample by the ramps (Frohn et a1 1989). A variant on the pillar idea is placing the sample on a piezo tube which is concentric with the scan tube (Snyder and de Lozanne 1988, Besenbacher et al 1988).

Demuth et a1 (1986) introduced a second class of coarse positioning mechanisms. Their sample is attached to some. lever connected to a (differential) smw. The lever reduces the movements of the screw by some factor which enables accurate positioning Of the sample. (Smith and Binnig 1986a, Smith et a1 1987a. SOMenfeld et a1 1987, Jericho er ut 1987, Kaiser and Jaklevic 1987a,b, Pashley er al 1988). Dum movement Of the scan unit by a differential screw (Dovek et a1 1988h, Bando et a1 1988) or an inchworm (Gregory and Rogers 1988) is also a possibility. Advantages of these screw-and-lever mechanisms are that the sample is rigidly connected to the scan unit and the reliability of such a construction. A disadvantage of these mechanisms can be that a large mechanical apparatus connected directly to the sample may give rise to instabilities. Some authors therefore use a sample holder which can be clamped combined with a retractable actuator, an idea which is also applied to the louse. A second disadvantage can he that 1 !ever hlr nrg fine degree cf fipegez, a spot on the sample becomes impossible or complicated. A combination of dfferent levers can solve this inconveniency (Hemen et a1 1987).

4.1.5. Tip materiak andpreparation techniqw. The most commonly used tip materials

Scanning tunnelling microwom 1195

are tungsten, platinum or platinum-iridium wires. The latter materials are specially suited for an atmospheric STM because of their inertness The advantage of tungsten is that it can be easily etched electrcchemically. Tbngsten wires have usually a prefer- ential (110) orientation. The use of (111) oriented tips (e.g. cut from single crystals) may have certain advantages (Neddermeyer and Drechsler 1988), but it is certainly not necessary to obtain good results. A more exotic tip is 0.5 nun pencil lead. which

0.1 to 1 mm, the advantage of thicker tips being a higher resonance frequency. For the same reason, tips should be as short as possible.

As the shape oE the tip !its the maximum obt2inable resolution, a good and reliable tip preparation method is very important. For example, Wmtterlin et a1 (1989) achieved atomic resolution on an Al(111) surface only after applying a pulse of -7.5 V to their sample. They concluded that some material was transferred from their sample to the tip because their feedback signal remained displaced by 2.5 nm after the tunnel voltage was reset to its original value.

There are a lot of recipes for sharpening the tip, usually consisting of two stages. The first stage is performed ex sifx and consists of macroscopicaUy sharpening the tip. Some possibilities are electrochemically etching (e.g. Bryant et a1 1987, Nicolaides et a1 1988, Laiiho et 01 198?, Iijima and Yasuda 1988), grinding (with sandpaper or

methods may be followed by rinsing with demineralized water and/or (ultrasonil;llly) cleaning in propanol; they all seem to provide good tips.

The semnd stage consists of some in situ treatment to sharpen or to clean the tip on a microscopic scale. This stage is not always needed, tips can perform SatisfactoriJy without any further treatment. Methods to obtain microscopically sharp tips are often based on experience and asmibed to rearranging the atoms at the outer tip, removing atoms from the tip (contaminations or the tip material itself) or addmg atoms to the tip. Some examples are: heating the tip by electron bombardment, operating the tip in a field emission mode for some time (with or without scanning) or until a drastic change of the current is seen, switching on some apparatus in the neighbourhood of the STM, making the tip touch the sample very gently (or very crudely by adjusting the feedback system so that it starts resonating). There are lots of such tricks in the

The microscopic sharpening of the tip can be studied and controlled by field emission microscopy (Fink 1986, Nishikawa et a1 1988, Kuk and Silverman 1986) and electron microscopy. This has led to some tip recipes using ion millmg (Biegelsen 1987, Tiedje 1988) or annealing (Binh 1988, Binh and Marien 1988).

An amusing way of looking at the tip is presented by van de Walle er a1 (1986). They pushed a tungsten tip deliberately into a (soft) sih'er single crystal. Afterwards, the indentation could be smnned with the same tip: a clearly faceted structure became Visible, which can be asswned to he a repkca of the tip structure.

4.2. Different environments

4.2.2. Ulfra high vacuum. The advantage of a UHV system iE the fact that surfaces can UT y,rprGu UL a WGU "GLLIICU UUILG) c1Ga11 U, uG,n"Gna.ln)r "J P"I"L"-u

gases, epitaxiaUy grown layers etc. In UHV, only a selected range of materials and components should be used (Weissler and Carlson 1979). Special attention should be given to the sample holder: stainless-steel sample clips may contaminate the sample's

pSrfQES ratkfactQfl-~ in Zir !Q!to!! U r?l 197). Dkmet,, d !he %L%S K?zge frem

,gjj&to=e), cEtt&g 1 p& "f r&soc 9' ps&&&z &..;tL 2 !~$h. -AJ! t..;tLc~p

KtpEtlllp 2nd they pln he *.&J!, eyea ;t $key zre "et fE$ onnegoga.

l. ---.."-"A :" ~ -. ,a A " f " ^ l ".*.a "I-"" -- .I^l:Ln...*-L. L~"."".:""."l~ I... .Ar... I.-A wIILaIII"Ia.CY

11%

surface (van Loenen et al 1988), a better choice is molybdenum. Furthemore, the bake-out temperature should be lower than the Curie temperature of the piezoelectric material used.

Manipulations with samples, tip or other STM parts in UHV are more difRcult than in a normal atmosphere. It is wry useful to be able to change the tip of the STM without opening the UHV chamber. Opening the chamber means a new bake-out cycle and a new sample preparation, both of which are t h e consuming.

An advantage of UHV is the absencx of acoustic coupling of the S m with the laboratory. However, there is strong couphg between the sTM and the vacuum chamber and some =%ration isolation is necessary. The Muence of vibraiions of the cbamber can also be reduced by increasing their frequency: this can be achieved by designing a small, ‘square’ chamber and by using thicker materials for the walls of the chamber.

4.22 Atmqhere. The main advantage of an atmospheric environment is easy amss to sample and tip.

The majx disadvantage is that most surfaces degrade if they are exposed to air. Even if they do not, a ‘fluid’ contamination layer will be present, giving rise to large forces between tip and sample (section 7.1; see also section 4.2.3). The degradation of the sample can be prevented by operating in a conditioned atmosphere (e.g. a glove box, Amelmetti et al(l988)).

The coupling of sound to the STM and its sensitivity to draught and temperature variations can be handled effectively by some shielding and a thermally compensated design.

4.2.3. Liquid. It is evident that in Sinr studies of liquid-solid interfaces can only be done if the STM is operated in a liquid environment Measuring in a liquid has some, not immediately, obvious advarages. The liquid can prevent the surface from degrading due to exposure to air. This is certainly the case for some biological samples whose natural environment is a liquid and which will collapse if dried. In air, both tip and sample are likely to be mvered with a thin liquid film. Large capillary and surface tension form on result if these films form a bridge between tip and sample. The interaction forces of a bulk liquid between tip and sample are expected to be several orders of magnitude smaller (Drake et nl 1989).

It turns out that it is no problem to operate an STM in a non-conducting liquid. The liquid can consist of a small drop on the sample (SoMenfeld et al 1987) or an open cavity which is filed (Sonnenfeld and Hansma 1986b). Except for the tip, the exposure of other parts of the STM (e.g. piezo-ceramics) should be avoided. It may

A conducting liquid poses a problem: how to distingukh between the tunnel current and the conduction current via the liquid (Rradaic currents). This problem can be avoided by the use of an AFM, which works well in a liquid (e+ Schneir et a1 19%). Spurious currents can be minimized by coating the entire tip except for the OUtennOSt part with glass (SoMenfeld and Hansma 1986a,b), with an epoy (Schneir el a1 1988c) or with silicone (Trevor et al 1989).

4.24. Law temperatures. An STM can be operated at low temperatures by simply immersing it in some cryogenic liquid PHe, Smith and Bmnig 1986a, van Bentum et al 19- sHe and 4He, Fein er a1 1987), by immersing an entire vacuum chamber


inteaere wit!! the operation of the STM ma_ it wil! pertaS!y ”amhat. the !*!idG

Scanning tunnelling microscow 1197

in the liquid (N2, Drake et a1 1986; *He, Elrod er al 1984) or by using a cold finger in a vacuum system (de Lozanne er a1 1988). A dilution refrigerator allows a lower temperature but also complicates the design (Burger er al 1989).

Several technical problems may arise: ti) The piezo sensitivity will diminish (Keira 1986). (U) The tipsample distance can change dramatically upon cooling. Some kind

of in siru rough approach mechanism is desirable, together with a symmetric and thermally compensated design.

(iii) During cooling, a lot of contamination gases may condense on the sample. This can be prevented by evacuating or flushing the sample environment. (Note that evacuating prohibits convective cooling and may ask for extra conductive cooling paths.) The best solution is an in Sinr cleavage possibility (de b z m n e er aI 1988).

(iv) Cryogenic Iui& tend to boil, which causes mechanical noise. In the case of helium, boiling can 3e prevented by reducing the pressure above the helium so it becomes supemuid. The addition Gf boiling chips to liquid nitrogen may be of help (Drake er a1 1986). as may the use of a double mostat, even for measurements at liquid nitrogen temperature.

4.3. EIecmonics and data processing

the s a signals and to store the acquired data. Much more flexibility in data storage and handling can be achieved by using a computer system (Becker 1987, Aguilar er al 1987, Bapst 1987). Such a system can control the approach from the sample to the tip, it can provide 2' and y scan signals and aquire the z signal or even more ChaMdS, e.g. B I / B s or the current at several voltages.

During or after the scan, the data can be displayed as a line image or as a grey scale image. Grey (or colour) scale images are very useful for regular surface structure. More sophisticated displaying techniques are computer graphics such as solid modelling with flat or Gouraud shading or stereophotographs (Rosenthaler et aI 1988).

Several image-processing techniques can be used to enhance the quality of the results. lb compensate for a tilt of the sample, a plane can be subtracted from the &+zp. r,,p""r:&z fer fk..ma! d.;& pzc p"'" kySre:e& & &e p&&. G=.y can be used more efficiently after histogram equalization. Noise reduction or contrast enhancement can be achieved by digital filters such as median filters, convolution filters, statistical differencing (Widson and Chiang 1988). If the structure is periodic a very smooth picture of a unit cell can be obtained by correlation averaging (SOethOUt et a1 1988).

5. Operating modes of an STM

5.1. Topography

5.1.1. Comtatu current mode. In most cases, topographical images are obtained in the so called constant current mode. The bias voitage is b e d and a feedback circuit (figure 10). regulates the current by adjusting the distance between tip and sample. A computer generates an x-g scan and simultaneously records the feedback signal, which is a measure for the local surface height. This method is relativeb straightforward but some points of attention should be mentioned:

A wavefarm sy!Lth&er mmbhed with a starage aScaQsmpe can be used to generate


COMPUTER

W E N T AMP

Z i Y TIP SAMPLE PI-

Wgzm 10. Schematic ViRV af the signal paths in the wastaut current mode. The fouowiag elements p-r the computer which gemares the scanning motion of the tip and which gathers the daes J, the imegrator, lm-pas filter no 1 to optimize the the feedback p f o m n c e and to prevent the system h m monaung; HV, highvoltage a m p m e filter 2, a low-parr filter adjusted to the data acquhtion rate (see tat). The z - p i m IS adjusted by thls feedback system so that the c u m t I stays qual to the pTeset Value I..,.

(i) The time mnstant with which the feedback signal is filtered before it is fed to the computer @iter no Z) shoui6 be wmparabie witn tne time spent by the i ip on a location (2 ,~) . If it is much larger, the mntriiutions from the previous location(s) will be too strong and the image will be smoothed too much. On the other hand, it is advantageous to choose the filter time to be as long as possible to reduce noise. If the filter time is smaller than the time spent on one location, aliasing effects may occur (Press et ul 1988).

(ii) The scan times should be large enough to allow the feedback to reach equilibrium at a new location of the tip. The characteristic time scale of the feedback system depends, amongst other factors, on the mechanical piezo characteristics.

(iii) The stability of the feedhack depefds on the open loop gain and the phase shif t These quantities are not only determined by the electronics and the mechanical propeaies of the sm, but also by the hias voltage and the current The latter two quantities determine tbe (non-linear) response of the tunnel junction. This dependence can be eliminated by the use of a logarithmic current amplifer. Being linear, the system can he analysed by standard feedback theory, which yields detailed design criteria for the gain and frequency response of the feedback ampliser (Pohl 1986, Park and Quate l987a). However, good results can also be obtained without the use of a logarithmic ampli6er (e.g. van de Walle et al (1985)).

5.1.2. Conxtant height mode. Usually, the factor limiting the scan speed is the m e chanical performance of the STM. A higher speed can be obtained if the tip is scanned aeross the sUrtaee without adjusting its height. This is called the wnstant height mode (or 'skating mode', Sarid et a1 (1988)). In this mode, the signal speed can be fast enough to allow a real-time video display of the surface (Bryant et a1 1986). This mode can only be applied if the surface is very flat: corrugations larger than the

still present (figure 11) to maintain a constant average distance. The time constant of the feedback filter is larger than the scan time, so during one scan the tip stays Wenthy. at the same height. As the information on the surface structure is obtained

tip S"!e separ&In A) wg t&e zip E&. m$ fp&z& &&Lm & J


via the current, a direct gauging of height differences is no longer possikle. This is not a ?:rious problem: as the small cormgations which can be measured with this method are in most mes connected to features which are associated with the density of states, absolute heights have no value at all.

I TIP SAMPLE

Figure 11. Schematic vim of the signal paths in the mrm~fant height mode. Compared with figure 10 (the mo~fant current mde) the cnt-08 fregufflcj of law-pass filter no 1 is so low that the up d o a not falloar the mntoum of the surface while being seamed. The information on the surface structure is now mfained in the curreat sipal which is fed m the mmputer.

The ratio of feedback filter time and the scan time can be varied. This results in an operating mode somewhere in between the constant Current and the wnstant height modes. The Ilatness of the sample is now restricted only on a scale determined by the feedback ater time muitipiied by the scan speed.

5.2 specfrosco~

5.21. General features. Any single measurement in STM is characterized by five variables: I, y, z, I and V. An image consists of a three-dimensional cut through the live-dimensional parameter space. The topographical constant current mode can be characterized by constant I and V, the topographical constant height mode by a eonstant V and z.

Spectrosmpy covers those types of measurements in which V is not constant. Such measurements can yield information on the surface electronic structure (sections 2.4 and 3.2) and on several aspects of the tunneUig process.

Compared with topography, one extra parameter can be varied. This can increase the number of data points tremendously: suppose one measures I( V) curves consisting of 50 points at 100 x 100 locations and each measurement t aks 2 byte, then 1 Mbyte of data is produced for one image. Another dficnlty is such a 1 Mbyte image takes much longer to measure. Drift and other instabilities could easily spoil such an image. Despite these difficulties, such a big data file contains a lot of information and can be worthwhile.

The diUidties associated with large amounts of data and large scan times 011)

often be prevented by realizing what kind of data is required. If one is interested in a detailed measurement of the electron density of states, a high resolution in the voltage is "cessary, Usually not at a lot of points. The points can be selected before or during the scanning p~cess . In such cases, AC (Iock-in) techniques can be valuable

1200

for obtaining BI/BV directly. The quantity of interest is (OI/aV) / (I /V) , which is expected to follow the electron density of states most closely (section 2.4).

On the other hand, if the spatial distribution of some state is the subject of interest, a measurement of a few well chosen voltages at a fine grid of locations is the better choice.

The shape of the tip plays an important role in spectmsmpy. Again, different tips

but blunt tips have the advantage of being less position specific, enabling to probe the density of states averaged over (a part or) the unit cell.

There is a constraint on measuring speed in spectroseopical applications, caused by the capacitance of the tip and the leads to the tip (typical values: 0.1 to 10 pF). Any change in bias voltage causes a charge transfer A Q = CAV on that capacitor. This causes a current to Bow which has nothing to do with any electronic property of the tip or sample. There exist two general ways to obtain spemosmpic information. The charging current behaves differently in each of them:

(i) The DC method the bias voltage is switched instantaneously. In this case the capacitor is charged via an exponential decreasing current. If the time interval between the voltage step and current measurement is long enough, the contribution of this chargins current can be ne~leaed me relevant time scale is an R,C time. defined by the capacitance mentioned earlier and the output impedance R, of the bias source and the current sensor.

(ii) The AC method: aI/aV is measured ria a lock-in technique. A modulation AV is applied to the bias voltage. Thii causes a modulation of the tunnel current of (a1JOV)AV plus a charging current AVl(2rfC). Suppose that OI,/aV = R;', then the charging current can be neglected if f Q: (2r&C)-*. A possible but tricky way to distinguish between charging and tunnel current is the fact that there is a phase differexe of r / 2 between the two components. If the current sensor does not give a phase shift, the zero phase component should be the tunnel current,

Note that in both methods the limitation on the measuring time is an RC time, but in the AC method R is the tunnel resistance (Et), while R in the DC method is the bias and lead resistance R..

5.22. Constant current modes. The simplest way to obtain spectroscopic information is to compare constant current topographical images measured at different bias voltages. If the electrons tunnel from the sample to the tip (nzgative sample bias), the occupied (bondng) states in the sample are imaged. If they tunnel the other way (positive sample bias), the empty (anti-bonding) states appear. lb measure their relative position accurately, the images should be measured more or less SimultaneOUSly: for example, the voltage can be switched at each h e . Some points of attention are:

(i) Spurious results caused by different tip shapes. The exact shape of the StNG tures seen is usually not reliable, better parameters to describe the situation are the lowest fourier components of the surface corrugation (Feenstra and Stroscio 1987a).

(ii) %e switching of the voltages should be slow enough to allow the feedback system to reach equilibrium before the actual measurement of the tip height is made.

This method emphasizes the spatial distribution of the electron states (figure 12). If more detailed spectroscopic information is desired, the following variant can be useful: measure the conductance (aI/aV) as a function of voltage while keeping a constant current (figure 13). The specific features of this method are:

L E C van de Leemput and H pun Kempen

~-~ .=f.ui iu dhmefeiii sMrp a ~ e spaiia; resoiunon

Scannhg Nnnellhg microscopy 1201

Pipom 12. Constant current imagcs of a Si(ll1)Z Y 1 surface acquired SimultancouslY at sample voltages of + I V (0) and - I V (b). shavlng nspeellvcly the empry and lhe Slid slates. The emss hain M laaled at the same surface locations m esch Image. Note Ihe duTcrent 10011~on~ of the maxima (while spu) in Ihe luo difercnt pictures. These meaJurCmCnIs h e l m 10 s c k t the riel surface mONtNClion out of 6-l proposed models (Fceastra and Straio 1987a).

Y TIP S p t E

Figure 13. The signal paths tu one of Ihe specvmeopinl Wmtant current mods The lack-in ampliaer meaJureS the variations in I due to the mOdulatlon in the bias voltage. The bmi marked - is a generator wbich pmvids Ihe bias modulation. The wmpukr can obtain infamalion on Ihe d m i v of slates by adptmg the bias voltage and recording che resulting variations In a I p V .

(i) One cannot scan through Zero voltage as the feedback will then push the tip into the sample.

*

12G2 L E C van de Leemput and H van Kempen

(U) If the tunnel current behaves according to Ohm's law (metals). the WnduG tance diverges when the bas voltage approaches zero.

(E) The exponential increase of the conductance in the high voltage limit (section 27) is automatically compensated for because the tip is retracted to keep the current constant.

(i) Some typical values are: V,, = 20-150 mV, fmOd = 0.2-1 V,, = 0.1- 9 V (van de WaUe et al 1987, Fuchs and lbsatti 1987, Baratoff et a1 1986).

5.2.3. Cmtant resitance modes. These are variants of the constant current modes, mainly used to prevent the divergence of the eonduaance at low bias voltage. The feeciback system adjust the tip in such a way that a constant DC tunnel resistance is maintained (Kaiser and Jacklevic 1987a). Although this method still does not .,"-"a., Y Y . . . W """"p .5.,L" .wL..p, L U W W " " " ~ ~ . ~ " ' , V " w p.uyu.uuuar ,U

( a I / a V ) / ( I / V ) , which is not only the quantity of interest but it also does not diverge if the bias voltage approaches zero.

nn.hln .r.xnninn (L*n..nh --m .mInn- +ha P T I PT, :- ----A..L..-~I .-

F@m 14. The signal paths m Ule spectmseopical comlanl separation mode. Ihe bax marked Ss H represents Ihe integralor, which is now equipped With a sample-and-hold cireuil. The mmputa controls chis emuit and the bias voltage, its input mmkm at lhe local surfsce height and Ihe " e ~ t .

5.24. Constant separation modex The previous modes do not work in cases where no current is flowing: at zero bias voltage or in a band gap. This limitation is overcome in constant separation modes In these modes, the tip is temporarily frozen at a Iixed height above the surface, using a sampleand-hold circuit. Then a current

feedback system is allowed to regulate the tip position (figure 14). The following technical points should be eonsidered

(i) The timing is subtle: if the sample-and-hold acts for too long, the mechanical instability of the STM and the electronical drifI of the sample-and-hold circuit will cause the separation to change. The lower l i t on the hold time is set by the RC time of capacitance of the tip and the leads together with the internal resistance of the bias source and current sensor. 'Ijrpical sample-and-hold times range from 0.5 ms (Hamers et a1 1986) via 3 ms (Tinaka et a1 1988) and 10 ms (Strmcio et a1 1988a) up to 50 ms (Feensaa et a1 1987); typical times to measure one data point range from 10 ps (Tromp et al 1986a,b) to 6oQ ps (Berghaus et a1 1988).

meas.uRd a~ severai djerent vuiages. in ~~ m e ~ . u ~ ~ ~ ~ ~ ~ &&,

Scanning tunnelling microscow 1203

(ii) At higher bias voltages, the current increases very rapidly and leaves the range of the analogue-to-digital converter or even the current sensor. lb stay within a reasonable current range, the measurement can be repeated at several separations. This is discussed in more detail in the next

(iii) (8I/aV)/(I/V) can be obtaine ri0u nwnencaUy from the measured data. (iv) lb reduce noise, ditferent I( V) c u m can be averaged (Colton et a1 1988).

This method can be used to obtain I( V) characteristics, but it is also eminently suited to show the spatial distribution of different surface states or resonances. For this purpose, the current can be measured at several voltages at each point of the surface. Then pictures should be made representing the current at lked bias voltages or the ditference in current between two bias wltages. The latter highlights the contribution of a state lying just in between the chosen voltages (figure 15). This technique is known as current imaging tunneiiing spenmscopy @lsj (ijemutn er ai 1988, Hamers et a1 1986, 1987).

F b W IS. Cm h g e a of occupied Si(lll)7 x 7 surface states: (a) adatom state at -0.35 V; (b) dangliapbnd slate on rest-atoms at -0.8 v; (c) backbond state at -1.7 V (Hamus a d 1986).

5.25. Vkriable sparation “fa. In the constant current and constant resistance modes, the automatic adjustment of the separation prevents the current moving out

1204

of the measurable range. The following methods can be used to vary the separation in a controlled way with the aid of a sample-and-hold mechanism:

(i) I( V) curves measured at different separations can be glued together by assuming a simple exponential relation between current and distance. Different separations can be obtained by: (a) stabilizing the feedback loop at different bias voltages, each of which corresponds to a particular distance that is fromn with the sample-and-hold (Strocio et al 1986, Kubby et al 1987); and (b) displacing the tip a ked distance while the sample-and-hold is active (Feenstra and Strocio lWa, Fein 1987).

(U) The separation can be changed by applying a ramp to the piezo during the I (V) scan (Suocio and Feenstra 1988). This can be combined with detection of aI /OV ria an AC technique (Feenstra and Martenson 1988, mrtenson and Feenstra 1989).

L E C van de Leemput and H van fimpen

5.2.6. Constant average current modes. In these modes a rapidly oscillating voltage is applied at the tip. The current signal is then fed to a low-pass filter (Reihl et al (1986), V = 0-5 V at 180 Hz) or to a lock-in amplifier (Sarid et a1 (19%8), a triaI@uIar voltage of 1 Vat 100 Hz), the output of which is regulated constant by the feedback system. The unfiltered current signal is simultaneously fed to a computer or a storage oscilloscope to obtain the I( V) curves.

It is even possible to obtain aI/aV by using two lock-in amplifiers: one operating at the relatively slow sweep frequency (f = 1Q-20 Hz, Le Due et a1 (1989); f = 1 kHz, de Lozanne et a1 (1985)) and the other operating at a high modulation frequency. The slow one is used in the feedback circuit, the fast one measures aI/aV against the sweep voltage.

5.3. Work function measurement

As the tunnel current depends on the work function (section 2.2), it is possible to measure the work function (6) ria the tunnel current if all other parameters can be eliminated. From the tunoel formula (equation (5)). it can be seen that (aI/as)/I=-(1/s+C,d1/2) (C, = 1.025A-l eViI2). Atypicalworkfunction is a few electrowolts, so the first term depending on the bamer width s (in A) can be neglected The quantity (aI/as)/I is known as the apparent barrier height. However, the tunnel formula is based on a square barrier which is not realistic. Several corrections should be taken into account (section 2.3). It is particularly awkward that the averaged barrier height depends on s, so extra terms will appear in the formula.

Payne and Inkson (1985) calculated plots of BI/as against I at constant voltage, and of aI /& against V at constant current. They included the classical image potential by using the resulls of Simmons (1963). Despite the image potential, the plots at constant voltage showed a linear behaviour with a slope slightly dependent on the applied voltage hut in good agreement with the actual work function. The plots at constant current are h e a r but with slopes corresponding to work functions which are too low by approximately a factor of two (depending on the current density).

In practice, allas is measured by applying a modulation As on the tip (via the t piezo) while operating in the constant current mode. The resulting current modulation can be measured via a lock-in amplifier. Care should be taken that the mndulation frequency is well above the cut-off frequency of the feedback system.

Scanning funnelling microscofl 1205

If not, part of the modulation will be compensated for and the measured current modulation will be too low.

A measurement of the work function can provide information on the barrier shape, the sample's surface and contaminations on top of it. Bmig el al (198%) measured the work function of metals with their protrnype STM even before it could scan. The work function can vary over the surface, a spatial& resohred map of its value can provide useful information (examples: Khaikin and ltoyanovsldi (1985); Wiesendanger ef a1 (1987)).

As the work function is measured via B l / B s , exact knowledge of the tip displacement is of mchl importance. The distance modulation should be applied along the direction in which the current Bows. A severe disalignment of the sample or a sloped facet on it requires at least an angledependent correction. Even worse is the fact that on such slopes, or on a rough surface, the locus from which the current leaves or enten the sample or tip may shift laterally, giving rise to a change in current due to a change in the local density of states or a change in the local geometry. In such cases, it may become very diilicult or even impossible to disentangle the different contributions to the resulting current modulation.

Sometimes, measured hamer heights are lower than 1 eV. Such anomalously low results are explained by Coombs and Pethica (1986) as the result of a mechanical (isolating) mntact bemeen tip and sample. The actual change in the width of the tunnel barrier is in that case smaller than the piem displacement, due to an elastic deformation of the tip and the sample. This provides a useful method to check the quality of the tip and the sample. Suppme an sm b operated in a constant current mode. If the preset current is chaneed by a factor of two, the gap width should be reduced by the piezo a few tenths of an hgstmm. If the piezo responds much more, then the barrier height is apparently much smaller and a mechanical " a c t is very iikeiy to be present, so no reiiabie pictures snouiai be expected

A totally Merent mechanism which lowers the apparent barrier height can be present at semiconductor surfaces. The applied voltage causes a band bending inside the semiconductor. The actual voltage across the vacuum gap depends on the electrode separation. Thus a distance modulation not only modulates the barrier width but also affects the barrier height. Weimer ef al (1989) showed that in such cases the apparent barrier height can be very low and depends sensitively on the separation and the bias voltage.

An interesting alternative method to measure the work function is photothermal modulation of the barrier width. A focused, pulsed laser beam heats the surface, 1eSUlting in a periodic expansion of the surface. ppical expansions are somewhat smaller than 1 A The resulting modulation of the current provides information on the workfunction (Amer et al 1986).

5.4. Potenrimterry technique uses the STM to determine the potential distribution on the surface of

a sample across which a voltage difference is applied. Several methods can be used. The applied voltage across the sample can be a DC voltage while the entire sample is modulated with an AC voltage with respect to the tip. The AC tunnel current is derected via a lock-in amplifier which drives a feedback circuit. This circuit m turn keeps a constant tunnel current by adjustiig the height of the tip, as in a constant Current topographic imaging process. The current is also averaged and a second feedback circuit applies a DC hias to the tip to keep the average mio. This bias

1206

corresponds to the local sample potential provided that the I( V) curve is symmetric. This is the case in metals (Muralt and Pohl 1986, Muralt et 01 1 W ) but not in semiconductom (Muralt 1987).

Kirtley ef a1 (1988) use anusher method They use a standard feedback system with a sample-and-hold circuit. During the hold period, they change the voltage between tip and sample by an amount AV and determine the tunnel resistance & from the resulting current change. The local potential can be derived by subtracting I& from the known absolute potential of the tip. Pelz and Koch (1989) extend this method with the use of AC techniques, in this way lowering the noise level.

The local potential can be determined in a straightforward way from I( V) characteristics measured by current imaging spectroscopy (section 52.4).

An m can also be used to determine the local potential. The AFM measures the electrostatic force between tip and sampla This force is proportional to the square of the applied voltage (Martin ef al 1988a). Applications of thb operating mode can be found in section 8.3.


6. Other scanning lip miemscopes

I. I 7%" "."-:.- &.an ...i.-."",-""" I..= U,",,.", ,",CL .,..... V " C " p -1.

6.1.1. OperafingprincipIes. An atomic force microscope (AFM) probes the force between the surface and a scanning tip. The tip is mounted on a lever which is brought very close to the sample. The forces exerted on the tip by the sample wiU bend the lever. This deflection can be measured by optical methods (interfeIOnIetry) or by a tunnelhmg tip (as in an sTM).

R

BLOCK (ALUMINUM1

~

C: STM-TIP ( A d U CANTILEVER.

STM SAMPLE

(b) Pisure 16. Schematic d m m g of an atomic force micI"pe (Binnig a a/ 1986b). Ihe SIM and APM piao-drives are facing each other, sandwiching the diamond tip that is glued U) the lever

Figure 16 shows schematically an AFM in which the deflection of the lever is measured by an "4' tip. As in an sm, the current flowing from the tip to the lever is highly sensitive to the distance between tip and lever. There are several modes for

Scanning funnelling microscon 1207

operating such an AFM. In the frrst mode, a feedback system establishes a constant deflection of the lever, providing a direct mapping of a constant force contour of the surface. A second mode uses the output of the feedback system to change the distance between tbe tunnel tip and the lever. A minor variant on this mode is to use no feedback at all and use the tunnel current to measure the deflectioa These modes yield a mapping of the deflection of lever. If a step with a height Ah occurs on the sample, the lever will move A2 = Ah kint/(kl - kint). (k, is the compliance of the lever, kin, b the first derivative of the tip-surkce force in the normai Ciaion.) As kint is unlolown and may vary over the surface, the results of this mode cannot be interpreted in a straightforward way.

A different way of probing the tipsurface interactions is to use an oscillating lever, driven by an oscillating sample, by an external stimulator, or by an AC voltage between tip and sample thus generating an electrostatic force (Taubenblatt 1989). The response of the lever is determined by it$ own properties (compliance k, and resonance frequency U,,), together with the interaction compliance kint.

A totally different appraach is based on the fact that the resonance frequency of the lever (uO) depends on the tipsurface interaction via AV,, = $kiJklvv The lever is connected to a piem which drives the lever at its resonance frequency. A change m tbis frequency can be detected by a phase shiit between the driving oscillation and the resulting modulation or by a change in amplitude of the modulation.

Finaiiy, ii is possiiiie to use a siighiiy moa~eed STM to probe forcer. Tne sampie is mounted with a spring-like construction WhiEh causes the sample to oscillate. The tipsurface interactions inlluence the spectrum of these oscillations which can be obtained by measuring the noise in the tunnel current @tirig er a1 1986, Png et a1 1988). A variant of this method is mounting the sample on an electret microphone, which turns out to be a very sensitive force detector (Schreck et a1 1990). A slight disadvantage is its high sound sensitivity.

6.1.2. Conshuction of an AM. Like an STM, an AFM needs a vibration isolation, a mane positioning mechanism and piezo actuators. Special parts of the AFM are the force-sensmg tip, the lever on which it is mounted and the deflection measuring system.

The lever is characterized by a force constant kl and a resonance frequency vW As a smaii kl yklaS a iarge deflection, it is advantageous to choose a small kl. However, kl also govems the amplitude of the thermally induced noise. The amplitude a, of this noise can be calculated from the equipartition theorem: fkbT = fkla$ A noise b e l of 0.03 nm at room temperature poses a lower limit on kl of 5 N m-l. The mini" detectable force if the DC bending of the lever is measured is roughly a& < lo-'' N. AC techniques can measure the force derivative k,, with an accuracy of N m-l. The force can then be obtained by integration with a slightly higher amracy than with DC methods (e.g. Manin and Wlckramasinghe (1987)).

The resonance frequency of the lever determines vibrational immunity (section 4.1) and l i t s scan speed, so the resonance frequency should be as high as possible. This can be achieved by making small and light levers.

In the first AFM, Binnig et a1 (1986b) used a thin gold foil (0.8 mm x 0.25 mm x 0.025 mm) as a lever with k, = 100 N m-l. A diamond tip was glued to the ieVe1. in a second design Bhnig et al (1987), used a microfabrication technique to construct a rectangular SiO, lever (ZOO pm x 20 pm x 1.5 pm) with a spring constant of O M N m-' (U,, = 17 *). The edge of the lever served as tip. Thermal

1208

fluctuations were indeed visible, but were reduced drastically when the lever was hrought into wntitct with the sample. This is caused by the contact area which acts as an extra parallel spring, yielding an effective force constant K = k + kint. Further evidence for such effects is the lowering of vo from 17 to 10 kHz when a tunnelling tip is b'mught close to the sample. With this apparatus, they obtained atomic resolution on graphite using a contact force of N.

Albrecht and Quate (1987, 1988) constructed a V-shaped lever which provides a sharper tip than a rectangular lever, improves the lateral rigidity and has a very high resonance frequency (k = 2 N m-', uo = 100 e). They used the edge of the lever as a tip but also small diamonds and small cones grown by an evaporation technique. Kirk et a1 (1988) incorporated such a triangular lever in a low-temperature AFM.

Several constructions using wires are described by Marti et a1 (1988a). Yamada et a1 (1988) glued an etched 30 p m wire to a lever made of gold foil. Heinzelmann et

piece, cut out of a ribbon of metallic glass (700 p m x 50 p m x 15 pm, uo = 20 kHz). Bryant et al (1988) use a conducting force-sensing tip. This enables instantaneous

switchmg and comparison between AM and STM operation on conducting samples. AU designs mentioned in the previous seetion measure the deflection of the lever

by a tunnel current which flows from a second tip to the back of the conducting force sensing lever. Such a system is sensitive to drift and the risk of damaging the very fragile levers with the tunnel tip is not imaginary (Marti et a1 198%). Furthermore, the tunnel tip probes the lever very locally, which causes the apparatus to be very sensitive to a lateral movement of the lever (caused by drift or bending at high steps on the surface). Alternatively, optical interferometry can be used. Possible approaches are described by Martin et a1 (1987), McCleUand et a1 (1987), Erlandson et a1 (1988) and Rugar et al (1988). Depending on the mode of operation optical

probes a large part of the lever. The simplest way to detect a lever displacement is via a position-sensitive detector

(Meyer and Amer 1988, Alexander er a1 1989, Drake et a1 1989). The reflection of a laser beam from the tip illuminates two closely spaced photodiodes whicb are connected to the positive and negative inputs of a differential amplifier. Movement of the tip results in a linear change in the output signal. This apparatus is not the most sensitive one but it does not require a lengthy adjustment procedure.

61.3. Forces in AFM. Forces which act between the tip and surface are the physical basis of an AFM and may also influence STM measurements. Several forces are active if a tip is close to a surface:

(i) The attractive van der Waals force originates from fluctuating dipole momenm of molecules (Israelachvili 1985). Martin et a1 (1987) determined this force as a function of tip-sample separation. They determined the derivative of the force by measuring the shift in resonance frequency of the AFM lever. Integration yields the force. '@pica1 values were 1 N m-l and N. Meyer and Amer (1988) determined the force directly by measuring the DC bending of the lever while approaching.

Both methods can be applied at distances where the interaction does not pull the lever against the sample. 'lb pull the tip out of the attractive well, a force must be applied to ovemme the maximum attractive van der Waals force. This force can be determined by measuring the distance over which the tip has to be pulled back until it is released from the sample. Both authors find values of this "m


a1 (1987) obtained pod resu!ts wing a lever and fn1ce-sensing tip consisting of one

interfemmetlv ir lerr renritive tn thennil drift snd r n w f m e irremilaritiea 11s the heam -..-.. .-"" .- ...-._. I. -.-. ".._ - -..- ---...

Scanning tunnelling microscop 1209

force in the range of lo-’ N. Martin et a1 (1987) mapped thh maximum force with sub-micrometre resolution over a Si wafer wbich was partly wvered by a photoresist.

(U) Due to the Coulomb interadon of the electron clouds, a repulsive force will exist between tip and sample if the tip is pushed against the sample. The magnitude of this force is govemed by the elasticity of the tip and the sample. The compliance of a mntact of a few atoms diameter will be about 10 Nm-’ (Pethica and Oliver 1987, see also ’bminek et a1 1989).

(iii) If a voltage is applied between tip and sample, the capacitively stored charges on them will cause an electrostatic force. Erlandson et a1 (1988) applied voltages up to 17 V to the tip of an AFM and used the resulting force to image structures of photoresist. Their results demonstrate very clearly an increased resolution if the tip is closer to the sample. Martin et ul (1988a) determined the electrical interaction hetween tip and sample by appIying a high-frequency voltage on the tip of an AFM and measuring the induced motion of the tip. They measured forces in the range of 10-9-10-8 N, varying with the separation between tip and sample in accordance with a model of the electric force in a parallel plate capacitor. The minimum capacitance they detected was lo-’* E Note that this is only that part of the capacitance which varies with dstance.

This method can be used to measure the distribution of dielectrics on the surface as the presence oi a aieiecuic iniiuences the capacitance. Another appiicarion is mapping the voltage distribution in a PN junction as the force also depends on the applied voltage (see section 5.4).

Stern et a1 (1988) deposited an excess charge on insulating PMMA and mica surfaces by applying a voltage pulse of 100 V to their m tip. They were able to image the charge on the surface by measuring a wntour of constant force gradient which was dominated by the electrostatic force. They followed the decay of the localized charge which took place at a time seale of approximately 1 h. qpical fo rm involved are

(N) A magnetic force will act between tip and sample if they have a magnetic moment, The momens can have ditferent origins a permanent magnet, a coil wound around the tip or the sample or a para- or diamagnetic moment in the tip induced by the sample (or the opposite: a moment in the sample induced by the tip).

Modei caicuiatlons €or fhs force are performed by Saenz et al (1987), Wadas (1989) and Hamnann (1989). Wadas considers a magnetic tip which scans a surface consisting of parallel stripe-lie domains that are magnetized in alternating directions. He finds typical forces in the range of N, which oscillate while scanning due to the domain structure. The amplitude and shape of the oscillation depends on the distance hetween tip and sample (typical 100 nm), the picture is smoothed if the tip is moved away from the surface. Hartmann shows that if some experimental criteria are met, the tip can he approximated by a simple dipole.

Martin et a1 (1987, 1988b) have used a magnetic tip in a AFM to obtain images of a recarding head and of magnetic domains written by a small laser spot on a magnetic disk. They used an iron lever which was magnetized by a brief exposure to a permanent magnet or by a current passing through a coil wound around the tip. A resolution of 100 nm was clearly demonstrated at distances of some tens of a nanometre. Griitter et a1 (1988) obtained a resolution of 10 nm using a Ni tip to image Bloch walls in an Fe-Nd-B alloy. Mamin et a1 (1988) and Abraham et ul (1988b) showed the depndence of the magnetic force on the direction of the magnetic moment of the tip. They both used a lever consisting of a magnetic wire

N, typical charges ar, 1200 electrons.

_ _

1210

with a 4S0 bend near the end to define a force-sensing tip. AUenspach et a1 (1987) demonstrated the influence of magnetic forces on an s m

the use of a magnetic CoCr tip yielded corrugations which are much larger than in the case were a non-magnetic tungsten tip was used.

(v) An AFM can be used to mwure the friction between a tip sliding along a surface if the deflection of the forwensing lever is measured in the direction in which the tip moves. This can be a very valuable application for studying friction, wear and lubrication processes (tribology).

Mate et a1 (1987) observed atomic scale features on graphite when a tip was pressed against it with a load of ahout N. mid friction forces they measured were N. They showed that a periodic elastic force acted on the tip, together with an inelastic force. This inelastic force did not change the surface structure, so

studied a magnetic disk on a scale of 3 Hm. (vi) A theory describing the tip and sample as continuous materials breaks down

if the size of the relevant parts of the tip and sample gets in the range of a few atoms, specially if the variation of the forees while scanning along the surface is considered. Methods must he used which explicitly take into aomunt the atomic structure. Such methods are rather complex so a very simple tip consisting of one or a few atom is mostly used to keep the calculations manageable.

One possibility is summing a suitable two-atom interaction over a lattice of atoms. Abraham et a1 (1988a) calculate the force between a tip consisting of one, two or four atoms and a Si(aO1) dimerized surface by summing a Stilliger-Weber interatomic potential, allowing for relaxation of the atom positions in the surface layer. A very pronounced dependence of the image on the tip shape and orientation is predicted.

caicuiare the farce beiweeii tip siiii raiiiijie i&ig a S& consistent field calculation allowing for a relaxation of the electronic charge. Atomic relaxation at a self-consistent field level had not been included up till now. Landman et a1 (1989) investigate the dynamics of forces in STM and AFM via molecular dynamics. They calculated not only the normal but also the lateral components of the force. The latter shows the characteristic atomic slip-stick behaviow which has also been measured (Mate et a1 1987, previous section).

6.2. Scanning thermal proper

In this device, a tungsten tip has been mated with Ni so that a thermocouple is formed. This tip is heated and its distance to the underlying surface is modulated. A feedback system adjusts the tip height in such a way that a constant heat leak is E&?:&&. %.e tip $0 t ! ~ sq!e .in the ai! depends largely on the properties of the air and is not expected to vary from spot to spot on the surface. So the tip-sample spacing is more or less constant during the lateral Sean (Wdtiams and Wickramasinghe 1986). However, another heat conduction mechanism may also act: interacting electric fields outside the surface due to thermally excited charge fluctuations in the solids (Dransfeld and Xu 1988).

6.3. Scanning noise microscon A tunnel junction produces noise, This noise consists of 1/ f noise, which is related to the current, and Johnson noise, which depends on the tunnel resistance via the Nyquist formula. If no current is flowkg only Johnson noise is present M6ller et a1


:. "-..,,I _^. L.. A..- . "- L..,"".:" AaC - .: " ,.c .La "-..ln ~- A.. v""nl.,. ,,OPP, 1, WWU llVI UT YYT L Y 011 YITILUUC Y I L V l l l l D L L V S l "I U S I Y ~ l r y r r Wa Up - r D W (AZYY,

Sarra and C h c i

sf kea: f:~%

Scanning tunnelling microscofl 1211

(1989) used this noise as input for a feedhack system. Their images made in thjs way are very similar to images obtained from the same area via normal STM, proving the effectiveness of this method.

64. Non-linear alternating current tunnelIing microscopy

Generally speaking it is impossible to use an STM on an insulator. This is not because electrom cannot tunnel to an insulator but because tunnelled electrons buiid up a surface charge which prevents extra electrons from tunnelling. An AC voltage causes the electrons to travel back and forth bemeen tip and sample, so a net current results. Unfortunately, this current will drown in charging currents of cables and stray capacitauces. If the tunnel junction has a non-linear I( V) characteristic, a way out of this dilemma is using a higher harmonic to detect the tunnel current.

The non-linear alternating current tunnelling microscope uses the thircl harmonic to detect the tnnnel current. (The second harmonic is not useful as it will be zero if the I (V) curve is symmetric.)

' Kochanski (1989) measured features of nanometre size at the surface of copper oxide and WSe, with this device.

65. Scanning ion conductance microscope

In this micrompe, the tip is replaced by a small micropipette with an opening of O.W.1 ~ m . The feedback adjusts its heiglxt to obtain a constant ionic conductance over a surface in a conducting liquid. Examples of materials which have been studied with this microscope are commercial filters and plant leaves (Hansma et af 1989, Marti et a1 198%).

66 Detection of secondaiy pamkles Most surface science techniques work via the Pmo principle: particle-in particle-out. As an STM injects electrons, PIPO techniques which use electrons as particle-in can, in principle, be performed with an sm as electron gun. An STM tip starts Eeld emitting in a narrow beam if only a few volts are applied (Fink 1%, McCord and Pease 1985). The tip can be very close to the sample, in this way enabling a good resolution.

Different particles-out can be examined. Fink (1988) used a channeltron to detect SecotIdaty low-energy eleetrom. Allenspach and Bischof (1989) even measured spin polarized secondary electrons originating from a Fe-based metallic glass.

If a voltage of a few kilovolts is applied to the tip and an electron energy analyser is installed, a field emission scaraing Auger microscope results. Such a device can also he used for electron energy loss spectracopy (kihl and Gimzewski 1987). If a photon detector is used inverse photoemission (IPE) becomes possible. with a Spatial IesOlutiOn in the sub-nanomeue range (Coombs et a1 1988, Reihl et a1 1989). Gimzewsld et a1 (1989) measured the radiative decay of a surface plasmon aaived by tunnelling electrons in this way.

6 Z Ballistic electron emhion micmopy

Sample consists of some substrate (the colleetor) with a thin layer on top of it (the base). If the collector is a semiconductor and the base a metal, a Schottky bamer is formed Electrons tunnel from the tip into the base in which they travel ballistically

$e *a st4fiy g4*aczfae &&*m z;(+ se; ;9=,. yue

1212

towards the collector. They will enter the collector with some probability if their energy is large enough to overcome the barrier, otherwise they will be reflected. The current flowing from the base to the collector depends on the energy with which the electrons are injected (the tunnel bias). A plot of the collector current against tunnel bias shows a zeroeurrent region up to a certain threshold voltage which equals the harrier height. Above the threshold, the current starts to increase. This collector current against tunnel bias plot contains information on the barrier and on the electronic structure of the collector (Bell and Kaiser 1988).

L E C van de Leempur and H van Kempen

7. Surface science with STM

% I . Graphire

The most studied (and most debated) material with the sTM is beyond any doubt graphite. Graphite is special because of its layered structure. Other layered materials which behave similarly in some aspects are: NbSe, (Dah er a1 1988), MoS, (Weimer er a1 1988, Stupian and h u n g 1987, Henson er a1 1988, Albrecht and Quate 1983, and GaSe (Humbert er a1 1987).

ture. They are stacked in such a way that half of the atoms are located exactly above an atom in the layer below it (A sites) and the other half sits above the centre holes in the hexagons of the layer below it (B sites). It is easy to obtain atomic resolution on a cleaved (MX)l) surface. This has been achieved with an STM in UHV (Binnig er a1 1986b), in air (Park and Quate 1986), under water (Schneir er a1 19%), under liquid helium (at 4.2 K, Smith and Binnig 19%). and with an AFM in air (Bmig er a1 1987) and under oil (Marti e? a1 1987).

gqF& E&&*3 =f .+,F&& a kGceim&& wric-

Although the atomic structure can be seen easily, three peculiarities occur: (i) A triangular lattice usually shows up, apparently only half of the atoms are

(E) Corrugation heights have been reported up to 20 A! This has to be compared

(i) All types of anomalous patterns with non-triangular symmetry can arise. The first question which was raised is which atom is imaged, type A or B. F"

charge density calculations, the following chemical picture is revealed type A atoms, which have neighbours directly below, form a weak chemical bond with those neighbours. This leads to slight charge transport to the region under the atoms, resulting in a depletion of charge above the A atoms. Since B atoms cannot form such a bond, the charge density is higher above the B atoms. So the B atoms are expected to correspond with the highest features on the surface. The A atoms must he associated with the saddle points between two B atoms and the holes surrounded by three A and three B atoms are the centres of the hexagons.

The same phenomenon can be described in a physical way: The wavefunctions of the electrons at A atoms from adjacent layers couple and form a hand with a width of about 1 eV around the Fermi energy. Those on B atoms do not couple, leading to a very narrow band at the Fermi energy. At low voltages, the STM p'obes the density of states at the Fermi level. This means that the entire band at B is imaged, While only part of the band contributes at A sites (Batra and Ciraa 19% lbmanek el al 1987, l b d n e k and Louie 1988, Selfoni et a1 1985, Bmnig e? a1 1986b, 'IhSOff 1986).

imaged.

with the interlayer spacing of 3.35 8,

Scanning tunnelling micrmcofl 1213

(Measuremenm of the electronic density of states have also been done: ReM et a1 (1986), Fwhs and lbsatti (1987). Selloni el a1 (1988) and Bando et a1 (1988).)

The second question to he answered was that of the giant COrmgations. ErsOff (1986) showed that the electronic structure of graphite can account for apparent corrugations up to 2 k Although this is large compared With the interlayer spacing, it is still too small to account for the measurements.

When the m is operated in a constant current mode, the tip tries to approach

explanation for the large corrugations is the following. If the surface layer is easily defamable, the tip can push it quite far; the tip displacement is much bigger than the actual change in tipsample distance (Soler et al 1986). The forces involved are large (lo-' N, Mate et a1 (1989), Xing et a1 (1987)) and therefore it is very unlikely that this force is exerted hy a single atom (Pethica 1986). Instead, a contamination layer on the tip or surface mediates the force whie a small tunnelling tip pierces through it. Alternatively one can assume that a layer of graphite is dragged along while scanning. Strong indications are that a clean tip on a clean sample in UHV does not result in a giant corrugation (Mamin et a1 1986) and that the corrugation increases with the time during which the sample is exposed to air after cleaving (Morita et a1 1988, Cricenti et a1 19%). Another indication is that Smith et a1 (1986) imaged the lattice without using the feedback mechanism, thus with a tip virtually touching the surface.

the appearance of a double tunnelling tip certainly not impossible. M h s et a1 (1987) showed that adding the contributions of multiple tips can account for any measured pattern, with or without siK- or threefold symmetry (figure 17). In the neighbourhood of defects and grain boundaries, multiple tips can lead to very peculiar pattem (Albreeht et a1 1988a). The observation of single defects shows that at least sometimes a single tip is acting (Salemink et a1 1987).

Tiedje er al (1988) showed that a contamination of the tip with soft, carbonaceous Eakes is highly likely while measuring on graphite. Such flakes may cause several kinds of artefacts. Stoll (1988) remarb that carhon-contaminated tips are better suited to obtain good resolution due the better matching of the electron wavevector in tip and sample.

ZZ SiliconClll) 7 x 7 Semiconductors are very fruitful research objeets for STM. There are many different Surface reconstructions which can be clearly visualized. The most famous example is the complicated Si(ll1) 7 x 7 recnnskuction. Due to its very large unit cell, it is diflidt, if not impossible, to obtain the correct structure from le-space experiments. The fust real-space STM observations immediately ruled out a class of proposed models (Binnig et a1 1983h, 1985~). Measurement of steps showed that the 7 x 7 unit cell extends right up to the step edge and that the pattern is continued on the other side of the step. Steps align with the unit cell edges and terraces have a width of an integer number of unit cells pecker et a1 1985~). Spectroscopic STM measurements could spatially resolve the different surfaoe states (figure 15, Hamers et a1 1986, 1987). lb check different proposed models for the 7 x 7 reconstruction, ?tOmp et a1 (1986b) calculated STM images for each model, assuming a spherical

image shows that the dimer-adatom-stackhg-fault model (Xikayanagi et a1 1985) is the most probable, in agreement with results from sevexal other techniques (figure 6).

+hn -..A".- ",ha- ir ir ,,krnrn ., rpn:,.n -f In.., Aanm:k, nf stntnc The nenamlh, w. -en+eA U" 1 . u n a w "".," 1. Y -""I" - ."e"" ". ."" ""YY., "L "._.W. ...- &-.L-.'Y., "-y."..

n, BFAenrp Of 2 r""'"F&q2"-" !Eyer prsn& bep"reeE fip n,,i s2Fsp!" p&=

C ? X ~ C &w;% ~ a t i e d Z G Z C ~ aimi. &iiipa&oi, of these resuim With a measured


Figom 17. Anomalous images of graphite ( M k et a1 1987). Xhe erpuimental images are dkplayed m the left-hand column. They have been filtered and tilted in order to compensate for t h m a l drift. The computer-generated images componding to the aperimental data are displayed in the right-hand column. They are a hear combination of three sine waves. Xhe amplitudes and phaJcE of the sine waves have k e n adjusted 10 match the data. A multiple tip D probably respnsrble for the modification of lhe Fourier ~e8i"rcieots.

The simple calculation neglects all types of electronic structure and is based only on .uw p,",U*L,.b ~....Lgwn.""L U& "1- a,u,,m. I,,= ,,IG.wU,GU * lm u,,asG a b pur.nrr ra,,,pw

bias represents this geometric structure. However, at negative bias an asymmetry is measured between the faulted and unfaulted halves of the unit cell. This asymmetry must be of electronic origin.

,La "--...a..:" "--n-. n...~-.+ ..c.xa ...,...." 'PL" ...an"..-arl 1-1 ,.* .. :.*..," -..ln


1.3. Metals The electron states in metals differ from those in semiconductcors in that they are much more delocalized. Due to this reason, it has been thought for a long time that it is not possible to obtain atomic resolution on close packed metal surfaces (e.g. Au(ll1)). Other, bigger, structures could be imaged without many problems; e.g. the Au(ll0) 3 x 1 and 2 x 1 reconstructions which are due to missing rows of atom

(Binnig et a1 l983a). Another example is a hexagonal reconstruction of the top layer of Pt(100). This results in a corrugation with a periodicity of 14 A and a height of 0.4 A STM showed that boundaries between regions with a different orientation of the reconstructions always coincided with a step. In this way the energy associated with these boundaries is "ized (Behm et a1 1986).

Contrary to expectations, it turned out to be possible to obtain atomic resolution on Au(11l) (Hallmark et nl (1987) in LIHV and in air) and Al(111) (wffltterliffl et al (1988) in mnr) if a spec& tip preparation method is used. The measured corrugation is much bigger than expected depending on the tunnelling resistance, it can be close to 1 & It seems likely that the special tip preparation methods result in a small cluster of metal on the tip which deforms easily due to an interaction with the surface. Such an interaction can be expected M show the Same periodicity as the lattice. This model is in agreement with the fact that a tip which shows atomic corrugations is not very stable.

Z4. Non-regular structures Periodic and regular structures can be studied with many surface-sensitive techniques. STM is the lint technique to study individual small features such as defects and mono-atomic steps.

In the case of steps, information can be obtaked on the height of the step, its direction and the atomic structure of the terrace adjacent to the step. Jacklevic and Elie (1988) studied the time evolution of a crater in a Au(ll1) surface. The crater was made by (gently) touching the surface with the tip and its edges mnsisted of steps a few atoms high. Their measurements showed the gradual filling of the crater by surface diffusion of gold atoms to the step edges.

Atomic scale geometry of the surface is also the key ingredient in understanding crystal growth. Apart from monoatomic steps, STM has revealed macro steps, microscopically small facets (van de Leemput et al 1989), screw dislocations (figure 26) which are the origins of growth spirals, and many other defects. An example is given in figure 20, which shows several atomically resolved defects on a PbS(001) surface.

Z5. Adsorbate covered surfaces

Physical or chemical interactions can lead to the adsorption of gas molecules on clean SUrfaW. The surface can also act as a catalyst, speeding up chemical reactions by IOWeMg their activation energy. Only a small coverage of some adsorbate can be sufficient to change the reconstruction on the surface. S i a r processes can take place if a solid is deposited on the surface.

This 'ype of process is not only very interesting scientilically but also technolog- ically ai@@ important (catalysis, heteroepitaxy etc). The STM has unprecedented power in this field as it can determine not only the e m adsorption sites, but also the change in local electronic structure due to adsorption

and w ~ c h h e io WmgaiiQm with a height Of i.4 A (i X $j Of c.45 {i X a j


A lot of systems have been studied, not only with STM, but also with other techniques. usually, several techniques have to be combined in order to get a clear, unambiguous description of the structures and processes present.

An interesting example of the initial stages of hetero-epitaxy is the growth of silver on a s i l in ( l l1 ) 7 x 7 structure. At low temperatures the 7 x 7 remains intact and Ag islands grow preferentially on the faulted halves of the unit ceUs (section 7.2). At a substrate temperature of 90% small ring-like Structures grow, presumably because the Ag atoms are bonded to the inner adatoms and the dangling bonds of the second atomic layer. At l3O0C, the rings grow into triangles, covering the whole faulted half of the unit cell. If the coverage is increased, the unfaulted half of the unit cell also becomes covered (Tbsch and Neddermeyer 1988a,h).

The behaviour at higher temperatures is very different If the substrate is above 200°C. a 6 x 6R30° reconshuction emerges. This reconstruction can take up a certain amount of silver, excess silver coalesces into islands. STM measurements show a honeycomb structure. 'Itvo different models were proposed to explain the STM results: (i) a simple honeycomb (H) model, based on an array of Ag atoms embedded in threefold hollow sites of the Si surface (Wilson and Chang 1987a); and (U) a honeycomb top layer of Si atoms on top of an (embedded) layer of Ag trimers (RT) (van Loenen et a1 1987). A third possible model is a honeycomb arrangement of Ag at!" which are embedded in a missing top layer (MTL) structure where only half of the Si(l1l) double layer is present (W&on and Chang 198%).

The problem in sIu is that it is not easy to distinguish an Ag from a Si atom. Spectroscopy can be of help but can be a dangerous guide. The clue to this problem turned out to be the positions of the hexagom with respect to the underlying lattice. This is different for the first and thb last two propwed models. Figure 18(a) shows the different registrations together with the known registration of the 7 x 7 reconstruction. n:.. ..-- ton.\ :" ~ .... ~- _^^ _A:-,. "L L .L .,... II .. 7 ..-_I .L., 6 .. F'gYLT mi", w LI I"ca.DuLG'**GIII "I an, LI,c(t W,,,C,, 311uw3 " U U L LLLG I x I 011u L U G "a a &R30° recoustruction adjacent to each other. The registration of the underlying lattice can be deduced from the 7 x 7 and extrapolated to the & x d k 3 0 ' area. This unambiguously rules out the ET model (Wilson and Chang 1987b).

A nice example of adsorbate induced reconstruction is the Ni(ll0)-H system (Kuk er al 1987). A cleaa Ni(ll0)l x 1 surface exposed to H, shows a reconstruction which was known from LEED experiments as a 'streaky' 1 x 2. STM showed that this is in fact a 5 x 2 reconstruction of the Ni atoms (figure 19). The streaks in the LEED pattern are the result of the short domain size in the (001) direction.

An example of a gas reacting with a surface is NH, on Si(ll1) 7 x 7 (Avouris and Wolkow 1989, Wolkow and Avouris 1988). The Si(ll1) 7 x 7 system is very inteI€Sting as it contains several inequivalent Si atoms (figure 21). NH3 adsorbs dissociatively, resulting in NH, and H bonded to Si atoms.

it turns out that the so-caiieci rest-atom sites react first. Tnb can be attributed to a dangling bond -0.8 eV below the Fermi energy located at those restatomS. From spectroscopic STM measurements, it can be seen that the reaction removes the dangling bond.

Ikn different types of adatoms can be distinguished corner adatom (the ones adjacent to a corner hole) and centre adatoms. After the rest atoms have reacted, the centreadatoms react first. The two differ spectroscopically on a clean surface, but become equivalent at a surface at which the rest atoms have reacted. So their initial state is equally favourable for the reaction. Avouris and Wolkow (1989) propose that the difference must he attributed to strain in the underlying layers in the final State.


Fgum IS. A ~ E I ( I ~ I ) ( & X f i )R300 s t ~ c t u n : (a) adatam pasitions for the Si(ll1) 7 x 7 DAT 8 ( ~ c t n m (top) and three models for the Ag&(lll) surface @ottom); (b) SIM image, with anIrast enbmmenr, d a Sr(l11) 7 x 7 to ApSi(ll1) (& x &))a3Oo domain baundary, recorded at a tip bias of VT = -2.0 V and I = 2.0 nA. lbp nRu with dark %(Ill) mesh superimposed to show re@tration. White repmenu elevated feat- and mall squares on the mesh mark adatom sites of the DAS model (Wilson and Chiang 198%).

19. H y d q m adsorption on Ni(1lO) (Kuk n a1 1987). (a) Schullntic representation of surface atwture of Ni(llO)-H(5 x 2). where open circles represent the fils1 layer of Ni atoms, hatched cmiC8 the -na iqer, and doiied cireieS hie ;+did is)*-. (b) 120 X 90 A topograph of Ni(llO~H(5 x 2). A unit cell of the reMnslmclion is s h m . Antiphase boundaries are indicated by a-

The products of the reaction a n be imaged at -3 V sample bias (occupied states). It turns Out that two sizes of adsorbed species can be distinguished; tentatively these a?" be irlentserl with s;m2 ana si-H group.

1218 L E C van de Leemput and H van ampen

Figure 20. (a) Atomically resolved image of defecls on Ihc PbS(001) surface (Zheug a al 1988) Bright spas indicate Pb2+ and Sz- ions at the surface. VIP bias is -0.5 Y I = 0.8 nA.) (6) and (e) show WO different models of the SIM mage shomng edge disletions at p i t i ons A, B and C. n e Burgers V ~ C ~ O K are also S b m : open mle. Pba+ ions; dots, S’- ions; dotted circles, interstitial atom

There also exist systems in which the adsorbed layer stabilizes the surface so that STM measurements can be obtained in air. Examples are the observations of a p(2 x 1) overlayer of sulphur on molybdenum(OO1) (Marchon et 01 1988a,b) and several different structure8 of iodine on platinum (Schardt et a1 1989).

8. Solid state physics

8.1. Charge density waves A charge density wave (CDW) is the ground state of a metal in which the conduction electron charge density is sinusoidally modulated in space (Overhauser 1988). Such a state may occnr below a certain transition temperature. The wavevectors are in- commensurate (ie. are not a rational combination of lattice. vectors) but can become

An STM sees the CDW as a height modulation (Coleman et a1 1985). Depenahg on the material, it is possible to see the atomic structure, the cDW or both feetures, superimposed on each other (Coleman et a1 1988, Thomson et a1 1988).

An elaborated review on the use of STM to study CDW has been written by Coleman et al (1988).

c”mmersL%te a !!%er tmpe..t...S .

Scanning runnelring micmscopy 1219

I \ I I

-2.0 -1.0 0 1.0 2.0 -2.0-1.0 0 1.0 2.0

ENERGY CeV) ENERGY (eV)

Fjgurc 21. NH3 on Si(ll1) 7 x 7 (Avouris and Wokow 1989). (a) l b p p p h Qf the unoccupied s t a t s of the clean Si(ll1) 7 x 7 surface (top) and atom-resalved tunnelliog spectra @elow). Curve A giMI the specmm over a rest-atom site, C U N ~ B over a corner- adatom site, and c u m Cover a centwadatom site Neptm energies indicate mxupied states, while po6itive energies indicate empty states. (b) Topagraph of the unmxupied states (top) and atom-mIved tunnelling spectra (below) of an NHa ex@ surface. Clwe A gives the spaum onr a ma& rest-atom site, cum B (braken N N e ) mer a reocred mmer adatom, whde w e s B (full e w e ) and C @e the specIra over unreucwd corner and centre adatam, repcsiveiy.

8.2 SuDerconductors

Spectroscopic tunnelling in planar junctions has been used for many years to study superconductors (Giaever 1974). It can be used to obtain the quasiparticle density of states, the energy gap in that spectrum and the phonon spectrum (McMillan and Rowell 1969). Another famous example is the Josephn effect (Josephson 1969) which is the basis of today’s voltage standards.

The STM opens up new possibilities in superconductor tunnelling. First of all, a vacuum tunnel junction can be easier to make than a sandwicb junction. A vacuum junction consisting of a piezo-driven tip above a surface was already used before the STM was invented by Poppe (1981,1985). Based on the STM idea, but far more rigid, are squeezable tunnelling junctions. %IO flexible substrates are separated by spacers and a squeezing force adjusts the gap between the electrodes (Hansma 1986).

1220 I. E C van de Leemput and H van Kempen

- - E 2 25 5~~~ A = 2.8mV

1 - 2 5

-50 . 0 10

VOLTAGE (m) -10

Figure 22. An I( V) c u m obtamed d l h an EIM using an iridium tsp on a NhSn sample (de lDzanne el a1 1985). The T, of NbsSn is 18.3 K. Ihe gap ia lhe supermnduclor density of stales shows up cleariy as a currentless region around the mgm Note lhe voltage scale, which is much smaller than in 'nomaI. elastic spectroseapy.

' hne l l i g spectroscopy of classical superconductors with an STM (figure 22) has been performed satisfactorily in constant average current mode (Elrod et a1 1984, 1986. de Lozanne et a1 1985, Le Due et 01 1987) and in a fvred or variable separation mode (Fein et a1 1987). Le Duc et al (1989) showed that an STM can be sufficiently stable to obtain a phonon spectrum (which is contained in the second derivative of the current to voltage).

Another possibility is to press the tip against the sample and to use the natural oxide layer between tip and sample as a spacer. This method has been particularly successful with the high T, superconductors (Johnson et a1 1989, Kirk et a1 1987, Gallagher and Adler 1988, Naito et a1 1987, de Lozanne et a1 1988, Kirtley et a1

a1 1989). However, the reported results of such measuremen6 of the superconducting gap have much more scatter than can be explained by different sample qualities. An intrinsic problem of this method can be the applied pressure (figure 23) or the fact that it is not clear whether tunnelling occurs from the tip to a grain in the sample or in between some grains, a difference which gives rise to a gap twice as large. The I( V) curves may also be influenced by a Coulomb blockade caused by the very small capacitance of the tip or an underlying small particle (van Bentum ef al 19%). Other mechanisms which may cause spurious results are: leakage currents, local heating, lifetime effects of quasiparticles, proximity effects, gap anisotropy etc (Barone 1988). As good tunnelling results might be a clue to the underlying mechanism of superconductivity, there is a need for criteria for the junction quality, analogous to those existing for planar junctions (McMillan and Rowell 1969). A possible set of criteria is given by van de Leemput et al (1988). In particular, the value of the gap or other fit parameters which do not depend on geometry should not change if the tip sample separation is changed.

Another, very promising application of sm to superconductors uses the fact that it can spatially resolve the energy gap, a quantity which can be identified with the order parameter in the superconductor (d'hbrumenil and White 1984). A lot Of interesting physics is connected with the local variation of the gaps; examples are pro xi mi^^ effect, flux vortices, the pinning centres and the motion of those vortices.

The aim is to obtain a surface map of the gap value. Several tricks can be used to obtain a scalar quantity which has some relation to the energy gap. Volodin and

1987a; Moog et U! 1988.; vieim er or 19Bi Vobdi!! and ma&!! 19%; van Bentnm er

Scanning w e l l i n g micrascopy 1221

I PlEZO VOLTAGE /

Fiym U. I ( V ) "8 of an SIM junction made by pushing a tungsten tlp on an

applied forces. The variation of the gap with applied pressure cm be seen clearly. The insel shows the energy gap 2A as a function of wltage m r the p i m , which is pmpnional to the &me, lbe hear increase corresponds U) the measured pWUre dependence of T.. me satmalion at higher voltages can be explained by inelastic deformation of the tip as the yield presr~re of W is reached. me p m u r e underneath the tip is estimated to rdnge m m 10 to 100 war.

Khaikin (1988) measure the distance hetween the two maxima in aI/aV. I(irt1ey e1 a1 (198%) perform a numerical fit to evety I (V) m e , one measured at each pixel. De Lozanne eraI(1985) use an oscillating voltage (constant average current spe"Wpy) and plot the zero bias value of a I / & (K aI/aV) divided by the average resistance. This quantity is expected to be zero if the tip faces a superconducting patch of the sample, and one if the tip faces a normal patch. Dittrich and Heiden (1987) use the same spectroscopic technique but plot the average rectified tunnel current during one sweep. In the case of a large gap this average is smaller than in the case of a small gap. The same authors (1988) claim to have detected motion of vortices in a Nh foil by a specific kind of noise in their I (V) characteristics. Hess el aI (1989) have beautifully imaged a triangular lattice of vonices in NbSe,. 'They measured and plotted aI/aV at the gap edge while scanning in a constant current mode (figure 24).

8.3. Conducfion in inhomogeneous materials For problems coneeming the electrical conductivity in inhomogeneous media, it is important to know the potential distribution with high resolution. An sm operated in a potentiometric mode can obtain this information.

The first application was on a gold island metal-insulator-metal structure. Possible conduction paths hetween two metal electrodes are assumed to exist of gold islands coupled by carbonaceous filaments. Measurements showed sharp voltage drops along sharply defined boundaries (Muralt and Pohl 1986, Brauer ef al 1989).

Several semiconductor interfaces have also been studied: the voltage drop across a GaAs pn junction (Muralt 1987), an AIGaAs-GaAs laser diode (Muralt et aI 1986a)

'I; :& ;;n!n& E q ! c $?E BEl'nE d .! E???). ElRerSE! C!!Ees !q!*SeE! dl!?ere!!t


F*re 24. A grey =le plot of aI/aV at the gap edge (13 mv) of NbSez dt 1.8 K. The triangular flux lattice can be seen clearly . The Sean region is about 6000 A. The grey scale corresponds to arlav ranging from approximately 10-8 fl-' (black) to 1.5 x fl-' (white) (Hw n 4l 1989).

and a Si pn junction (Martin er a1 1988). KordiE et a1 (1990) investigated the influence of forward or reverse hias on the tunnel current from the tip to a Si pn junction.

By comparing I ( V ) characteristics measured at different sides of an AIGaAs- GaAs heterostructure, Salemink et al (1989) succeeded in measuring the step occurring in the conduction hand minimum at the interface. Hosaka et a1 (1988) used CITs (section 5.2.4) to investigate a Si pn junction structure. By mapping the current at a seiected voitage, they could easiiy determine tne p and n type regions.

8.4. Phonon delecrion The detection of phonons via the I( V) characteristic of a superconducting tunnel junction has already been described in the previous section. Smith et a1 (1986) found evidence of phonon peaks in the second derivative of the tunnel current of a normal tunnel junction. The proposed mechanism is phonOR-assisted tunnelling.

Heil er a1 (1988) demonmated the influence of a sound wave on an STM image. An sm is much to slow to detect the motion of the atoms due to the applied ultrasonic wave (1 MHz to 1 GHz). However, the motion of the a tom leads to a characteristic smearing.

8.5. Spin polarked tunnelling

The possibility of using spin polarized electrons opens up new possihilities for studying magnetism on an atomic scale. PoSible applications on superconductors and

Scanning tunneUing microscopy 1223

ferroinagnea are discussed by MeSeNey (1988) and Pierce (1988). An interesting model material is GaAs in which spin polarized electrowhole pairs cifn be created by illumination by circularly polarized light.

9. Exotic applications in physics

9.1. LX.pIacemen1 sensors

As we have seen, an sm is an extremely sensitive device with which to detect variations in the tunnel gap width. The advantages of an sm compared with other displacement sensors are twofold. First, it has a very high sensitivity. Second, it has a reduced back action: with conventional transducers (piemelements, capacitances or inductances) the measured distance is inlluenced by the input noise of the measuring amplifier which is coupled to the dstance via the reciprocity of the sensors In contrast, the STM gap will not change due to the noise on the input of the amplifier (Bock0 et a1 1988). Of come, the sm must have some back action, otherwise it would violate the uncertainty principle. The back action of an sm consists of the impuke of the tunnelling electrons (shot noise!) and the force due the opposite charge on tip and sample. Maybe the latter can be eliminated by using the noise instead of the current to measure the distance (section 6.3).

The proposed working applications of an sm as a distance-measuring device are as an accelerometer (Baski et a1 1988), a magnetometer (Wandas et al 1989) and a gravitational wave sensor (Niich and Binnig 1988).

9.2. Detectors and mirers

As an STM is non-linear, it can be used as detector or as a mixer. Arnold et al(l987) measured beats up to 90 MHz on an STM tip which was illuminated with WO CO2 lasers.

Detection of laser fight with an Sm has been described in section 2.8. A theoretical study bas been performed by Schwartz (1987).

9.3. Quantum point contacts

If a wire becomes very thin (the diameter multiplied by the Fermi wavevector approaches one), it starts acting as a waveguide: only electrons which have a sufficiently low /cL vector can pass through it. The conductance of such a wire is expected to be simply ez jh multiplied by the number of channels which can pass through the wire. Increasing the wire diameter will result in discrete steps in the resistance (e.g. Escapa and Garcia (1990) and references therein).

An STM tip which approaches and tauches the surface coustitutes a contact a few a tom across, just the right size to observe the phenomenon described above. Jumps in the range of 1-20 kfl have been observed by Gimzewski and Moller (1987, also Gimzewslri et a1 1987) and inspired several theories on one-atom contacts (Lang 1987b, Ferrer et a1 1988).

1224

9.4. Electron spin resonance

Manassen et uI(1989) studied a oxidized Si(ll1) surface in a magnetic field of about 0.018 ‘I: This corresponds to a precession frequency of 500 MHz They could indeed detect an RF signal of this frequency in the tunnel current. The signal varied with applied field in the expected way and was localiid to distances of less than 10 k,

Although the mechanism by which the precessing spins interact with the tun- isei cwfeiii k iiui yei uiiiieijiuod, ihe observarion of an individuai spin shows the tremendous possibilities of the technique. (For comparison: standard electron spin resonance requires at least 10’O spins.)


10. Biology and organic chemistry

10.1. Introduction

STM (and AFM) is a very promising technique in this field. Although this has been clear from the beginning of the s m era, progress is slow and many problems remain to be solved (Hansma et ul 1988). Nevertheless, several beautiful results have been obtained the imaging of reeA DNA, DNA, several membranes, amino acids and even thp re+r;mp iv.zg-%g nf the b!~& &:$iq...g p r g ~ g g $ p r p E).

F@m 25. ‘&I awmic force m i m e o p e images that show the clotting of human b l d protein 6 b h g e u in real time (Drake et al 1989) T%e images were sekct.sJ f” before hVoduction of lhe clotting enzyme thrombin (A), and a1 vanow times after its inuaduction: 9 mi” (9’), 10 mia 20 s (10’20”), 10‘30”, 11‘20‘’, 12’10‘’. 12’40“, 14’50”, 17’10’’. 33’ for (E) through (0. Each image area is 0.45 Irm by 0.45 ulm.

Except for bulk samples, som$ preparation method is needed before specimens can be studied with an STM (of AFM): the molecules have to be adsorbed on a suitable substrate. These preparation techniques present the most difficult problem at the moment Some concepts can be borrowed from electron microscopy, others have to be newly developed.

- As - an -_ .STM a n ___ nn? __.. meagre nn Mndguhg surfacesj both substrate and sample should be conducting. The conductivity of biological and organial samples is subject to discussion (Bar0 el ul 1985, Smith et ol 1987a, Spong el ul 1989). The fact that quite large objects can be imaged shows that the conductivily can be large enough

Scanning tunnelling microscom 1225

for STM purposes An illustrative example is the imaging of 'insulating' Langmuir- Blodgett films with a thickness of U) nm. Using an AFM avoids problems with the mnductkity of the sample.

As the molecules generally have an inhomogeneous composition, the work funo tion can wy strongly. This can blur the measured geometry, but, on the other hand,

1985, Spong et a1 1989). Another general pmblem is the rigidity of the samples. The force between tip

and sample can easm deform the sample (Persson 1987). Such deformations will be smaller if the spM/AFM operates in water, which also allows for physiologically more realistic environments (Drake 1989). The lack of rigidity can also be used to image the specimens by measuring the local deformation (Lindsay 1988).

A different way of s o k g the conductivity and rigidity problem is coating the sample with a metallic layer or making a replica of the sample.

These methods also solve a thud major problem: specimens, which are loosely bound to the substrate, can be easily dragged along by the scanning tip. Another solution to the same problem is to use a special way of scanning: the tip does not scan along the surface but is retracted each time a lateral movement is made. At each pixel, the height is measured by approaching the sample with the tip. (If the sample mm auvay, step on it ! Jericho et a1 (1990).)

Several construction tricks can be very useful: a combination of an STM with a high magnilication light microscope (Guckenberger 1988a) or a very large scan range (Blackford et a1 1987, Emch et a1 1988b).

10.2 Preparation methods ond examples

10.2.1. Sin& CI.VSIR~. A crystal of an organic material can be a good conductor. In such cases, its surface can be readily studied by sm. An example is tetrathiafulvalene tetracyanoqainodiiethane (m-ma) (Skater and pcho 1988). Gould er al (1988) used an AFM to study an amino-acid crystal (DL-Leucine).

102.2 Spechens on a substrate. The properties of a substrate must be rigid (not to be deformed by tip or specimen), flat (so that a specimen can be observed clearly), inerr, Sticking (it should immobilize the specimen), conducting, and provide a good electrical contact to the sample (the last two items do not apply for an AFM). Possible choices and their speeifc properties are:

(i) Graphite: good conductor, very flat and easily cleavable, but not very rigid, bad sample immobilization and very hydrophobic. (It can be made hydrophilic by exposing it to a glow discharge, ltavaglmi et a1 (1987).)

(U) Au(ll1): good conductor, rather inert, hydmphilic if freshly prepared but becomes hydrophobic after a while. There are several ways to obtain a Au(l11)

wz:h is first heated with a hot flame and then cooled quickly shows (111) facets (Schneir el a1 1988b, Lindsay and Barris 1988) (these facets are small but very flat); (e) an evaporated gold film on mica has a (111) structure. This method is cheap and produces large areas of Au(ll1) (Dovek et a1 1988a, Emch et a1 1989).

"- ^C *ha ""L C.."rri,." ...,.fila -n &.a ..l.=f*.l artr- infnrmntinn m.rn Dt "1 .." "- ".., ""*'. L""I.."" r.""... -.. --.". _.." ....., .... "...... \I".- -. I-

surface: (a) &!!g!e Qpte!! @hey ere IlfhP? q!es&.e); @) p SXZ!! p!g

(iii) PtC film on mica (Amrein et al(19&!9), Rec-A DNA).

1226 L E C van de Leemput und H wn Kempen

(iv) Amorphous carbon film on a finder grid roughness < 1 nm. After a good specimen has been chosen by STEM, the finder grid enables positioning of the STM to within 10 pm of the desired spot (poM membrane (Stemmer et a1 1987)).

(v) Quartz plate: only suited for AFM (purple membrane of Halobacterium halo- bium (Worcester el a1 1988)). Several techniques can be employed to deposit the

(vi) The Langmuir-Blodgett technique. Examples: arachidic acid and Cd-arachide on graphite (Smith er a1 1987, Fuchs 1987, Lang er a1 1988, Eng et a1 1988) and several other materials (&be et a1 1988, Marti er a1 198&,b,c, Dovek et al 198&, Albrecht er a1 1988b).

(vii) Electrochemical depositing: DNA on gold (Lindsay and Barris 1988, Lindsay er a1 1988) and polypyrole Fang er a1 1989). (a) Measuring in a solution, suspension or liquid phase with the tip in the solu-

tion The sample deposits itself on the substrate in some way or another: detergent monolayers (Wu et nl 1988), real-time image of blood clotting (figure 25, Drake et a1 (1989)) and liquid crystals (Foster et nl 1988).

(ix) A drop of a solution or suspension of the specimen is allowed to dry on the substrate: several parts of bacteriophage 429 (Baro er a1 198.5), DNA (Beebe et a1 i%Tj and minu aciris (Few er ai i9ESj.

(x) Exposing the substrate to a vapour of the specimen: acetone on graphite (Hubacek et al 1988).

10.2.3. Coatings nnd replicus. Both the coating and the replica techniques have been used extensively to study biological materials with an electron microscope. The advantages of coating a sample on a substrate are obvious: it demobilizes the sample, makes it conducting and makes it more rigid. Some coating materials are Pt, Au, PtC and PtIrC (examples: Ttavaglini et al (1987, 1988), Rec-A DNA; Blackford et a! (1988), the cell sheath of MethanospidIum Hungatei; Reneker and Howell (1988): PTFE on mica; Guckenberger et a1 (1988b): HP! protein crystal). A disadvantage Of coatings is that they limit the resolution by their grain size (3.5 nm in the case of PtC (Guckenberger et al 1988b)).

The replica technique has more or less the same (dis)advantages. It mnsists of depositing a thin conducting film on the sample, removing the sample, and then ex- amining that side of the film which was in contact with the sample. The replica should be supported firmly to minimize the result of interactions with the tip. Zasadzinski el a1 (1988) imaged the ripple phase of dimyristoyl-phosphatidylcholine (DMPC) bilayers using thk technique.

spec;”.?. e!! ‘!E s”h%L?te:

11. Electrnchemistny

Electrochemical reactions occurring at a solid-liquid interface are technologicaliy very important. They are used for wntrolled chemical reactions in production proCess€S but they also occur spontaneously; e.g. corrosion of metals in liquids or in a humid sEvk%”%ent.

Electrochemical reactions are very wmplex to describe: several different mm- ponents constitute the liquid, the solid surface has many different adsorption sites, an electrical double layer exists, particles from the liquid can adsorb in different orientations, diffusion from molecules in the liquid plays a role, etc.

STM can be used to elucidate several aspects of these reactions (&a 1987):


(i) structure of the electrical double layer under non-equilibrium; (U) determination of roughness characteristics; (iii) imaging the topography of the metal surface at the early stages of corrosion,

(iv) mechanism of passive layer growth (two-dimensional and three-dimensional

(v) adsorption of inhibitors for corrosion, growth etc; (vi) organic film formation and structure; (vii) structure and characteristics of passive layers as a function of the water

(viii) aging effect on passive layers.

There are several experimental problem assoriated with sTM in electrochemical

grad and electmadsorptionldesorption;

nucleation and growth);

content; and

"..a...:..-" r:-* ..b "11 .ho " ,.,.. G,..." :...,,.I.,'d "_ ,.*-.. ..-". ..," mn,i..rtinn P,.nrl..r. .Y","LL"uu. 1 I lD . ut all, L U G z,".",W.W "L."...." 0,- "".I,. .I*, I.... ..".."".A".&. ...,'.""- tive currents can be minimized by coating the tip (section 4.2.3).

A second point for attention is the pctentiumetric control of the cell. The STM tip constitutes an extra electrode and c?.r~ must be taken to minimize the electrcchemical activity at the tip (Itaya and 'ibmita 1988, Robinson 1988, Uosald and Kita 1989, Green et a1 1988).

Examples of systems which have been studied with STM are: electro-faceting (Gomez et al1986) and the correlation between nanometre scale electrode topography and catalytic activity (Pt, Vazquez et aI (1987); Au, G6mez et a1 (1989)); the initial stages of electro-cytalliition of Au(ll1) (Schneir et al 1988~) and Ag (van der Eerden er a1 1989); the deposition of Pb on Au(ll1) (Green et aI 1988, 1989). Ag on Cu (SoMenfeld and Schardt 1986) and Cu on Pt (Uosaki and Kita 1989); and the corrosion of stainless steel (Fan and Bard 1989).

Figure 2b shows a very nice exampie of oxidation reduction cycies of Aujiiij electrodes ('Revor et al 1989, Wiechers et al 1988, Twomey et a1 1988).

12. Technological applications of STM

12.1. T d o I w : wear and fiction

STM and AFM can provide information on the microscopic roughness of a worn out surface. The direct measurement of lateral forces occurring when a tip is dragged along a surface is more interesting. Not only can the friction force be measured very sensitively, but also with a high spatial resolution. The force on a tungsten tip sliding along graphite shows a modulation which correspor!ds to the lattice spacing of the graphite (Mate et 01 1987). Such experiments may lead to an understanding of friction on an atomic scale.

12.2. Nanomachining and nanolithography

An STM tip can mod@ the surface and material can be transported from the tip to the sample and back If these actions can be performed in a controlled way, tremendous possibilities would arise: information storage devices (1015 bit Thomson (1988)), nanometre patterning techniques which can be used in IC technology and in basic physics, e.g. x-ray optics or electron localization, manipulations of big molecules (DNA) and the building of small devices.


k”’e 26. Images of a Au(l11) film on mica at +0.7 V wth respect to the normal lnldmgen elecimde in 510-5 M HCI, 0.1 M HCIO,, showing the emergent pints of two dislocations @ever a 01 1989) 31- ZWO A x 2000 A. (a) After cycling io 16 V and back to 0.7 V at 20 mV 6-’; (b) same image as (a) but presented as a grey scale map of &/a=; (e) after cycling to 1.9 v; (4 after three cy& to 2 0 V

The most straightfolward way to machine a surface by STM is by pushing the tip into the surface. This can result in a hole (van de Walle er a1 1986, Packard er a1 1988) but also in a small hill (typical size 50 A), which is created when the surface material adheres to the retracting tip (Giewsk i and Moller 1987). A thin insulating layer deposited on a conductor can be removed in a controlled way: the tip, tunnelling to the ~~ i idue ihg subsirate, wiii scratch the iayer of the sampie whiie scanning j&Wmci and Pease (1987a): 20 nm OF on Si). In this way, shavings of a diameter less then 1 lull are produced (figure 27).

Features created in gold are shown to disappear due to surface diffusion (Jacklevic and Elie 1988). In contrast, van Loenen er a1 (1989) showed that holes punched in an unreconstructed Si(ll0) or (001) surface remained stable for at least a week in UHV.

Marks can also he created by applying a large voltage pulse to the tip. Schneir er a1 (1988b) made holes and hilis on a Au(ll1) surface under a fluorocarbon grease. They raised the voltage from 0.1 V up to about 3 V until a sudden change in tip position occurred. After that, the bias voltage was reduced back to 0.1 V Peculiarly, they cannot predict whether a hole or a mount will be formed. Emch er a1 (1989) created holes in Au(ll1) by short (lCLl00 ns) pulses of several volts. Also blister-like mounts occur if the voitage during scanning k above a tbreshoid vaiue (Nagahara er a1 1988). nspical size of all the features is 50-100 k Li et a1 (1989) find that the formation of holes and mounts seems to correlate with the initial height of the tip above the surface. Mount formation seems more likely for small heights. A suggested

Scanning tunnelling microscow 122Y

Figmm 27. Shaving machined by the SIM by scanning through a thin (20 nm) isolatmg layer of aluminium fluoride on top of a conducting substrate (McCard and Pease 1987~).

mechanism for the surface modifications is a local melting due to the very high power density under the tip. This is not beyond doubt: the heat conduction of Au is rather good, so very high power is needed. It seems to be impossible to make marks on Pt, which conducts heat worse than Au (Nagahara et a1 1988).

Staufer et a1 (1987) proposed more clear cut candidates for a local surface melting: metallic glasses in which both the electron mean free path and the heat conduction are a factor 100 smaller than in crystalline metals, so much higher temperatures are possible. They succeeded in creating mounds and l i e s on the surface (typical size: 2d nm). A mound could also be erased by creating a new one next to it.

Another proposed mechanism is the transport of material from the tip to the surface during a voltage pulse (Abraham 1986). The existence of such a mechanism is ” i n n e d by Becker et a1 (1987) who deposited Ge atoms stuck to their tip back onto a Ge(ll1) surface by means of a voltage pulse. After writing several dots, they had to ‘recharge’ their tip bv (gently) touching the surface. Bell et a1 (1988) and Ben Assayag et a1 (1987) used a Ga-coated STM tip as a liquid metal ion source. They could write lines of Ga with a width of 100 nm.

Jahanmir et a1 (1989) created dots and l ies on a layer of a-SiH, they proposed that a pulse causes a phase transition in the layer.

An STM can also be used in combination with an organometallic gas. The high electric field creates a plasma under the tip in which the gas is decomposed. The metal atoms ‘fall’ onto the underlying surface. If the writing voltage is present continuously, the tip retracts to keep a constant current which results in a reduced resolution. A better way is to apply pulses which are too short to be foilowed by the feedback (Silver et a1 1987, Ehrichs et a1 1988). Wical liewidths obtainable are 10 to 20 nm. McCord et a1 (1988) wrote lies and also succeeded in creating a tungsten pillar of 25 nm width and 280 nm tall! (figure 28). Such a pillar would be a perfect tip for an STM.

Part of the deposited material is due to a contamination layer present on the Surface: the contamination resist. Writing is also possible by using this coating (Ringer et a1 1985). The Srm pins the ‘fluid’ contamination layer to the surface. McCord and Pease (1986) produced l i e s in this way and used them successfully as a

... 1230 L E C van de Leemput and H van Kempen

FIgurr 28. Micrograph of a high aspect ratio venial dol averaging 25 nm in diameter and standing 28U nm tall (Mecord U 01 1988) It was deposited with Ihe SIM in 16 mTorr W(C0)s operated a1 25 V and 20 nA dunng 2 s (SEM tilt 45’).

mask against sputter etching, thus producing gold lines. Deliberately applied ‘contaminations’ can also be pinned down: Foster et al (1988)

glued molecules of di(2-ethylhexy1)pbthalate on a graphite substrate by means of a voltage pulse. A sewnd pulse removed the entire molecule or only a part of it. Dovek er aI (1988a) were able to cut a chain of PODA (poly(octadecy1 acrylate)) lying on a substrate. The mechanisms underlying the pinning and cutting of molecules are still poorly understood. There might be a correlation between the threshold voltage for pinning or cutting with the Cc binding energy (3.5 evf.

Several other known techniques of resists and masks have been combined with s W . McCord and Pease (1987a) used an STM to expose a CaF resist. Linewidths down to tens of nanometrea are obtainable. One of the limiting factors are reflected electrons which cause a spreading of the beam (McCord and Pease 1987b). Using a lift-off metallization technique the same authors (1988) succeeded in creating a resistor of 2.5 ki2 and a size of 0.15 p m x 2 pm.

Finally, two other possibilities for surface modification should be mentioned. Far- rell and Levinson (1985) propaed the possibility of a change in surface reconstruction, induced by the excess surface charge created by the potential at the tip. However, their calculations showed such a process to be unlikely in most systems.

Stern er a1 (1988) deposited a charge on an insulating surface. They wuld determine the shape and sue of their deposit by an AFM (typical size a few micrometres). Unfortunately, the typical decay time they measured is about 1 h.

13. Conclusions

Scanning tunnelling microscopy has proved to be an extremely powerful technique.


It can give topographical and spectroscopical information on subnanometre scale. Its imaging capacities are used in a broad range of scientific and technological applications. Some of these are already well established, e.g. the imaging of metals and semimnductors in ultra high vacuum. Other areas are still evolving, like STM in biology and STM as a mechanical tool at nanometre scale.

The key design considerations and basic operating modes are worked out quite

available, research tool. However, young operating modes (e.g. BEEM and photon related techniques) are still being developed and new ones will be discovered

*e!!, =*g 'hp $-&<g f"E"!!&.lp &q**pe E c w C f i q re!&b!q =mmt'r&?!!y

Acknowledgments

We thank P J M van Bentum and Th Rasing for their careful reading of the manuscript and M P B van de Leemput-van Helvoort for sorting out big piles of articles and for many improvements to the text. This work was part of the research programme of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) and was made possible by the financial support from the Nederlandse organisatie voor Wetenschappelijk Ondemek ( W O ) and from Philips Research Laboratories.

References

Abeilao J, Chmn R and Onuoo M 1967 Php Stmu Solidi A 101 46W Abraham D W, Ma& H 3, Gam E and Clarke J 1986 IBM J. Res L h 30 492-9 Abraham F E Batra I P and Cuaci S 19& Phys Rm. La, 60 1314-17 Abraham D W, W&ms C C and Wicknmasinghe H K 1988b J. M w r m 152 8634 A m G C and Leavens C R 1986 Solid Stme C- 60 427-30 Agullar M, Gama A, Pasfual P J, Presa J and Santiteban A 1987 Sa$ Scr 181 191-9 Albrechl T R and Qua= C F 1987 L Appl Phys 62 259W02 - 1988 J. cylc Sci TechL A 6 2714 Albrechl T R, Mizes H A Noggami 3, Park S I and Quale C F 1988a Appi Phys. L a 52 3624 Albrechl T R. Dwek M M, b a g C A , Grueuer P, Quale C F, Kuan S W 1. Frank C Wand Pease R F

Alexander S. Hellemam L Mani 0, Schneir J, Elings V, Hansma P K, Langmire M and Ourley J 1989

AUenspch R and Bkhof A 1989AppL Phys Len 54 587-9 AUenspch R, Salemink H, Bisfbof A and Weibel E 1987 2 Phys B 67 125-8 Amer N A Skumanich A and Ripple D 1986 AppL Phys La, 49 137-9 Ammn M, Duerr R, Slasiak A Gmss H and 'Itamglint G 1989 Sa" 243 1708-11 Anders M, Thaer H and Heiden C 1987 Swf. Scr 181 17- ANelmelli T Wesendanger R, Geiser V, Hidber H R and Guentherodl H-J 1988 J . M i m m 152 509-14 Amnld L Krieger W and Wallher H 1987 AppL Phys Lea 51 786-8 ANia A J 1987 Stof Sci I81 78-91 Avain D V and Ukbarev K K 1986 L Low Tmp. Phys 62 345-73 Awuris Ph and Walkcm R 1989 Phys Rm. B 39 5091-1W Bando H, Morita N, lbkumoto H, Mmlani W, Watanabe K, Hamma A. Waktyama S, Shgena M, Endo

K and Kajimura X 1988 J. Voc Sci T m M A 6 344-8 Bap1 U H 1987 Swf. Sei 181 15764 Y-aWY '=, DUUUb U, r Y C I I I n, 3al"a" P ana DlOll c ,%m sq. JU ,mi 1,-, Bardeen J 1961 Php Rm. Lnt 6 57-9 Ram AM, Miranda R, Alanman 3, Garcia N, Binnig 0, R a h m H. Gerber C and C a m s ~ m J L 1985

Bamne A 1988 PhvSiCo C 153-5 1712-18

W 1988b J . AppL Php 64 1178-84

J. AppL Phys 65 164-7

m"-..-e A -:-..:-E .-._-c. *. "..~-- r ~~1 ^.~.. - .""~ " . " . .-

NaWe 315 253-4

1232 L E C van de Leemput and H van Gmpen

Baski A A, AlbReht T R and Quale C F 1988 1 M c m . 152 724 Batra I P and olraci S 1988 I. Voc Sci T h o 1 A 6 313-18 Baz A 1 1967 Sot! I. Nucl Php 4 182-8 Beck- J 1987 Su$ Sci 181 203-2439 Becker R S, Golwchenko J A and Swanzentruber B S 198% Phys Rev. Lea Ss 987-90 Becker R S, Golovchenko J A, Hamann D R and Swartzeatruber B S 1985b Phys Ro. Len 55 20324 Bgker R S, Golwchenko J A, MeRae E G and S W a n Z e n t ~ k B S 198Se Phys Rm Len 55 2028-31 Becker R S, Golovchenko J A and SwartEentNber B S 1987 "In 325 419-21 Beebe T E Wilson T E Ogletree D I7 KaU J E Balhom R, Salmemn M B and Siekhaus W J 1989

Behm R 1, Hoerkr W Ritter E and Binnig G 1986 P h Rnr Lea 56 22a31 Bell L D and Kaiser W J 1988 Phys Ro. Len m 2368-771 Bell A E, Ran K and Swanson L W 1988 1 Yor Sci i?cW B 6 306-10 Ben krsayag 0, Sudraud P and SWans~n L W 1987 Su$ Sci 181 362-9 Berghaus Z Bmdde A, Neddermqer H and Tmch S 1988 I. VOC. Sci Tmhol A 6 483-7 Besenbcher F, laegsgaard E Moneasen K, Nielsen U and Stensgaard I 1988 Rm Sci Inmwn 59 1035-8 Bemcke K 1987 Sur$ Scr 181 14U3 Biegelsen D K, Ponce F A, 'llamonlana J C and Koch S M 1987 Appl Phyi Len 50 6964 Binh V T 19S3 L Minarc 152 355-61 Binh V T and Manen J 1988 Sv;- Scr 202 153949 Binnig G and Gerber Ch 1980 rBM Tech. D u c l ~ Bull 23 3369-70 Binnig G and Rohrer H 1982 Heh? Phys Acta 55 726-35 Bmnrg 0 a d S h i h D P E i986 Km SCL im- 57 i6%9 Binnig 0, Rohrer H, Gerber Ch and Weibel E 198% Appl Phys Len 40 17-0 - 1982b phys Rnr Len 49 57-51 - 1983a Su$ Sci I31 L379.84 - 1983b Phys Rm. Len 50 120-3 Binnig G, Gareia N and Rohrer H 19Sa Phys Rw. B 32 133a Binnig 0, Frank K H, Fuchs H, Garcia N, Reihl B, Rohrer H, Salvan F and Williams A R 1985b Phys,

Binnig G, Rahrer H, Salvan F, Gerber Ch and Bam A M 198Se S U ~ Sci 157 L373-8 Bmnig 0. Quale C F and Gerber Ch 1986b Phys Rnr Len 56 9305 Binnig G, Fuchs H. Gerber Ch, Rohrer H, Stoll E and T-tttl E 1986c Ewophys Len 1 31-4 Binaig G, Gerber C, Stoll AIbreeht T R and Quale C F 1987 Ewphys Leu 3 1281-5 Blackfnrd B L, Dahn D C and Jericho M H 1987 Rm S a I m m 58 134H Blamord B L, Walaaabe M 0, Jencho M H and Dab" D C 1988 J Micrmc. 152 237-43 Bock0 M F, Stephenson K A and Koch R H 1988 Phys Rnr Len 61 726-9 Bono 1 sad Good ii ii 1r i% Smj Sci i S i 5G-52 - 1987 Surf Sei 188 153-63 Brauer S, Pagnia H, Rucker M, Sotnik Nand Winh W 1989 2 And. Chon 333 337-9 Bryant A, Smith D P E and @ate C F 1986 Appl Phys L a 48 832-4 Btyant P J, Kim H S, Zheng Y C and Yang R 1987 Rm Sa In" 58 1115 Btyaat P J, Miller R G and Yang R 1988 AppL Phys Len 52 22335 Burger J, Meepagala S C and Wolf E L 1989 Rn? Sci I m m 60 735-8 Bumem E and Llmdgvist S 1969 Biittiker M 1983 Phys Re%! B 27 6178-88 Buttiker M and landauer R 1982 Phys Rm Len 49 173942 Cam R 0 1988 I. M i c m 152 37945 Chen C J 1988 1 mc. Sci TechnoL A 6 319-22 Chian R, Onuno M and Abellan J 1987 Swf Sci 181 107-11 Chung M S, Feuchrwang T E and Cutler P H 1987 Sur$ Scr 187 5 5 9 4 Clinton W L, &rick M A and Sacks W S 1987 Phys Rn? B 35 4074-7 Coleman R V, Drake B. Hansma P K and Slough G 1985 Phys. Rnr Len 55 394-7 Coleman R V, Giambattisla B, Hansma P K, Johnson A, McNairy W Wand Slough C 0 1988 A& Ph.

Coltan R J, Baker S M, Baldeschweler J D and Kaiser W J 1987 A w l Phys Len 51 305-307 Colt00 R J, Baker S M, Driseoll R J, Youngquist M 0, Baldeschwieler J D and Kaiser W J 1988 I. mc

SClE?lCce 243 3703

Rm Lea 55 9914

7 d @ P h o m r m ? in So/& pew York: Plenum)

37 559-644

Sci TmhoL A 6 349-53


Coombs J H and G “ k i J K 1988 J . fficrox 152 841-51 Coombs J H and Pelhica J B 1986 ISMJ. Rer Dnr 30 4554 Coombs J H, Gim~mmki J K, R e i B. Sass J K end Schtittkr R R 1988 J. MUmx 152 325-26 C o b B W, Ringer M and Gunfaodt H J 1985 J . AppL Phy. 58 394753 Crirrnti A, Selci S, G e n d R, God E and chiamtti 0 1988 J. MivaFc 152 789-94 cutler P H, Fevchtwang T E, Huang Z ?song T 1; Nguyen H, Lucar A A and Sullivan T E 1987 L

Physinue CMB 101-106 D’iunbrumd N- and -w-hle R M- i g a so= j,a, cm 50 Dahn D C, %mabe M 0, Blackford B L and Jericho M H 1988 J . AppL P h p 63 31548 Das B and Mahany J 1987 Phys Ra PB 36 898403 De Lozanne A I, Elmd S A and Quale C F 1985 Phys Rn. LaI 54 24336 De h n a e A L, Ng K W, Pan S, Silber R M and Berevn A 1988 J . Murex E 2 117-P Delsing P, Claeron 1; Jikharw K K and KvUnin L S 19SiJa Phys h. B 42 2539 Delsing P, likhharev K K, Kuzmin L S and Claep~n T 1990b Phys h. Len 63 11lbl-3 Demvth J E, Hamera R 1, Tmmp R M and Welland M E 1986 J. V a Sci EchnoL A 4 1320-323 Demulh J E, Van laenen E 1, pomp R M and Hamcis R J 1988 J . V a Sci TcI-L B 6 18-25 Devoret M H, Fslm D, Grata7 H, Ingold G L, Pothier H and Urbina C 1990 Phys R n Lut 64 1824 Diluich R and Heideo C 1987Jpn J . AppL Phys. SuppL 26-3 1649-50 - 1988 I Voc Sci EchoL A 6 263-5 Dovek M M, Albrrchi T R, Kvaa S W J, tang C A, Emch R, Gruetter E Frank C W Pease R F W

Dwek M M, Heben M 3, Iang C A, I.6wi.s N S and Quale C F 198w &. Sci I m m 59 23334 Doyen G and Dnkova D 1986 Surf: Sci 118 375-81 Doyen G, Drakm D, Kopalzld E and Behm R J 1988 J. Voc. Sci TcchnoL A 6 327-30 Drake E. Sonnenfeld R, Schneu 1, Hansma P K, Slough G and Coleman R V 1986 Rm Sci I m m 51

4415 Dmke B, Prater C B, Weisenhom A L, Gould S A C, A l w h l T R, Quale C F. Clnneli D S, Hansma

H 0 and Hansma P K 1989 Scimce 243 1586-8 Dmnsfeld K and Xu J 1988 J. Micro% 152 35-42 Duke C B 1969 T t U i n g in S& (NRY York Academic) Diing U, Gi“ski J K and Pohl D W 1986 Phys &. Lut 51 2402-5 Ehnchs E E, Yocn S and de h ~ e A L 1988 AppL Php Lea U 2287-9 Elmd S A, de h n n e A L aud Quale C F 1984 AppL Phys Len 45 1240-2 Elmd S A. Bwant A, de lnmnne A L Park S, Smitb D and Quale C F 1986 IBML Res &. 30 387-95 Emch R, Niedemana P, Dseauts P and F k h r 0 1988a 1 Bc. Sci TNhnoL A 6 379 Emch R, DescouIE P and Niedemann Ph 1988b I Micmc 152 85-92 Emch R, Nogami J, Dwek M M, lang C A and Quale C F 1989 1. AppL Ph:i 65 79-84 Eog L Hidber H-R. Rosenthaler I, Slaufer U, Wlesendaoger R, Gunthemdl H-J and %mm L 1988 J.

Erlandson R, McClelland G M, Male C M and Chiang S 1988 J. Voc SCL TechnoL A 6 26670 -pa L and Garcia N 1990 S d g ”eUingMinareopy and Rebed Mehods ed R J Behm. N Garcia

and H Rohrer pordrechc Kluwer) eh 7 Fan F R F and Bard A J 1989 J. E k ~ m Soc 136 166-m Famll H H and Levlnson M 1985 Phy Rev B 31 35934 Feenstra R M and Maltensson P 1988 Phys Rev. L a 61 447-50 FeensVa R M and Stmseio J A 1987a Phys Scz T 19 55-64 - 1987b.J Bc Scr T e h L B 5 922-9 Feenstra R M, Svoseio J A and Fein A P 1987 Sw$ Sci 181 295-306 Fein A P, Kin19 J R and Feenslm R M 1987 Rev Sci b” §8 180610 k n g 1 HU C Z and Andrade J D 1988 1. M ~ r o x 152 811-16 Fenante J and Smilh J R 1979 Phys Rev. B 19 3911-20 - 1985 Phys Rev. B 31 3427-34 Femr J, Manm-ROdero A and Florep F 1988 Phys Ro? B 38 10113-15 Feuchiwang T B ana Cutier P H igsB Php Sa 38 U m Feuchtwang T E Notea A and Culler P H 1989 Surf: Sci 201 547-57 Fink H-W 1986 IBM J. Rer Dor 30 460-5 - 1988 Phys Sn: 38 260-3 Fmter J S and Fmmmer J E 1989 “W 333 542-5

and Quale C F 1988a I. M h 152 229-36

Vac. SCi Tcdvlol A 6 3584

1234

bier J S, Fmmmer J E and Amel P C 1988 N a w e 331 324-6 Fmhn 1, Wolf J E B m k e K and lkske M 1989 RN Sci hrrnun 60 1200-201

Fuchs H and 'lhwlri E 1987 Eumphys .2e 3 74- Fullon T A and Dolan G J 1987 Phys Rw. Lea 59 109 Fullnu TA, Gammel P A Bishop D J and Dnnkleberger L N 1989 Php Rw. Len 63 1307 Gallagher M C and Adla J G 1988 J. M i c m , 15.2 123-8 Garc~a N and Flores F 1984 physic0 1278 13742 Garcia N, Oca1 C and Flom F 1983 Phys Rnr L a 56 2002-5 Gar& R, Saena J J, M d e r J and Garcia N 1986 Z pnys C SoGd Smte Phys 19 L131-4 Gareia R, Saena J 1, Sola J M and Garcia N 1987 Su$ Sci 181 69-71 Gama Cantu R and Huerta Gamica M.A 1987 Sus. Sn. 18121.5-22 Gerkr Ch, Biaaig G, Fuchs H, Mani 0 and Rohrer H 19% Ra Scr Imwm 57 221-4 Geedim L J and Mmij J E 1988 Phyma 1528 212 Giawer I 1974 Rw. Mod F'hp 46 245-50 G i m s k i J K and Miiller R 1987 Phys Rru B 36 1284-7 Gimzwslo J K, Mdler R. Pohl D W and Scblrttler R R 1987 Sur$ Sci I89nW 15-23 G i m s k i J K, Sass J K, Schliner R R and Schatl J 1989 Europhys Len 8 435-40 GIM~ S M, Glazman L I, Jonsau M. Penn D R and Siiler M D 1990 Phys RE. Lett 64 3183 G6mez J, Vique2 L Bar6 A M, Garcia N, Perdriel C I, lhaca W E snd Awia A J 1986 Name 323

G6mez 1, Vique2 I, Bar6 A M, Perdnel C L and Atvia A J 1989 Ekcmhim Acta 34 619-24 Gould S, Man1 0, Drake B, Hellemans I, Bracker C E, Hans" P K, Keder N I, Eddy M M and

Green M P. Richler M, Xing X, Scherson D, Hanson K 1, Ross P N Jr, Cam R and Lindau I 1988 J.

Green M P. Hanson K 1, Scherson D A, X!ng X, Richter M, R w P N, Cam R and b d a u I 1969 1.

Gregory S and Rogers C T 1988 I. a c . Sci l?chnoL A 6 390-2 GNrter E Meyer E, Heinzelmann H, Rmenthaler L H l d k H-R and Guentherodt H-J 1988 J. &c. Sci

Guckenberger R, Kosslinger C and Baumeister W 198& I. Vnc Sci TehnoL A 6 383-5 Guckenbwger R, Wegraebe Wand Baumeister W I!?&% J M i c m 152 795432 Gueret P, Baraioff A and Marclay E 1987 EwophF Leu 2 367-72 Gundlach K H 1966 Solid Slate Elecuan 9 949-57 Hallmark V M, Chmg S, Rabolt J E Swalen J D and Wilson R J 1981 Phys Ra Lett 59 2 8 7 H 2 Hamea R J, l b m p R M and Dnnuth J E 1986 Phys Rev Len 56 1912-5 - 1987 Surf. Sci 1 1 346-55 Hansma P I( 1982 (ed) i'iiel&g S p e c m o ~ : Cqabihtiq Appli&rq md New Tkhntque (New York:

Hansma P K 1986 IBM I. Res Dm 30 3163 Hansma P K, Elrngs V B, Man, 0 and Brackr C E 1988 Science 242 209-16 Hansma P K, Drake B. Mani 0, Gauld S A C and Prater C B 1989 Science 243 641-3 Hanman T E 1962 J. AppL Phys 33 3427-33 Hanmann U 1989 Pbs. Len 137A 4754

Hauge E H, Falck J P and Fjeldly T A 1987 Phy Reu B 36 4203-14 Hell 1, Waner J and Gnll W 1988 J. AppL Phys 64 193!?-44 Heinzelmann H, Gmetter P, Mejer E, Hidber H, Rosenthaler 1 Ringger M and Guenthemdt H-J 1987

Hensan T D, Sand D and Bell L S 1988 J . Miwax 152 46132 H e m e n J G H, van Kempen H, Nelisen B J, Soethoul L h van de Walle G F A, Weijs P J W and

Hers H E Robinson R B, Dynes R C, Valles J M and WaJzaak J V 1989 Phys Rm. Len 62 214-16 Hosaka S. Hosoki S, Bkala K, Horiuchi K and NaWnaki N 1988 AppL Phys. Lex 53 487-9 Huang Z Feucbhvang TE, Gaod R H, Kam E, N g w n H 0, Park S K and Cutler P H 1988 I. Physique

Hubacek J S, Bmekenbmugh R '& Gammie G, Skala S h Lyding J W, lallen J Land Shaplej J R 1988

L E C van de Leempur ~ n d H van Kempen

FUCU H 1981 phys SO: 38 26bs

612-14

Slucky G D 1988 N o m 332 3324

M i n a n 152 823-9

Php Chan 93 21814

TechnoL A 6 279-82

Plenum)

Hmge E H I!d s!mP!!g I 4 1980 !?E%? M d E?ys 61 9!?-36

.W# SCL 189ll90 29-35

W d e r P 1987 Surf Sci 181 183-90

C6 49 17-22


J M i 152 221-7 Humber( A, Salvan F and MOUtIeI C 1987 Sluf SCL 181 307-12 Ihm I 1988 Php SCE 38 269-71 lijima T and Yaruda 11988 Jpn I. AppL Phys. 21 1 5 6 7 Israelaehvili J N 1985 InrmMl" and W a c e FMU (London: Academic) I m p K and "ita E 19m swf: Sci 201 150742 lahmmir J. West P E and Hsieh S 19891 And Phvr 65 2064-8 . = ~ ~ ~ ~ ~

., - ~~~ ~ ~ ~~ ~~

Jaklvic R C and Elie L 1988 Phys. Rex Lm 6Q 120-3 Jericho M H, Dahn D C sad Blackford B L 1987 Rev Sci INaun 58 134952 Jencho M H. Bhckford B I. Dahn D C, Frame C and Maclean D 19901 Kzc. Sci T c h L A 8 661-6 Johnson R E 1989 Phys. Rei B 39 4693-4 Joma M 1980 Sold State Can" 33 743-6 Jmepbson B D 1969 S q w m z d ~ ~ u v i y ed R P Parks (New York Mareel DekLer) Kaiser W J and Bell L D 1988 Phy RN Len 60 1406-9 Kaiser W J and JaWevic R C 1987a swf: Sci 181 55-68

l" l lL P..S e-. *a, . ,.,v-,, - *lo," l.yJ. 0.. -.-.... Kab& H and Siu B 1988 Jpn I. AppL Phys 21 L773-6 Kajimura K, Baado H, End0 K, Mimtani W, Murakami H, Okano M, Okayma S. Ono M, Ono U,

Kaneko R 1988 I. Mianrr. 152 363-9 Khaikia M S and TqanmkIi A M 1985 Sow Tech Phys Lm 11 511-12 Kirk M D, Srmth D P E, Mitzi D B, Sun J Z Webb D 1, Char K, Hahn M R. Naito M, Oh B, Beasley

M R, GebaUe T H, Hammond R H, Kaprtulnik A and Quale C F 1987 Phys Rn. B 35 885M Kirk M D, AlbmhI T R and Quale C F 1988 Rev. Sci I n " 59 833-5 Kinley J R, 1Suel C C Park S I, Chi C C, Rozen J and Shafer M W 1987a Phy Rm B 35 7216-19 Kinley J R, Raider S I, Feenstra R M asd Fein A P 1967b AppL Php Len 50 1607-9 Kinley J R, wdshbum S and Brady M 1 1988 Php Rm Len MI 1546-9 Kochanslti G P 1989 Phj& Rev Len 62 2285-8 Kopaahi E, Doyen G, Drakma D and Behm R J 1988 1 M r ~ m 152 687-95 Kordm S, van Lwneo E 1, Haeven A J and Moras1 H K 1990 J. fit. Sa TwhaL A 8 549-52 Kotler Z and Nimn A 1988 I. C h Phys 88 3871-8 KUbby J A, O a t h J E, B e c k R S and Vicken J S 1987 Php Rm B 36 6 M M 3 Kuk Y and Silverman P J 1986 Appl Phys Lea 48 1597-9 Kuk Y, W e m a n P J and Ngyen H Q 1987 Phy& Rm Len 59 14525 K m l n L S, Delsing P, Clensan T and liwlarev K K 1989 Phy. RN Len 62 2539 laibo R, Levola T and Snchaa H 1987 Surf Scr 181 370-5 Lalayam Th, heap A A, Vlgnemn 1% lambin Ph and Morawifz H 1988 J. Micrarc 152 53-63 Lambe J and Jacklevlc R C 1968 Phjm Rm. 165 821-32 landman U, hedrke W D and Niean A 1989 Surf Scr 210 L177-84 lang N D 1986a Phys Rm Lea 56 1164-7 - 1986b P h p Rev. B 34 5947-50 - 1987a Phys. Rev. Lnt 58 45-8 - 1987b Phys. Rw. B 36 81734 lang N D and Kahn W 1970Phys Rm B 1 455S9 hang C A, Horber J K H, Hansch T W, HecW W M and Mahwald H 1988 I. Vnc. Sci TechoL A 6

lbkumota H, Saw F, Watanabe K and Nkiyama 5 1987 Swj S d 181 165-73

368-70 2 Dic E c., E-- .A, 1 a& stcm ; A i98.App; F;p sG i9ji-3 Le Duc H G, Kalser W 1, Hun1 B D, Bell L D, Jaklmc R C and Youngqulst M G 1989 AppL Phy&

Lesvens C R 1988 Php R a B 38 2169-71 Leavens C R and Aem G C 1986 Solid Smte C o m a 59 285-90 - 1987a Solid Smte CO- 63 11014 - 1987b Solid Stat* Com" 63 1107-111 - 1988a I. Var Sci Tichnd A 6 305-10 - 1988b Snltd State Convnw 61 1135-42 - 1989 Phy Rw. B 39 12024 - 1990 Scmujng T m l h g Miiannopy and Rclnted M&& ed R J Behm, N Garem and H Rohrer

Lm 51946-8

(Dordrecht: Kluwer) eh 3

1236

Li Y Z Vauluez L, Piner R, Andres R P and Reifenberger R 1989AppL Php Leu. 54 14244 Lndsay S M and Banis B 1988a I. Voc. Sci "L A 6 54d-1 Lindsay S M, Thundai T and Nagahara L 1988bI. Micmc 152 213-20 h l e l l i M and Lamlmley 0 1988 Rot Sci I n " 59 661-3 buns E and Flares F 1987 Phys Reu B 35 143% Louis E, Flom F and Echenique P M 1986 Solid Sue C m 59 453-5 Lum A A, Vngnmn J P, Bona 1. Culler P H. FeUch(arang T E, Gaod R H Jr and Huang 2 1984 I.

Lucas A A Mmawiu H, Henry G R, Viguemn J-e Lambin P, Culler P H and Feuchmng T E 1988a

h c a s A A Culler P H, Feuchlwaq T E, Ikaang T T Sullivan T E, Yuk U, Ngyen H and Silverman P

Lucas A A, Marawiu H, Henry G R, Vignemn 1-P. Iambin Ph. Cutler P H and Feuchmng T E 1988c

Mamm H 1, Abraham D W Gam E and Clarke J 1985 Rot Sci In" 56 2168.10 Mamin H 1, Gam E, Abraham D W Thoma R E and Clarke J 1986 Phys. Rev. B 34 9015-18 Mamin H 1. Rugar D. Stern J E, %mi6 B D and Lamben S E 1988 AppL Phys. Lm 53 156f5 Manasen Y, Hamers R 1, Demulh J E and Castella A J Jr 1989 Phys Rex LCu 62 2531-5 Mareban B, Ogle3ree D E Bussell M E, Samnqai G A, Salmeron M and Siekhaus W 1988a I. MicmM

Marchon B, Bemhardt P, Bussell M E, Samojai G A, Salmeran M and Siekhaus W 198% Phys. Rm.

L E C van de Leempul and H van Kempen

?&side c9 4: 12.5-32

I. Voc Sei Rhnd A 6 29b3

J 19881, I. Vor. Sei Rclmd A 6 461-5

phvs &. B 31 ioioazo

152 421-39

Lm 60 1166-9 ManensEon P and Fee" R M 1989 P h y RW~ B 39 714e53 Marti 0, Drake B and Hansma P K 1981 AppL PAYS, Lm 51 484-6 Mani 0. Drake a, Gauld S and Hansma P K 19% I. Voc Sri TechoL A 6 208s92 Mani 0, Elings V, Haugan M, Bracker C E, Schneir 1, Drake B, Gould S A C, Ourley J, Hellemans L,

Mani 0, Rib1 H 0, Drake B, Albreehl T R, Quale C F and Hansma P K 1988c Science 239 50S2 Manin Y and Wiekramasinghe H K 198lAppL Phys Lm 50 1455-1 Mania Y, Ab=+" D Wand Wckrammuge H K 1988a AppL Php Lm 52 1103-3 Manin Y, Rugar D and Wdmmasiqhe H K 198SbAppl Phys Leu 52 244-6 Uvt in Y, Wlhams C C and Wckmmasinghe H K 1987 I. AppL Phys 61 4125-9 Manin-Radem A, Florcs F and March N H 1988 Phys. Rev B 38 1004140 Mate C M, McClelland G M, Erlandsson R and Chiaag S 1987 Php Rex Leu. 59 1942-5 Mate C M, Erlandsson R, McCleUand 0 M and Chiang S 1989 Swj Sci 208 413-86 Macey J R. Crandall R S, BlyEki B and Bn'ggs 0 A D 1987 Rev Sri I m m 58 561-70 MeCleUand G M, Erlandrson R and Chiang S 1987 Rm Fm# in Quat. Non-Desm. EvaL 6 1307-14 McCard M A and Pease R F W 1985 I. Vm Sri T e c M B 3 198-U)l - 1986 I. Voc Sei Techd B 4 86-8 - 198la I. Voc. Sci T m M B 5 4303 - 198lb swf: Sci 1 1 218-84 - 198le AppL Phys Leu 50 569-70 - 19881 Voc Sci Rdvtd B 6 29% McCard M k Ken, D P and Chang T H P 1988 I. Voc. Sci TechoL B 6 1871-80 McGreer K A Wan J C, Anand Nand Galdman A M 1989 Phys &. B 39 122603 McMdlsn W L and Ravell J M 1969 lilnneUing and slmngsaupling supermnducriniy S u ~ o n d u c ~ d ~

Memvey R 1988 Phys So: 30 2126 Meyer 0 and Amer N M 1988 AppL Php Leu 53 1045-1 M ~ s h k y N M, Culler P H, Feuchlwang T E Shepherd S J, Lucas A A and Sullivan T E 1980 AppL

Mizep H A Park S and Harrison W A 1981 Phys Rex B 36 44914 MirUer R, Ecslinger A and Koslowski B 1989 AppL Phys Leo. 55 2360-2 Mmg E R. Hawley M E, Gray K E, Liu 3 2 Hinks D G, Capne D W II and D m e y J 1988 I. Law

Marawiiz H. Balm I P, Reiniseh R and Henry G R 1987 SI@ Sci 180 333-S2 Marila S, mukada S and Mikoshiba N 1988 I. Voc. Sci Tcdvtd A 6 354-1 MuUen K, Ben-Jacob E, Jaklevic R C and SchUgE 2 1988 Phys. Rot B 31 98-105

Shaw K, W e m h m A L, Zasadzinski J and Hansma P K 1988b I. Mtcm.% 152 803-9

ed R P Parks (New Yark Mareel Deker)

P& LQt 31 18942

Temp. Phys 11 393-402

Scanning runneUing microscon 1237

M d t P 1987 Sur$ Sci 181 324-32 Mural1 P and Pohl D W 1986 AppL Phys Lnr 48 514-16 Mural1 P, Meier H, Pohl D Wand Salemmk H 1986a Svpcrloa Miaarrmct 2 519-20 M w l t P, Pohl D W and De& W 1986b ISMI. Rrs m. M 443-50 Nagahara 1, lioaSay S M, Thuadat T and Knipping U 1988 I. Micmsc. 152 145-7 Naito M, Smith D P E, Kirk M D, Oh B. Hahn M R, Char K, Mitzi D B. Sun J 2, Webb D J. Beasley

M R, Fiseher 0, Gebalk T H, Hammond R H, Kapitulmk A and Quale C F 1987 Phys Rnr B 35 -31

Nazamv Y V 1989 Sm. Phys-JETP 60 5616 Neddermeyer H and Drechsler M 1988 I. Miaarr. 152 459-66 NlienEaes R. tiang Y, i'aclrani -w E, Fu Zw, BIaEirstead H A, Chin K K, Dow J D, Furdyna J K, H u

W M, Jakle-vic R C, Kaiser W I, Pe lm A R, zeller M V and Belliaa 1 Ir 1988 I. Vac Sci T+L A 6 445-7

N U M and Binnig 0 1988 I. Vu. Sci T m h L A 6 470-1 Nishikawa 0, "ilori M and Minakuchi A 1987 Sur$ S a 181 210-15 Nishikawa 0, lbmitori M d Kaeuki F 1988 J. hiicrcx 152 63?41 Okno M, Kajimm K, Wak@ama S, Sabi F, Mmlani W and Ono M 1987 I. Vac Sci T m M A 5

Omsz L 1988 Phy& Rnr B 37 6490-2 Overhauser A W 1988 Solid Slon S-e Bod: ed S P Parkr (New York: MeGmw-Hal) p 142 P a c W W E, Liang Y, Dai N, Cow J D, Nicolaides R. JaklRnc R C and Kaiser W J 1988 J. Mi-

Park S and Quale C F 1986 AppL Phys Len 48 112-14 - 1987a Rnr Sci I n " 58 ZQ0$-9

Pashley M D. Haberern K W and Friday W 1988 I. Vac Sci T m h L A 6 488-92 Payne M C and Inkon J C 1985 srof Sci 159 485-95 Pelz J P and Koch R H 1989 Rnr Scr I n " 60 301-5 P e w n B N J 1987 C h phgs. LPD. 141 3 6 M - 1988 Phys S a 38 282-90 Pusson B N J and Baraloff A 1987 Php &. Lac 59 33942 - 1988 P@& Re&! B 38 9616-27 P e m n B N J and Demuth I E 1986 Solid Stmr C m " 51 769-72 Pethica J B 1986 P h Rev. Lm 51 3235

3312-20

152 715-25

- i98m RN sa ss m0-17

~ ~ . . PetInca J B and Olier W C 1987 P@& Sa T 19 6 1 6 Pierce D T 1988 P h Sa: 38 2916 POM D w 1986 IBM I. RCC m 30 417-27 - 1987 Rn. Sci I n " 58 54-7 Poppe U 1981 Phpica lO8B 8056 - 1985 I. M q n M o p M m 52 15740 Press W H. Flannay B P, Teukokw S A and Vetterling W T 1988 NwnsiclJ Reclpm in (cambnd$e:

Rak J P, San0 M, Batehelder D and Kabtehev A A 1988 I. M i 152 57343 Reihl B and G i J K 1987 Sur$ Sci 189/190 3643 Reihl B, coombs J H and Ginuewski J K 1989 S 4 Sei 21u2Lz 156-64 Reihl 9, G-ki J K, Nicholk J M and h t t i E 1986 Php Rev. B 33 5770-3 Reoeker D ti and Howell B F 1988 I. Ynr S a T&d A 6 553-4 Rinser M, Hidber H R, Schlwgl R, Oelhafen P and G u e n t h d t H J 1985 AppL Phys Len 46 8324 Robinson R S 1988 I. Mi- 152 5416 Rawnthsler 1 Hidber H-R, %nin A, Eng 1 Slaufer U, Wesendanger R and Gunthemdl H-J 1988 I.

Rugar D, Mamin H J, Erlandson R, Stem J E and l h i s B D 1988 &. Sci Inmwn 59 2337-40 Rybachenko V F 1967 Sm. I. NVCL Phys 5 6353 Sacks W S and Noguem C 1988 I. Miaarr. 152 23-33 Saeb W, Gauthier S, Rowset S, Klein J and Brick M A 1987 Php &. B 36 961-7 Saem J J, Garcia N, Gmetler P, Meyer E, Heinzelmann H, Wterendanger R, R-thaler I., Hidber H

Salemink H W M, BaIra I P, Rohm H. SloU E and Weibel E 1987 Sur$ Sei 181 U 9 4

Cambridge Universily Press)

Vac Sci TnhnoL A 6 393-7

R and Guenlhercdl H-J 1987 I. Appl Php 62 4292-5

1238

Salemink H W M, Meier H P, Ellialtioglu R, Gerritsol J W and Muralt P R M 1969 AppL Phys. Len 54

Wid D. Hewn T D. Atmsmng N R and Bell L S 1988 AppL P h p Len 52 22524 Schadt B C, Yau S Land W d i F 1989 Science 243 1050-3 Schneir 1, Sonnenfdd R, Hansma P K and TkmE J 1986 Phys &. B 34 4979-84 Scbneir 1. Mad 0. Remmenr G, Glaser D, Sonnenfdd R, Drake B, Hansma P K and Elings V 1988a I.

Schneir 1. Sonneafeld R, Marti 4 Hansma P K, Demulh J E and Hamap R J 1988b X 4 p L Phys 63

Schneir 3, Elings V and Hansma P K 1988c X E k D " Sa. 135 2774-7 S&k E. Knitlel J and Dransfeld K 1990 Scvnning liuvrrlling Minoscopy Md Relned Mehodr ed R J

Schwaiia C 1987 I . AppL PhyJ. 61 177 Selloni A, Camevali P, ?bastli E and Chen C D 1985 Php &. B 31 2602-5 Sellom A, Chen C D and l b n i E 1988 Phys S a 38 297-300 S e " P A, Soler J M and Garcia N 1986 phys Rn? B 34 67614

Simmons J G 1963 I. AppL Phyf 34 17-03 Simps00 A M and WOKS W 1987 Rn? Sci Inmwn 50 2193-5 Sleator T and '&co R 1988 Phyf &. Lur 60 1418-21 Smith D P E and Elrod S A 1985 Rnr Sri Inmwn 56 19704 Smith D P E and Bnnig G 1986 Rnr Scr Smith D P % Bumig 0 and Quae C F 1986 Appr Phys Len 49 16413 Smith D P E, Bryant A, Quate C F, Rake J P, Gerber Ch and Swalen J D 1987a ploc N d Aced Sci

Smith D P E, Kirk M D and Qnate C F 1987bI. Chen Phys. 86 6034-8 S m o h R T M. van Bentnm P J M and WO Kempen H 1990 k,.&a 16568 63-4 Snyder C W and de Iazanne A L 1988 Rnr Sci Immm 59 5414 Soethaul L L and van Kempen H 1990 Adx E l m m Ekcum Phys 19 155369 Socthont L L, Gemitsen J R Gmeneveld P P M C, Nelwn B J and van Kempen H 1988 I . Mi"

Soler J M, Bam A M, Garcia N and Rohrer H 1986 Phyx &. Len 51 444-1 SoMenfeld R and Schardt B C 1986 AppL Php Len 49 11724 SoMeofeld R and ffinsma P K $986 Science 232 211-U SoMenfeld R, Schneir 3, Drake B, Hansma P K and aSpnes D E 1987 AppL Phys Len 50 17424 Spang J K, Mires H A, laca" L J Jr, Dwek M M. Fmmmer J E and Faster J S 19&¶ "we 338

Siaufer U, Wesendanger R, Eng L, Roseathala L, Hidbcr H R, Gunthcmdt H-J and Garcia N 1987

Stemmer A, Reicheli R, Engel A, Rosenbuseh J P, Ringgcr M, Hidber H R and Gunlhemdt H J 1987


1112-14

Sci lkhnol A 6'283-6

717-21

Behm, N Garcia and H Rnhrer (Dordrsht: Kluwer) ch 25

FIL.- D U ml.*"'. c ..A _I A r In- A__# #,G__ .".. e. .,,7 n YY.... .. ..* u"....k. I L -"U "e -I",- r. I*,-. " p p ",y* - 91

51 2630-1

USA 04 969-72

152 2514

1374

AppL Phyf Len 51 24M

Surf. Sci 181 394-402 Stem J E, Unis B D, Mamin H J and Rugar D 1988 AppL Phys Lea U 2717-19 SloU E P 1988 I. Php. C Solid SIR@ P h p 21 L9214 Stall E. Baraloff A, Selloni A and Camevali P 1984 X Phw C: Solid Sfae Phys 11 3073-86 Stmseio J A and Feensva R M 1988 X V6 Sci m h L - B 6 1472-8 SlrasCio J A, FeensvB R M and Fein A P 1986 Phy. h Lea 57 Z 7 W 2

Slupian G W and kung M S 1987 Appl Phys Lwt 51 156W2 Sumelsltii M Yu 1986 ElP Lm 44 3694 Tagliacazo A and l b u i E 1988 P h p Ssn 38 301-8 lbkayanagi K, Tanishim Y, B h h a s h i S and Takahashi M 1985 Sur$ Sci 164 36742 Tanaka M, Mizutani W. Naksshuu 1: Morila N, Yamwh S, Bando H, Ono M and Kajimura K 1988 X

.2..rai r d -^a D 11" v-.".* n *I .."A I%;" d D .D(1Q I Vlr ,-' T-!.",,, .4 A *DOLO).) ""_."" .I""YO ..&, ... "." ..& -..". -." -. lzoy.. ."*. ".% ....*. ". ~- "

Tauimblalt M A 1 9 s APPL Phys LUL s i i o i i TmnIiJ 1986PhyJ. Rn? Lnr 51 440-3 - 1989 P& Rnr B 39 1052-7 TmnIi J and Hamann D R 1983 Phys Rw. Le& SO 1998-2(101

Scanning tunnelling micrawom, 1239

- 1985 Phys Re%! B 31 805-U m o w n D J 1988 I. Micmrc IS2 627-XI 'Ihomson R E, Walter U, Gaoz E, Clarke 3, ZelU A, Rauch P and DiSaIvo F J 1988 P h p Rnr B 38

liedje I: V m n J, Deck" H and Stokes J 1988 1 Vac Sci T u h l A 6 372-5 lbmanek D and Louie S G 1988 Phyx m. B 37 8327-36 lbmanek D, Louie S 0, Mamin H 1, Abraham D W, Thomson R E, Gam E and Clarke J 1987 Phy.

lbmanek D, Ovemey G, MiyszaLi H, Mahanli S D and Guestherodl H J 1989 P h p m. Len 63 876-9 lbseh SI and Neddermeyer H 198a Phys Rn. Len 61 349-52 - 1988b J. M c r m 152 41542 ?favagli 0, R O W H, Amrein M and G m H 1987 SI@ Sci I81 38a-90 ltavaglini G, R O W H, Stall E, Amrein M. Slasiak A, Sogo J and Grass H 1988 Phys Scr 38 309-14 lkvar D J, Chi- C E D and hiacona D N 1989 Phys Rei! Lca 62 929-32 l b m p R M, Hamers R J and Demuth J E 1986a S&ur U4 3044

Ibulrsda M and Shima N 1987 I. phvr Soc J n p 56 2375-85 Womey 1; Wiechns 1, Kolb D M and Behm R J 1988 I. Mxrmc. 152 537-40 Uosahi K and Kim H 1989 I. E k c d Chsn 259 301-8 Uamm K, Nakamoto K and Fujmka K 1988 Jpn 1. Appl P h p 27 L123-6 van Benlum P J M, van de Leempul L E C, Sehreurs L W M, TeunisSen P A A and van Kempen H

van Bemm P J M, van de lsemput L E C, Smokers R T M and van Kempen H 1988a J. M i c w 152

mn Bentum P J M, van Kempen H, van de Leempvl L E C and Sunissen P A A 1988b Phys Rew Len.

van Bentum P J M, Smokers R T M and van Kempen H 198% P h p Rm Len 60 25434 van Bentum P J M, Hopve~s H F C, van de leempul L E C, de NmUe M J M F. Schreurs L W M,

Smoker6 R T M, lkuoissm P A A and van Kempen H 1989 Phys Scc T 25 91-6 van h m e n E J, Demuth J E, l b m p R M and Hamers R J 1987 Phys Rn. Len 58 3734 v u raeneo E J, "gwmp U ano n m n A i i9G i. liiman. iSi 48i-96 van h e n E J, Dijklramp D, Hawen A 1, Lenssinck J M and Dieleman J 1989 AppL Phys Lmn 55

van de LeemPUI L E C, win Bentum P 3 M, Dri~sxn F A J M, Gemitsen J W, van Kempen H, Schreurs

van de Leemp.11 L E C, van Bentum P J M, Driersen F A J M, Gem~sea J W, van Kempen H, Scluevrs

van de WaUe G F A, Genilsen J w; van Kempen H and Wyder P 1985 Rnr Sci Im- 56 151% van de Walle G FA, van Kempen H and Wer P 1986 Swj Scr 167 L219-24 van de Walk G F A, van Kempen H, Wyder P and F l i p C J 1987 Sqf Sci 181 27-36 van der &den J P, Mickers M A H, Gemlsea J Wand Halteahuis M H J 1989 Efecnochim A m 1989

W u e z L, Gomez J, Bam A M, Gama N, Mare- M L, O o m l e s Vela- J, Vara J M, Ama A J,

Vieua s 1986 m.ux ~ e s m 30 5 s Vi& S, Ram- M A, H o m l M A and Buendia A 1987 S e Sci 181 376-9 Vleira S, Ram- M A, Vallel-Regi M and Golualez-Calbel J M 1988 Phys. Rev. B 38 9295-8 VOlodm A P and Khaikin M S 1988 JETP Len. 46 58M1 Wdas A 1989 I. Ma@ Mag& Mam 78 263-8 Wlmsley D G 1987 Sqf S d 181 1-26 Wan J C, McGreer K A, Anand N, N m k E and Goldman A M 1990 Phys Rnr B 42 5604 Wandass J N, Murday J S and collan R J 1989 Se" mtd Acmtm 19 211-35 Weimer M. Kraw 1. Bai C and Baldeschieler J D 1987 P h p Re%! B 37 42925 Welmer M, h m r J and Baldeschvrieler J D 1989 Php Rnr. B 39 55R-5 Weissler G L and Carlson R W 1979 (4s) M e W of Eqwimatol Physic$ vol14: Rmwn P h p m mi

Wecheta 1, lkromey ?: Kolb D M and Behm R J 1988 I. E f ~ ~ L Ch I 248 45140 W-nbnger R, Eng L, Hldber H R, Oelhafen P, Rosenlhaler L, Stavler U and Guenlhemdl HJ 1987

10-3

Re%! B 35 7798-3

- i986b pnys m. B 34 1388-91

1987 Phys Re%! B 36 843-5

11-21

6Q 369-72

..--~. .= . -.>. .... ~~ .. ~~1 * . - ~ ~

1312-14

L W M and Bcnnema P 1988 J. Miaan I52 10545

L W M and BeMema P 1989 J. G M 98 551-60

1141-5

P m 1, Garcia A and Aguilar M 1987 1. Am C h m Soc 109 1730-3

Tehnofw (New York Academic)


Surj Sci lI39n90 24-8 Wiper E P 1955 Phys Rw. 96 ~ 5 - 7 W i h R, Ben-Jamb E and Jacklevic R C 1989 Phyi ReK Lea 63 801 Wdlrins R. Amman M, Ben-Jamb fi and Jacklevic R C 1990 Php Rm. B 43 8698 Williams C C and Wickramasinghe H K 1986 Appl Phyi Lm 49 1587-9 Wdmn R J and Chian$ S 1987a P h p Rn. Lcn 58 369-7l - 1987b P& m. Lca 59 2329-31 Wilson R J and Chiang S 1988 L V a S u Rshnol A 6 3 9 8 4 0 Wmtlerlin 3, Wiechem S, Gritsch l3, Hoefer Hand Behm R J 1988 L M i c m c 152 4134 Winttsrlin 3, Wiechem 3, BNne H, Grirsoh lh, HDefer H and Bebm R I 1989 Phys. Rn. Lm 62 59-62 Wolkav R and Avouris Ph 1988 Phy3. Rn. L a 60 104932 Womtor D L, Miller R G and Bryant P J 1988 I. Minarc 19.817-11 Wu X-L and Lie& C M 1988 I. Phyr chen 92 5556-1 Yamada H, Fuji T and Nakayama K 1988 I. EZG Sei Trclvtd A 6 193-5

Yurlre B, Kaminsky P G and Eigler D M 1986 Cyogwtks l6 435-5 ZangwiU A 1988 P h p h (U swfocu (Cambridge: Cambridge University Press) Zasaduaski J A N , Scbneir 3, Gvrlq J., Elin@ V and Hansma P K 1988 Science 239 1013-15 Zheng N 3, Whoa I H, Knippmg U, Burt D M, Knnslq D H and 'Bong I S T 1988 Phys &. B 38

Ye!!: 3, n$?!Sh! U Y, E-aES n E chrik!eL-!! L E!!! US!!d?iCcl.."" ur a 1989 r !hy. Chnn ?.? 5114

12780-2

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