lecture 2 - mipt

Scanning Probe Microscopy

Lecture 2

Introduction to nanoscience: dimensions What is nanoscience?

The word itself is a combination of nano, from the Greek "nanos" (or Latin

"nanus"), meaning "Dwarf ", and the word "Science". Nano refers to the 10-9

power, or one billionth.

A nanometer is one billionth of a meter:

1 meter = 1,000,000,000 nanometers

1 micron = 1,000 nanometers

Another common unit of measure is the Angstrom. There are ten angstroms

in one nanometer:

1 nanometer = 10 Angstroms

For comparison, a human hair is about 100,000 nanometers thick!

Nanoscience is the study of atoms, molecules, and objects whose size is on

the nanometer scale ( 1 - 100 nanometers ).

The beginning of Nanotechnology era

A famous lecture "There’s plenty of room at the bottom" by Feynman in

1959:

R. P. Feynman, “There’s plenty of room at the bottom,” Engrg. and Sci.

(Cal. Inst. of. Tech.), 22-36 (1960)

R. P. Feynman, “The wonders that await a micro-microscope,” Saturday

Review 43, 45-47 (1960), http://www.zyvex.com/nanotech/feynman.html

- The idea of miniaturization of functional elements

down to the sizes of molecules (nanometers)

- Prediction of the human ability to produce molecular-size

functional elements by the end of XX century

Scanning probe microscopy

1918-1988

http://www.zyvex.com/nanotech/feynman.html


The gold rotor turns on a carbon nanotube

shaft, powered by two charged stators

patterned on a silicon surface.

Chronology of SPM developments

SPM Thecniques: Scanning Tunneling Microscopy

R. D. Young, Rev. Sci. Instrum. 37, 275 (1966).

Example: At 4.5eV, tunneling current drops down 10 times with 1-Å increase of the gap!

Electron tunneling.

Consider a flux of particles of energy E impinging on a potential barrier V(x) = V for x

= - s/2 to s/2 and V(x) = 0 elsewhere.

Under these conditions, the transmission probability T for this flux of particles is given

by

where

is the wave vector, m being the mass of the particle.

Under conditions when ks » 1, the preceding expression can be simplified to give

Note that k is the decay constant now. It describes a state of the particle (electron)

decaying in the +x direction.

To make connection to the typical setup in scanning tunneling microscopy, one can

consider electron tunneling between two metal surfaces separated by a distance s.

At low applied bias, one is essentially looking at electron tunneling from the Fermi

level (the upper limit of the occupied states in a metal) of one metal to another.

Therefore, (V - E) is equal to the work function of these two metal surfaces. We can then

write the tunneling current I as

Electron tunneling.

A = 10.25 eV-1/2 nm-1

The work function of a metal surface is defined as the

minimum energy required to remove an electron from the

bulk to the vacuum level.

Electron tunneling.

In general, the work function depends not only on the material, but also on the

crystallographic orientation of the surface.

For materials commonly used in STM experiments, the typical values of are listed in

Table 11.1.

SPM Thecniques: Scanning Tunneling Microscopy G. Binnig and H. Rohrer, “Scanning tunneling microscopy,” Helv. Phys. Acta 55,

726-735 (1982).

STM image of a single-crystalline silicon, Si(111). - a probe to acquire a signal

- a scanning system

- a feed-back system

For tunneling to take place, both the sample and the

tip must be conductors or semicondactors!

SPM Thecniques: Scanning Tunneling Microscopy

Rohrer (on the left) and Binnig (on the right): Nobel prize winners for Physics (1986)

G. Binnig and H. Rohrer, “Scanning tunneling

microscopy,” Helv. Phys. Acta 55, 726-735 (1982).

SPM Thecniques

SPM Thecniques: STM (operating modes)

Constant-height mode Constant-current mode

-Tip travels in a horizontal plane above

the sample.

-The tunneling current varies depending

on topography.

- This mode is fast, but useful only for

relatively smooth surfaces.

-STMs use feedback to keep the

tunneling current constant by adjasting

the height of the scanner.

-The tip-to-sample distance is constant.

-Can measure irregular surfaces with

high precision, but the the measurements

takes more time.

SPM: Other Thecniques

Near-field Scanning Optical Microscopy Nanolithography

Probe-sample interaction due to Van der Waals forces

(interatomic forces)

detector

incident light

subwavelength

scatterer (probe)

subwavelength

structure(sample)

propagating evanescent propagating

waves (sample) waves (probe) waves

STM can be used to modify

(atom by atom) the surface

deliberatlely.

Media : Xenon on Nickel (110)

[Eigler]

SPM Thecniques: Atomic Force Microscopy AFM probe deflection

(Detection of the cantilever’s vertical movement )

As the cantilever flexes, the light from the laser is reflected onto the split

photo-diode. By measuring the difference signal (A-B), changes in the

bending of the cantilever can be measured.

AFM tips and cantilevers are micro-fabricated from Si or Si3N4. Typical tip radius is from a few

to 10-s of nm.

SPM Thecniques: Atomic Force Microscopy AFM tips and cantilevers are micro-fabricated from Si or Si3N4.

Typical tip radius is from a few to 10-s of nm.

where E is the Young’s modulus of the lever and d, b and L the thickness, width and

length of the lever, respectively.

Atomic Force Microscopy: Measuring forces

Because the atomic force microscope relies

on the forces between the tip and sample,

knowing these forces is important for proper

imaging.

The force is not measured directly, but

calculated by measuring the deflection of

the lever, and knowing the stiffness of the

cantilever.

Hook’s law gives:

F = -Cz,

where F is the force, C is the stiffness of

the lever (spring constant), and z is the

distance the lever is bent.

AFM operates by measuring attractive or repulsive forces between a tip and the sample

(Binnig et al., 1986).

Atomic Force Microscopy: contact mode In contact-AFM mode, also known as repulsive mode, an AFM tip

makes soft "physical contact" with the sample.

The tip is attached to the end of a

cantilever with a low spring constant,

lower than the effective spring constant

holding the atoms of the sample together.

As the scanner gently traces the tip across

the sample, the contact force causes the

cantilever to bend to accommodate

changes in topography.

Atomic Force Microscopy: non-contact mode

The cantilever in an AFM can be vibrated using a piezoelectric ceramic.

When the vibrating cantilever comes close to a surface, the amplitude of the

vibrating cantilever may change. Changes in the vibration amplitude are easily

measured and the changes can be related to the force on the surface.

The feedback unit is used to keep the vibrating amplitude or

phase constant.

Atomic Force Microscopy: intermittent contact (tapping mode) Intermittent-contact atomic force microscopy (IC-AFM) is similar to NC-AFM, except that for

IC-AFM the vibrating cantilever tip is brought closer to the sample so that at the bottom of its

travel it just barely hits, or "taps," the sample.

The IC-AFM operating region is indicated on the van der Waals curve.

As for NC-AFM, for IC-AFM the cantilever's oscillation amplitude changes in response to tip-

to-sample spacing. An image representing surface topography is obtained by monitoring these

changes.

The feedback unit is used to keep the vibrating amplitude or

phase constant.

SPM Thecniques: Magnetic Force Microscopy

Magnetic force microscopy (MFM) images the spatial variation of magnetic forces on

a sample surface. For MFM, the tip is coated with a ferromagnetic thin film.

The system operates in non-contact mode, detecting changes in the resonant

frequency of the cantilever induced by the magnetic field’s dependence on tip-to-

sample separation.

MFM can be used to image naturally occurring and deliberately written domain

structures in magnetic materials.


An image taken with a magnetic tip contains information about both the topography and the

magnetic properties of a surface.

Which effect dominates depends upon the distance of the tip from the surface, because the inter-

atomic magnetic force persists for greater tip-to-sample separations than the van der Waals force.

If the tip is close to the surface, in the region where standard noncontact AFM is operated, the

image will be predominantly topographic. As you increase the separation between the tip and the

sample, magnetic effects become apparent.

Collecting a series of images at different tip heights is one way to separate magnetic from

topographic effects.


MFM image showing the bits of a hard disk. Field of view 30μm.

Atomic Force Microscopy: the scanner

Piezoelectric ceramics are a class of materials that expand or contract when in the

presence of a voltage gradient or, conversely, create a voltage gradient when forced to

expand or contract (Gallego-Juárez, 1989).

Most scanned-probe microscopes use tube-shaped piezoceramics because they combine

a simple one-piece construction with high stability and large scan range. Four

electrodes cover the outer surface of the tube, while a single electrode covers the inner

surface. Application of voltages to one or more of the electrodes causes the tube to

bend or stretch, moving the sample in three dimensions.

A typical piezoelectric material will expand by about 1

nm per applied volt.

Piezoceramics make it possible to create three-

dimensional positioning devices of arbitrarily high

precision.

Atomic Force Microscopy: the scanner

In a typical SPM, scan sizes run from tens of angstroms to over 100 microns, and from

64 to 512 data points per line. (Some systems offer 1024 data points per line.)

Atomic Force Microscopy: scanner nonlinearities

As a first approximation, the strain in a piezoelectric scanner varies linearly with

applied voltage. (Strain is the change in length divided by the original length, Δl / l).

The following equation describes the ideal relationship between the strain

and an applied electric field:

s = d E

where s is the strain in Å/m, E is the electric field in V/m, and d is the strain coefficient

in Å/V. The strain coefficient is characteristic of a given piezoelectric material.

Intrinsic Nonlinearity (from 2% to 25%) Hysteresis (20%)


Hysteresis in the direction perpendicular to the plane of the sample causes erroneous

step-height profiles, as shown in the Figure.

If the scanner is going up a step in the z direction, a certain voltage is required to allow

the scanner to contract.

But going down the same step the scanner extends, and extension takes more voltage

than contraction for the same displacement.

When the SPM image is represented by the voltage applied to the scanner, a profile of

the image would look like the Figure .


When an abrupt change in voltage is applied, the piezoelectric material does not change

dimensions all at once.

Instead, the dimensional change occurs in two steps: the first step takes place in less

than a millisecond, the second on a much longer time scale. The second step, Δxc in is

known as creep.

Creep


Creep As a result, two scans taken at different scan speeds show slightly different length

scales (magnifications) when creep is present.

You can trust only the measurement made at the scan speed that you used to calibrate

your SPM when creep is present.

Typical values of creep range from 1% to 20%, over times ranging from 10 to 100

seconds.

Effects of creep on a step:

Creep may cause an SPM

image to look like it has ridges

on one side of a feature and

shadows on the other side of a

feature.

Reversing the fast-scan direction and taking the same image helps separate creep

artifacts from true ridges and trenches.


The term cross coupling refers to the tendency of x-axis or y-axis scanner movement to

have a spurious z-axis component.

It arises from several sources and is fairly complex.

For example, the electric field is not uniform across the scanner.

The strain fields are not simple constants, but actually complex tensors.

Some "cross talk" occurs between x, y, and z electrodes.

But the largest effect is geometric.

Cross Coupling.


The x-y motion of the scanner tube is produced when one side of the tube shrinks and

the other side expands.

As a result, a piezoelectric tube scans in an arc, not in a plane.

A voltage applied to move the piezoelectric tube along the x or y axis (parallel to the

surface of the sample) necessitates that the scanner extend and contract along the z axis

(perpendicular to the surface of the sample) to keep the tip in contact with the sample.

Cross Coupling.


Cross coupling can cause an SPM to generate a bowl-shaped image of a flat sample. A

profile of such an image is shown in the Figure with an example of a step.

Effects of cross-coupling on a step

Cross Coupling.


Figure shows the sum of the effects of hysteresis, creep, and cross coupling in the

image of a single step. (The aspect ratio of the tip may also contribute to the shape of

the sidewalls: see the next section.)

Effects of hysteresis, creep, and cross coupling on a step.

Atomic Force Microscopy: Cantilevers

V-shaped cantilevers are the most popular, providing low mechanical

resistance to vertical deflection, and high resistance to lateral torsion.

Cantilevers typically range from 100 to 200μm in length, 10 to 40μm in width,

and 0.3 to 2μm in thickness.

Atomic Force Microscopy: Tip shape and resolution

The lateral resolution of an AFM image is determined by two factors: the step size of

the image and the minimum radius of the tip.


In the microscopy community, two asperities (peaks) are considered resolved if the image

satisfies Rayleigh's criterion.

In this application, Rayleigh's criterion requires that the height of the image dip at least 19%

between the asperities.

To determine the lateral resolution of an SPM experimentally, the asperities are brought closer

and closer together until the image no longer dips by 19% between peaks. The minimum

separation between resolved asperities determines the best lateral resolution of the system.

lecture 2 - mipt

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