UNIVERSITY OF HELSINKI REPORT SERIES IN PHYSICS

HU-P-D85

Effect of the Surface on Irradiation Induced

Damage in Covalently Bonded Materials

Jura Tarus

Accelerator LaboratoryDepartment of Physics

Faculty of ScienceUniversity of Helsinki

Helsinki, Finland

ACADEMIC DISSERTATION

To be presented, with the permission of the Faculty of Science of the University of Helsinki, for public

criticism in main Auditorium of the Department of Physics, on May 27th, 2000, at 12 o’clock noon.

HELSINKI 2000

ISBN 951-45-8940-8 (printed version)

ISSN 0356-0961

Helsinki 2000

Tummavuoren kirjapaino

ISBN 951-45-9182-8 (PDF version)

Helsinki 2000

Helsingin yliopiston verkkojulkaisut

1

J. Tarus: Effect of the Surface on Irradiation Induced Damage in Covalently Bonded MaterialsUniversity of Helsinki, 2000, 32 p.+appendices, University of Helsinki Report Series in Physics,HU-P-D85, ISSN 0356-0961, ISBN 951-45-8940-8

Classification (INSPEC): A3410Keywords (INSPEC): Molecular dynamics method, ion implantation, radiation damage

ABSTRACT

The classical molecular dynamics (MD) technique has been used to study ion beam interactions with

covalently bonded materials. By using MD one can obtain detailed information on defect creation

mechanisms and defect structures. The decreasing size of semiconductor devices means that the

ion implantation processing step will increasingly be in the immediate vicinity of the surface of the

devices. This raises the question of how much does the presence of a surface affect defect creation.

This study has concentrated on studying surface or near-surface damage produced by low-energy ions.

As simulations are always only a model of reality their predictions should be tested against experimen-

tal measurements whenever possible. We have tested the validity our simulation model by comparing

simulated and experimental mixing values. Mixing is one of the few experimentally measurable

quantities that depends directly on the outcome of collision cascades.

We have studied the differences between defect production in the bulk material and at the surface

for low-energy bombardment of Si. We have also studied the ion energy dependency of damage

production in that low-energy regime. Using both simulations and experimental measurements we

have also been able to study interstitial migration in Si.

We have also examined the role of chemical effects in ion implantation of materials. We investigated

the differences in defect creation during low energy ion bombardment of GaAs and Ge surfaces, and

carbon erosion by intensive hydrogen bombardment in fusion reactor divertors.

Finally, by using the classical MD method we have investigated the interplay between ion bombard-

ment and strain in Ge. We found a new surface damaging mechanism.

3

CONTENTS

ABSTRACT 1

1 INTRODUCTION 5

2 PURPOSE AND STRUCTURE OF THIS STUDY 6

3 ION BEAM INDUCED DEFECTS IN SOLIDS 8

3.1 Point Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.2 Complex Defects and the Amorphous State . . . . . . . . . . . . . . . . . . . . . . 10

3.3 Defect Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3.1 Defect Recognition in Simulations . . . . . . . . . . . . . . . . . . . . . . . 12

3.3.2 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 PRINCIPLES OF MOLECULAR DYNAMICS SIMULATIONS 14

5 POTENTIAL RELIABILITY IN THE LOW-ENERGY COLLISION REGIME 15

5.1 Static Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.2 Melting Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5.3 Threshold Displacement Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5.4 Ion Beam Induced Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5.5 Repulsive Part Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

6 SURFACE MODIFICATIONS 19

6.1 Ballistic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

6.1.1 Low-energy Bombardment of Si(001) . . . . . . . . . . . . . . . . . . . . . 19

6.1.2 Defect Migration Studies and Microexplosions . . . . . . . . . . . . . . . . 20

6.2 Chemical Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

6.2.1 Comparison of GaAs and Ge Surface Bombardments . . . . . . . . . . . . . 22

6.2.2 Carbon Erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

6.3 Strain Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

7 CONCLUSIONS 26

ACKNOWLEDGEMENTS 27

REFERENCES 28

5

1 INTRODUCTION

The need for faster components in semiconductor technology leads to decreasing sizes of integrated

circuit structures. There are three major reasons behind the need for decreased sizes; shorter charge

carrier paths and thus higher speeds for the components, reduced power consumption and hence also

heat production and increased packaging density leading to lower costs per transistor [1, 2].

Ion implantation is a routinely used method for integrated circuit processing [3, 4]. The main advan-

tage obtained by the use of ion beam doping is that it offers good control of dopant depths and profiles

[3]. The doping process is also highly reproducible. The main disadvantage of this method is that

the energetic ions damage the target material. However, the amorphisation of the bulk material can in

some cases be used as a means of controlling the dopant depths [3]. The processing of ever shallower

junctions is expected to involve implantation of dopants into layers only a few tens of nanometer-

s deep, and ion energies of only a few keV [5, 6]. As the structures get smaller, it is important to

know to what extent the presence of surfaces and interfaces affect the outcome of ion beam induced

collision cascades.

No experimental technique at the moment is able, without great difficulties, to produce a real three-

dimensional (3D) picture of the damage in bulk material nor to probe the collision cascades in situ.

Because of the complexity of this many-body problem, no analytical model is able to solve it, and thus

one has to resort to atomic simulation methods in modelling the collision cascade. The time scales

and system sizes which the classical molecular dynamics (MD) method can handle are ideally suited

for collision cascades studies. The MD method involves solving individual trajectories of atoms and

is thus capable of giving very detailed information.

The first MD simulations were carried out in 1959 by Alder and Wainwright using a very simple model

of hard spheres [7]. This early work has laid the basis for a simulation tool that is still gaining growing

popularity. The numbers of publications per year in the INSPEC database for 1967 - 1998 with the

words “molecular dynamics” anywhere in the abstract, title or keywords are shown in Fig. 1. The

number of publications has increased almost exponentially, showing the usefulness and importance

of MD as a research method.

The MD method has been extensively applied in studies of production and annealing of ion beam

induced lattice defects in bulk semiconductors (see e.g. [8–10]) and ion-beam induced amorphization

of silicon (see e.g. [11–15]). There are quite a few studies of ion bombardment effects at the surface

as well (see e.g. [16–20]).

6

1970 1975 1980 1985 1990 1995Year

0

200

400

600

800

1000

1200

1400

1600N

umbe

rofp

ublic

atio

ns

Figure 1: Number of publications in the INSPEC database for 1967 - 1998 with the words “moleculardynamics” anywhere in the database entry.

2 PURPOSE AND STRUCTURE OF THIS STUDY

The purpose of this study is not to give any direct answers to problems in semiconductor technology,

but rather to explore the basic physics of ion implantation. The main purpose of this study was to

improve the understanding of ion beam induced damage in covalently bonded materials. We placed

emphasis on to the role of the surface in defect creation. By using the classical molecular dynamics

method, it has been possible to get detailed information on defect creation processes and mechanisms.

The reliability of the model has also been tested by comparing experimental and simulated mixing

values. An overview of ion beam induced defects in solids will be given in section 3. Section 4

will give some details of the principles of the MD method. The reliability of model potentials will be

discussed in section 5. Section 6 presents the different surface related effects studied. The conclusions

are given in section 7.

This thesis consist of this preface and the following six publications, published in refereed interna-

tional scientific journals. The articles are referred to by the following Roman numbers in the text.

Summaries of the original papers

Paper I: Effect of surface on defect creation by self-ion bombardment of Si(001), J. Tarus, K.

Nordlund, A. Kuronen and J. Keinonen, Phys. Rev. B 58, 9907 (1998).

7

In this paper we studied the role of the surface on low-energy self-ion bombardment of the

Si(001) surface. To deduce the role of the surface a comparison was made with collision

cascade simulations in the bulk material. Emphasis was laid on getting a statistically reliable

picture by simulating a large number of events. Furthermore, we also determined threshold

displacement energies both in the bulk and at the surface and the melting point of silicon

predicted by the Tersoff potential.

Paper II: Heat spike and ballistic contributions to mixing is Si, J. Tarus, K. Nordlund, J. Sillanpaa

and J. Keinonen, Nucl. Instr. Meth. Phys. Res. B 153, 378 (1999).

The atomic mixing in silicon was modelled in this paper. The fairly good agreement between

simulated and experimental values serves as a validation of our simulation procedure. We

found that the heat spike contribution to the total mixing is much lower than that of ballistic

collisions.

Paper III: Surface defects and bulk defect migration produced by ion bombardment of Si(001),K. Kyuno, David C. Cahill, R. S. Averback, J. Tarus and K. Nordlund, Phys. Rev. Lett. 83, 4788

(1999).

We studied point defect creation and diffusion in the topmost layers of the 2 � 1 terminated

Si(100) surface under 4.5 keV He atom bombardment by both experimental and simulation

methods. The aim of this work was to find the threshold temperatures of vacancy and inter-

stitial mobility. We simulated the initial defect concentration on the surface, compared the

scanning tunneling results to them and found the interstitial migration threshold to be between

130 and 180 K.

Paper IV: Defect creation by low-energy ion bombardment on GaAs (001) and Ge (001) sur-faces, A. Kuronen, J. Tarus and K. Nordlund, Nucl. Instr. Meth. Phys. Res. B 153, 209 (1999).

The aim of this study was to determine the differences in defect creation on 50 eV ion bom-

bardment of GaAs and Ge surfaces. Furthermore, the model potential properties of the GaAs

surface was studied. It was found that, despite Ga, As and Ge having similar masses and both

materials having the same lattice structure, there were considerable differences in the final

defect distribution of different defect species. This illustrates the role of chemical effects in

low-energy ion bombardment.

Paper V: Suppression of carbon erosion by hydrogen shielding during high-flux hydrogen bom-bardment, E. Salonen, K. Nordlund, J. Tarus, T. Ahlgren and J. Keinonen and C. H. Wu Phys. Rev.

B (Rapid Comm.) 60, 14005 (1999).

Some recent experimental measurements have shown that the erosion of carbon by intensive

hydrogen bombardment decreases sharply at very high fluxes ( � 1019 ions/cm2s). No previous

8

model has been able to explain this fact. The MD method is very well suited to this kind of

problems and by using it we were able to show that the reason for the decreased erosion yield

is the buildup of a high hydrogen content at the surface, leading to a shielding of carbon atoms

by the hydrogen.

Paper VI: Strain effects in Ge surface cascades, J. Tarus, K. Nordlund, J. Keinonen and R. S.

Averback, Nucl. Instr. Meth. Phys. Res. B 164-165, 482 (2000)

Strained SiGe is a promising future material for integrated circuit devices due to its easy

bandgap altering and its high electronic speed compared to Si. We studied how the strain

affects the outcome of a collision cascade. As a case study we performed simulations of ion

bombardment of strained Ge. We found that large adatom islands are formed on top of the

amorphous zones created by the cascades. Strain relief was also detected in the samples as the

lattice atoms around the molten zone moved radially inwards.

3 ION BEAM INDUCED DEFECTS IN SOLIDS

As an ion1 penetrates into a medium it immediately starts to interact with it. The interactions can

be divided into elastic and inelastic collisions [21]. The first one is called nuclear and the latter the

electronic stopping power. Hence, the energy loss per unit length can be written as

�dEdx � total �

�dEdx � nuclear �

�dEdx � electronic � (1)

Which one of the two contributions, the electronic or nuclear stopping power, is dominant depends on

the velocity and the mass of the ion, and on the density of the medium. At high energies the electronic

one dominates, whereas at low energies the nuclear one becomes more important (see Fig. 2). At the

energies used in this study the slowing down of the projectile is governed by the nuclear stopping

power.

The events caused by ion bombardment can be separated into three different phases [23, 24]. As the

kinetic energy is transfered to target atoms, they can be removed from their original sites and collide

with other atoms. This phase, where violent collisions take place is called the collision phase and

depending on the ion and target atom masses and the energy of the ion, typically lasts 0.1–1 ps. The

energy is deposited to the atoms close to the path of the projectile.1To distinguish the target and projectile atoms the incoming projectile is referred to as an ion in this study, even though

there are no charge states in classical MD simulations.

9

0.01 0.1 1 10 100

Velocity of the Ion(v0)

0.01

0.1

1

10

Stop

ping

pow

er(k

eV/n

m) 10

-410

-310

-210

-110

010

110

210

3

Energy of the Ion (MeV)

I II III IV

Figure 2: Stopping power of silicon for 28Si [21, 22]. The solid line represents the electronic and thedashed line the nuclear stopping power. v0 is the Bohr velocity ( � c

�137, c is the velocity of light).

The deposited energy is then transfered further into the surrounding matter by heat conductivity. This

liquid-like phase, where the local temperature differences are evened, is called the thermal spike and

it lasts about 5–50 ps [25, 26].

After the thermal spike the target configuration is usually distorted, and from now on the evolution of

the system is governed by temperature activated relaxation and diffusion processes, when the atoms

seek the minimum energy configuration. This so called relaxation phase can last the lifetime of a

device.

3.1 Point Defects

There is usually an inherent concentration of point defects in semiconductor materials, because of the

thermal movement of atoms. Defects produced in this way are usually uniformly distributed in the

material. When an ion penetrates into the medium, it interacts with the lattice atoms and energy is

transfered to them. If the transfered energy is high enough, the lattice is damaged and the damage is

usually contained in a fairly small volume. Depending on the energy and mass of the projectile, either

point defects or larger distortions are produced. Simple point defects can be classified as follows [27]

1. An atom is called an interstitial if it is located somewhere else in the lattice than at the lattice

10

a b

c

d

e

f

Figure 3: Simple point defects: (a) self-interstitial , (b) interstitial impurity, (c) vacancy, (d) divacancy,(e) substitutional impurity, (f) vacancy-substitutional impurity complex and (a)+(c) Frenkel pair.

site. If it is of another species than the lattice atoms, it is called an impurity interstitial, and if it

is not, it is called a self-interstitial.

2. The defect is called a vacancy (also sometimes called a Schottky defect) if an atom is missing

from a regular lattice site.

3. An impurity can be in a lattice site.

The lattice around point defects is always somewhat distorted, and sometimes it is impossible to tell

whether an atom is a lattice or a defect atom. This is the case in the minimum energy interstitial

configuration in Si. It has been found to be a so called split interstitial configuration; the interstitial

and one of its neighbours form a dumbbell which is centered on the original site of this lattice atom

with various configurations (see Fig. 4) [27]. The�110 � -dumbbell has been found to be energetically

the most favourable [28].

Naturally, there can also be defects on the surface. A vacancy is defined in the same way as in the

bulk, and an extra atom on the surface is called an adatom.

3.2 Complex Defects and the Amorphous State

Combinations of point defects can also be formed. If the medium contains a large number of particular

defects, they tend to form clusters if the temperature is high enough for defect migration. Vacancies

can form divacancies, trivacancies and so on. Large clusters can arrange themselves into the shape of

chains, rings or platelets [27] (see Fig. 5). In Si interstitials often form rodlike � 311 � defects [30]. On

11

Figure 4: Different kinds of split-interstitial configurations: (a)�110 � dumbbell, (b)

�100 � dumbbell

and (c)�111 � dumbbell [29].

Si(001) surfaces, vacancies are predominantly missing dimer vacancies (MDV) [31], i.e. two atoms

missing from a reconstructed dimer site. At high temperatures the MDVs can form vacancy islands

or clusters with longer axis parallel to the dimer rows [32].

A lattice can also be so strongly distorted, i.e. it has no long-range order, that it cannot anymore

be considered to contain point defects, but should be considered as amorphous material. A perfect

diamond crystal consists of six-membered atom rings, whereas amorphous material is thought also to

contain five- and seven-membered rings [29].

Ion beam induced surface damage mechanisms (excluding chemical effects) have previously been

identified to four different classes [16, 33]. The first one is sputtering, which is simply caused by

kinetic energy transfer. The second mechanism is liquid flow onto the surface. Microexplosions

are considered to be the third mechanism, and coherent displacement the fourth. Liquid flow can

occur when the liquid produced by the collision cascade is connected to the surface so that the atoms

can flow onto the surface. Microexplosions occur when a liquid is formed near the surface, and the

expansion of this liquid makes the surface crack and clusters of atoms sputter. Coherent displacement

happens due to the same liquid expansion; this time the pressure created inside the bulk forces atoms

above it to slip along lattice planes leading to nicely formed adatom terraces on the surface. The first

mechanism has been known for a long time and even simple binary collision methods model it with

high accuracy [34]. The MD simulations, however, have revealed the real complexity of ion beam

12

Figure 5: The configuration in the�110 � multivacancy chain case (projected onto the (110) plane)

[29]. The bonds in non-six-membered atom rings are emphasized.

induced effects at the surface, and described the last three mechanisms. As it will be shown later in

the text, there is one more mechanism for surface damage production.

3.3 Defect Analysis

3.3.1 Defect Recognition in Simulations

There are various methods to detect defects in atomistic models of solids. One way is to detect the

potential energy of the atoms and declare those atoms whose energy is far enough from crystalline

energies to be defects. The presence of the surface makes the use of the energy analysis complicat-

ed. There are two very straightforward geometrical methods to analyze the defects in the sample,

namely the Wigner-Seitz (WS) cell method and a method based on the Lindemann radius [35, 36].

Both compare the final configuration to the initial configuration and thus the surface reconstruction is

automatically taken into account.

The WS method is based on dividing the volume of the lattice into primitive cells. As the name

implies they are Wigner-Seitz cells [37]. In this method a vacancy is identified when a primitive cell

of the lattice is empty and one interstitial or more are identified when there are more than one atom in

a cell.

13

Another way is to use the Lindemann radius, i.e. the amplitude of lattice vibrations of atoms at the

melting point. A vacancy is identified if there is no atom within the Lindemann radius from the lattice

point. All the atoms outside these spheres are labelled as interstitials.

The difference between these two methods is that the Wigner-Seitz cells are space-filling, whereas

Lindemann spheres are not. The WS method works well only when there are separated point defects,

whereas the Lindemann radius method is very sensitive for displacements in the lattice and is therefore

suited for detecting the amount of disorder in the lattice. Neither of the methods tells anything about

the final lattice structure. In addition, as these methods are based on the initial configuration of

atoms, they are not suited for cases where the initial lattice is under strain, and lattice atoms can move

noticeably and still remain in a perfect crystalline configuration.

In cases of high ion energies which result in amorphous pockets in the medium, one needs different

kinds of methods. On these occasions we have applied the structural order parameter procedure

[15, 38]. In this method the angles between the neighbours of an atom are used to recognize whether

the atom is in a crystalline or distorted neighbourhood.

3.3.2 Experimental Methods

There are many experimental methods for studying defect structures in solids, including such as

Diffusive Scattering of X-rays or neutrons (DXS), Extended X-ray Absorption Fine Structure (EX-

AFS), Positron Annihilation Spectroscopy (PAS), ion channeling, Transmission Electron Microscopy

(TEM) and Field Ion Microscopy (FIM) [39]. These all have their own strengths and weaknesses.

EXAFS gives information of the nearest neighbourhood of the defect but not of large defect struc-

tures, PAS detects only vacancies and channeling only detects interstitials in a crystalline structure.

DXS, TEM and FIM can in principle give a 3D picture of different defect structures in the bulk, but

there are numerous practical difficulties in their use.

As can be seen above there is no straightforward experimental way for studying ion beam induced

defect structures in solids, leaving simulations as a very valuable tool for these purposes.

On the surface, the situation is somewhat better mainly because of Scanning Tunneling Microscopy

(STM) and Atomic Force Microscopy (AFM). By applying these methods one can achieve almost an

atomic scale picture of the surface 2. The oxidation of the surface in some cases complicates the direct

observation of ion induced damage and the diffusion of defects also complicates the observation of

intermediate defect structures. Nevertheless, as will be seen later in the text, these experimental and

2To be precise these methods do not yield an atomic, but an electronic structure.

14

simulation methods can be used complementarily to get a good picture of the properties of ion beam

induced defects.

4 PRINCIPLES OF MOLECULAR DYNAMICS SIMULA-TIONS

In an MD simulation the evolution of an ensemble of atoms is followed by solving iteratively the

equations of motion. Thus, we get the evolution of the system, i.e. the trajectories of this ensemble of

atoms, in time. This gives very detailed information on the phenomenon studied.

In the simulations the atoms interact via a model potential. When we calculate the forces, the atoms

are treated as if they were fixed in their positions and the electron configuration is the ground state

configuration. This treatment can be justified by the Born-Oppenheimer approximation (adiabatic

approximation) [40]. This approximation is based on the fact that the velocities of the electrons are

much higher than the velocities of atoms. The typical electronic velocity is � 106 m/s [41], whereas

the velocity of a Si lattice atom at 300 K is � 500 m/s, so it is reasonable to assume that at a particular

atomic configuration all the electrons will be in their ground state. The velocity of a Si ion with an

energy of, say, 100 eV is of course much higher ( � 104 m/s), but with higher energies the effect of

the attractive part of the potential is very small , the projectile interacts mainly via the repulsive part

of the potential in which the outer electrons, which may not be in their ground state, do not contribute

significantly.

Since we use full MD simulations, we cannot use too high energies for the projectiles, as the penetra-

tion ranges would become too high, requiring large boxes and thus the updating of the atom positions

would become very slow. The present computer facilities limit the size of a system to a few million

atoms and ion energies to about a couple of hundreds of keVs. Also, because of the small time step

required ( � 10� 15 s) in MD simulations to get a realistic behaviour for the system, MD can be used to

get information of processes taking place in the system with time scales only of the order of nanosec-

onds. However, as the cascades produced by the collisions of the projectile do not typically last more

than a couple of picoseconds (or less), so MD is ideally suited to study these processes [42].

As only a small part of the material is used in simulations, we have to model the presence of the

surrounding bulk somehow. This is done by setting periodic boundary conditions to the simulation

box. In the presence of a surface, the bottom atoms of the box are usually fixed. The heat conductivity

to the bulk is modelled by setting some sort of energy drains to all box sides except the surface. To

15

decrease the simulation time and to remove thermal deviations, the temperature of the box is also

quenched down after the collision cascade has settled.

The electronic stopping of moving atoms is usually taken into account as a non-local frictional force.

The usual procedure for our collision cascade simulations is first to create a simulation box with the

right surface reconstruction, and relax it. Then to gain adequate statistics, independent ions are shot

into the box by varying either the starting point or angles of each ion, or both.

5 POTENTIAL RELIABILITY IN THE LOW-ENERGY COL-LISION REGIME

5.1 Static Properties

A simulation is always a limited model of reality. In general there are numerous factors that affect

how well the model describes the phenomenon studied. When considering collision cascades simu-

lated by the classical MD method, the main error source is the model potential which describes the

interactions between atoms. Semiempirical potentials used in the classical MD simulations are fit

to some number of experimental or ab initio calculation data. The amount of fitting data is always

limited, and usually only near-equilibrium properties are used. Very basic properties, such as bond

lengths, binding energies, elastic constants etc. are very well defined, but data for some other prop-

erties, such as defect energies, is somewhat spread. This contributes to complicating the construction

of model potentials.

There is a large number of model potentials for Si and Ge, but the most commonly ones used are

the Stillinger-Weber (SW) [43] and the Tersoff [44] potentials. Balamane et al. have made a fairly

comprehensive comparison of these two and other potentials for Si [45]. In conclusion, they noted

that all the potentials give a good description of some properties but none of them can be considered to

be superior to the others. Thus, one should always find the potential that is best suited for a particular

problem. This, of course, involves testing of the potentials.

From a fundamental point of view the difference between SW and Tersoff potentials is that the SW

potential is fitted only to the tetrahedral configuration and thus penalizes non-tetrahedral bonding

types. On the contrast, the Tersoff potential is fitted, in addition to the diamond structure, to over- and

under-coordinated configurations, and thus is expected to give a fairly good description of collision

16

0 1 2 3 4 5

r(A)

-5

0

5

10

15

20

25

4r2

(r)(

A-1

)

TersoffSWExp.

Figure 6: Experimental radial distribution function of amorphous Si0 � 5Ge0 � 5 compared with the onespredicted by the SW and Tersoff potentials. Experimental data is from Ref. [46]. We can see theincapability of the SW potential to reproduce the amorphous structure.

cascades. The inability of the SW potential to describe non-tetrahedral structures can be seen from

pair-correlation function of amorphous Si0 � 5Ge0 � 5 in Fig. 6.

5.2 Melting Point

So far we have only considered equilibrium properties. As ion bombardment is always a very dy-

namical process far from thermodynamical equilibrium, one should take dynamical properties into

account as well. One dynamical property usually checked is the melting point. In paper I we deter-

mined the melting point of Si predicted with the Tersoff potential. Even though there were already

some studies on this subject, we felt it was important to redo this, the reason being that in most of

the previous work it was done improperly, for example by using constant volume in the simulations.

Melting usually starts from surfaces and interfaces, and thus when comparing experimental and simu-

lated melting points, one should include such discontinuities to the simulation box to avoid over- and

undercooling problems. The method we used was the one discussed in detail by Morris et al. [47]; by

determining the temperature where a liquid and solid co-exist in equilibrium in the same simulation

cell, one should get a value that is comparable to experimental values. Our result was 2450�

50 K,

17

which is somewhat lower than what has been been proposed in other studies [44, 45, 48, 49], but it is

still considerably higher than the experimental value of 1683 K [50].

Thus the melting point of Si predicted by the Tersoff potential is not correct, whereas the SW potential

has about the right melting point [45]. It has been shown that the melting point has a large effect on

damage production in semiconductors [9]. Hence in cases where melting has a major influence on the

outcome of the simulation, one should rather use the SW than the Tersoff potential.

5.3 Threshold Displacement Energy

One dynamical property that is quite extensively studied both by experiments and simulations is the

threshold displacement energy, i.e. the energy required to remove the atom from its lattice site. We

calculated the displacement energies in the�001 � direction both in the bulk and at the surface [I]. It

was found that even though close vacancy-interstitial pairs are formed at lower energies in the bulk,

the actual replacement process which leads to a stable configuration takes place in both cases at about

16 eV. This value is within the experimentally measured range of 11–30 eV [51–54]. This indicates

that the model works well on a basic level but as the experimentally measured data is so dispersed

any definite conclusions of the accuracy of the potential is hard to draw.

5.4 Ion Beam Induced Mixing

There are very few experimentally measurable quantities that depend directly on the outcome of

collision cascades. The ion beam induced relocation of atoms, which is called ion beam mixing, is

one of those. By direct comparison of experimental and simulated values one can test the reliability of

the simulation model. So far the problem preventing this comparison has been that the high energies

used in the experiments have been beyond simulation capabilities.

In paper II we calculated the mixing produced by five different ion beams in amorphous silicon. The

primary recoil spectrum was obtained by simulating the interactions between the ions and target atoms

with an MD method which enables fast calculation of the slowing down of ions. Full MD simulations

were then used to simulate the mixing at various energies, giving the total atom relocation as a function

of energy. We developed a cumulative method to calculate the mixing at high energies ( � 10 keV).

Integration of the primary recoil spectrum weighted by the atom relocation gave simulated mixing

values directly comparable with experimental data.

18

Table 1: Simulated and experimental mixing parameter, Q, values.

Ion (energy) Qsim Qexp

(A5/eV) (A5/eV)

Ne (50 keV) 22�

3 40�

13a

Ar (110 keV) 33�

5 25�

9a

Ar (110 keV) 36�

5 58�

32b

Kr (220 keV) 45�

7 34�

6a

Xe (300 keV) 52�

8 44�

7a

a Ref. [56]b Ref. [57]

The simulations reproduced the experimental results to within the uncertainties, showing that the

MD simulations give a reasonable description of the ballistic properties of the collision cascade. We

found that the heat spike contribution to the total mixing seems to be much lower than that of ballistic

collisions. This is in contrast to what has been obtained in dense fcc metals, where the mixing has

been found to be derived predominantly from the heat spike [55].

5.5 Repulsive Part Correction

When atoms are nearby each others, neither the SW nor the Tersoff potential is valid anymore, since

they have been calculated using properties in or near equilibrium. Because we are dealing with ion

bombardment, there are strong collisions during the cascade, in which the configurations are far from

equilibrium. To treat the strong repulsive interaction between atoms at small distances, a database

calculated with the program package DMol [58], which is based on the density-functional theory

[59, 60], was used.

The original potential, Vorig, and the correction part, Vcorr, were smoothly joined together using a

Fermi function F�r � � �

1 � e� b f � r � r f � � � 1

Vtot � F�r � Vorig � �

1 � F�r ��� Vcorr � (2)

The values for b f and r f were chosen so that the potential remained smooth and the equilibrium part

of the potential was not changed.

19

Table 2: Results for surface cascades. Upper part: The average number of defects per one ion afterquenching. Lower part: The number of defects per eV (normalized to the 100 eV case).

Energy (eV) Vacancies Interstitials Adatoms Sputtered

25 0.25�

0.05 0.92�

0.05 0.31�

0.05 0.019�

0.01350 0.81

�0.08 1.39

�0.06 0.42

�0.06 0.007

�0.007

100 2.09�

0.15 2.41�

0.10 0.65�

0.08 0.034�

0.017200 4.79

�0.17 4.77

�0.13 0.92

�0.12 0.10

�0.03

400 9.51�

0.36 8.92�

0.30 1.37�

0.19 0.22�

0.06800 17.03

�0.43 16.13

�0.37 1.55

�0.21 0.35

�0.08

25 0.48 1.53 1.91 2.2450 0.78 1.15 1.29 0.41100 1 1 1 1200 1.14 0.99 0.71 1.47400 1.13 0.92 0.53 1.62800 1.02 0.84 0.30 1.29

6 SURFACE MODIFICATIONS

6.1 Ballistic Effects

6.1.1 Low-energy Bombardment of Si(001)

As noted earlier, there are quite a few studies of low energy ion beam interactions with semiconductor

surfaces. These studies, however, have usually been limited to the effects of one energy. In paper I

we present simulations where the main aim was to study the role of the surface in defect production

in low-energy self-ion bombardment of the Si(001)2 � 1 surface at several different energies below

1 keV. To deduce the role of the surface, we also simulated collision cascades in the bulk.

In order to get good statistics we calculated around 100 recoil events for most energies, both in the

bulk and at the surface. The potential that we used in this study was the Tersoff potential [44]. As

discussed already, it does predict the wrong melting point for Si, but as no real molten zones are

produced at these low energies, this should not be a significant problem.

As a result we found that the vacancy production at the surface is a superlinear function of energy

below 400 eV, i.e. the number of vacancies per incoming eV is higher at higher energies (see Table 2).

The same superlinearity was found also in the bulk (see Table 3). This superlinearity extends to higher

energies than could be expected on the basis of the Kinchin-Pease formula [61]. The defect production

20

Table 3: Damage production in bulk cascades. Upper part: The average number of defects per oneion after quenching. Lower part: The number of defects per eV (normalized to the 100 eV case, asthe 50 eV case is strongly affected by the low-energy Frenkel pair production).

Energy (eV) Vacancies Interstitials

50 1.15�

0.04 1.15�

0.04100 2.02

�0.07 2.02

�0.07

200 4.28�

0.11 4.28�

0.11400 8.98

�0.15 8.98

�0.15

800 16.27�

0.19 16.27�

0.19

50 1.14 1.14100 1 1200 1.06 1.06400 1.11 1.11800 1.01 1.01

becomes linear at energies higher than 400 eV, in agreement with previously found linearity at keV

energies [9].

The direct comparison of bulk and surface defects is somewhat complicated, as in the case of surface

bombardment an extra atom was introduced into the lattice, whereas in the bulk case a lattice atom

was used as a recoil ion. Despite the difficulties, we can see that defect production is somewhat

affected by the presence of the surface at least up to an energy of 1 keV. This is due to the fact that the

bond energy of a surface atom is significantly lower than that of a bulk atom and a large part of the

vacancies are produced in the surface layer (see Fig. 7). The difference in the numbers is less than

20% at 100 eV and only about 5% at 800 eV.

6.1.2 Defect Migration Studies and Microexplosions

Even though silicon, due to its central role in integrated circuit technology, has been studied quite

extensively, some of its very fundamental features are still unknown. One such property is the thresh-

old temperature of defect migration. The diffusion of impurities and dopants in solids are usually

governed by the properties of point defects. In paper III we utilised both experimental and simulation

methods to address this problem.

A Si(001)2 � 1 surface was bombarded with 4.5 keV He ions. The initial defect production on the

surface and also the defect distribution near the surface was obtained from MD simulations. As the

21

0 10 20 30 40 500.0

0.1

0.2

0.3

0.4

0.5

interstitialsvacancies50 eV

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0

Num

bero

fdef

ects

interstitialsvacancies200 eV

0 10 20 30 40 50

Layer

0.0

0.2

0.4

0.6

0.8

1.0

1.2

interstitialsvacancies800 eV

Figure 7: Defect probability distribution over the layers for 50, 200 and 800 eV recoils. The surfaceis layer 0. The lines are drawn to guide the eye.

bulk defects can diffuse to the surface and change its morphology [62] the surface of a bombarded

Si sample was scanned by STM measurements at various temperatures to detect the surfacing of

defects. There are usually many vacancies at the surface, but adatoms are seldom observed and thus

the analysis and discussions focused on adatoms. The surface protrusion found in the STM study are

referred to as bright spots because it is not possible to distinguish individual adatoms. We found that

the number of the bright spots at temperatures of 80 and 130 K are independent of temperature, but at

180 K the density of the spots was increased by a factor of � 3. From MD calculation we can estimate

that the increase is explained by interstitials within � 2 nm of the surface which migrate to the surface.

We also found, to some surprise, that despite the low mass of helium small micro-explosions can take

place on the surface. Up to 9 adatoms and 8 surface layer vacancies were produced, thus leaving

craters that should be experimentally visible (see Fig. 8).

22

Figure 8: A crater created on top of Si(001) by a 4.5 keV He ion.

6.2 Chemical Effects

6.2.1 Comparison of GaAs and Ge Surface Bombardments

The comparison of defect production in different materials can reveal how different chemical struc-

tures and bonds affect the outcome of collision cascades. For example, it has been shown previously

that the crystal structure has a large effect on many damage production processes [9].

In paper IV we studied the difference in defect production between GaAs and Ge. All the elements

involved have about the same mass and both materials have the same structure, so ballistic effects

should be virtually the same. As the recoil energy was low (50 eV), only point defects were expected

to be produced, and thus the WS method was used for defect analysis.

The interactions were modelled with different parameter sets of the Tersoff potential [63, 64]. The

importance of proper testing of the model potentials became underlined in this study. It was found

that the surface reconstruction of GaAs was unstable when the original parameter set was used. For-

tunately, by a small change in one parameter, the surface was made stable without changing any other

equilibrium properties.

The total number of defects produced was found to be almost exactly the same in GaAs as in Ge. Thus

we can say that the defect production is mainly a ballistic phenomenon. The final defect distribution

among the defect species, however, was found to be very different in these two cases. The number of

interstitials was considerably lower in GaAs than in Ge, whereas more adatoms and sputtered atoms

23

Table 4: Number of defects after quenching on bombardment of 2 � 1 reconstructed GaAs and Gesurfaces

System Vacancies Interstitials Adatoms Sputtered Events

Ge � Ge 0.78�

0.06 1.26�

0.04 0.50�

0.06 0.02�

0.01 210Ga � GaAs 0.78

�0.06 0.85

�0.05 0.85

�0.06 0.09

�0.02 200

were observed in the case of GaAs. The time dependence of defect numbers was also different. The

number of interstitials reaches a constant value faster in GaAs than in Ge, whereas the other defects

reach the equilibrium value later on. These facts indicate that there is a driving force in GaAs that

causes the initially formed interstitials to migrate to the surface and form adatoms. Hence we can

conclude that the differences between damage production in GaAs and Ge illustrate the role which

chemical effects can have in low-energy ion irradiation.

6.2.2 Carbon Erosion

In paper V we studied carbon erosion by intensive hydrogen bombardment. A central problem in the

development of a commercially viable fusion reactor is finding a suitable material for the divertor in

the reactor. The divertor section of the reactor first wall is subject to the most intense erosion. Since

the impurities will eventually lead to the extinction of the plasma, it is of utmost importance to find a

divertor material with optimal capability to withstand radiation damage and erosion.

The most promising divertor materials found to date are all based on carbon, the reason being its low

atomic mass and strong atomic bonding. Yet even the carbon-based materials erode substantially by

several different and poorly understood mechanisms. Some recent experimental measurements have

shown that the erosion of carbon by intensive hydrogen bombardment decreases sharply at very high

fluxes ( � 1019 ions/cm2s) [65, 66]. Previous models had not been able to explain this effect. This

problem cannot be handled as a purely ballistic problem, as the entering hydrogen atoms change the

chemistry of the surface. Thus the MD method is very well suited to study this problem and in fact is

probably the only available method at this time. Even though the MD method is not suited for studying

macroscopic erosion, it can give detailed information on the microscopic erosion mechanisms.

To mimic the conditions in the nuclear reactor, we first created an amorphous hydrogenated carbon

(a-C:H) structure with an H:C ratio of about 0.4, similar to the material found in divertors after the

reactor operation. We then simulated the sputtering and etching caused by 1 and 10 eV H, D and

24

0 1000 2000 3000 4000 5000 6000

Number of incident H

-2.0

-1.8

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0<

z>(A

)

0 1000 2000 3000 4000 5000 6000

150

155

160

165

170

175

180

185

190

NH

Average depth <z> of H atomsNumber of H atoms

Figure 9: The number and average depth of the hydrogen ions in a cumulative run of H bombardmentof a-C:H. The figure shows a fast hydrogen buildup on the surface leading to supersaturation.

T recoils impinging on this material, and studied how the a-C:H structure changed with multiple

impacts.

The results showed that during prolonged irradiation the hydrogen content in the samples saturated

due to a buildup of H in the surface layers (see Fig. 9), leading to a decreased H capture cross section.

This indicates that the T inventory in the first wall will decrease, and will also lead to a lower carbon

etching probability, which are crucial factors for the durability of the material in the reactor.

These two studies demonstrate the role of chemical effects in ion bombardment of materials. They

also show that the classical MD is very well suited for studying problems where chemical effects are

present.

6.3 Strain Effects

SiGe is a very interesting material because of its technological applications. Heterojunctions formed

with SiGe have many benefits over conventional homojunction approaches. One of the advantages is

that the bandgap can be altered by changing the proportion of the Ge content and strain caused by

the lattice mismatch [67]. SiGe is also faster than Si in terms of carrier mobility [2]. Development

in epitaxial growth methods, such as ultra-high vacuum chemical vapour deposition (UHV/CVD),

25

Figure 10: A top view of one cascade event. Initial and final positions of atoms that have moved morethan 0.5 A are joined. Strain relief seems to favour the

�110 � direction and this results in a four-leaf

clover pattern on the surface in case of symmetrical amorphous zone.

has enabled rapid production of highly uniform SiGe structures [68]. It has been found that ion

implantation of strained SiGe can cause strain relaxation [69]. Equally, as the ion bombardment can

change the strain in the sample, the strain can affect the outcome of a collision cascade.

We decided to approach this problem with a case study of 5 keV Xe bombardment of strained Ge

[VI]. Thick strained Ge layers cannot be formed experimentally. However, sometimes a non-reality

based case can be a more efficient way to start, than a study that directly reflects reality, as the effects

of interest can be more distinct in them. This time the (modified) Stilliger-Weber potential [9] for

Ge–Ge interactions was used, as the liquid material had a large role in this problem.

We found that large adatom islands are produced on top of amorphous zones. We also found that

lattice atoms around the molten zone move radially inwards and thus cause strain relief in the sample

(see Fig. 10). The strain was increased perpendicular to the surface, which has also been found

experimentally [69]. The mechanism for adatom island creation is as follows: During the collision

cascade, a liquid volume is first formed. As the atomic volume of the liquid atoms is somewhat

smaller than the atomic volumes in the surrounding lattice, the lattice atoms relax radially inwards to

the soft liquid core, causing the pressure in the liquid to rise. As the liquid cools, the transition to the

amorphous phase further increases the pressure owing to its lower density, causing formation of an

26

adatom island on the surface. At the same time atoms below the amorphous zone are pushed deeper

into the bulk and thus create strain in the z -direction.

Clearly none of the previously mentioned four surface damage mechanisms can explain the observed

phenomenon. The formation of adatom islands by nucleation of single adatoms and small adatom

clusters has been known for a long time, but in this case a large single adatom cluster is formed by

collective movement of the atoms to the surface. Thus, this phenomenon can be classified as the fifth

surface damage creation mechanism.

Preliminary tests show that the effect is also present in SiGe, although it is a lot weaker than in Ge.

7 CONCLUSIONS

It has been shown that the MD method is a very versatile tool for examining ion implantation caused

effects in covalently bonded materials. The method has been used for determining energy depen-

dences in defect production, defect migration in conjunction with experiments, mixing, chemical

reactions and strain effect on collision cascades.

The results from MD simulations may not be considered, mainly because of the limitations of the

potential models, to be quite correct at the quantitative level. However, the results demonstrate that

the MD method can be used powerfully to look for, for example, energy dependences or damage

creation mechanisms.

We have found that the vacancy production at low energies in Si is a superlinear function of energy.

It has also been found that the threshold temperature for interstitial migration is Si is between 130

and 180 K. We have shown that there are definite differences in damage creation in GaAs and Ge.

The decrease of carbon erosion at high hydrogen bombardment fluxes was found to originate from

hydrogen buildup at the carbon surface. We have also found a new damage creation mechanism in

strained Ge which cannot be attribute to ballistic effects.

27

ACKNOWLEDGEMENTS

This study was carried out at the Accelerator Laboratory between the years 1996 and 2000. I wish to

thank the former and current heads of the laboratory, Doc. Armas Fontell, Doc. Jyrki Raisanen and

Doc. Eero Rauhala for placing the facilities of the laboratory at my disposal.

I am grateful for my supervisor, Prof. Juhani Keinonen, the head of the Department of Physics, for

the guidance and advice during this work.

My special thanks are due to Prof. Kai Nordlund, who has been the driving force for me to get this

work done. I thank both Kai and Doc. Antti Kuronen for demystifying the wonders of molecular

dynamics for me. I also wish to thank all my co-authors and colleagues at the Accelerator Laboratory

for the informative discussions and refreshing moments we have had.

My warmest thanks are due to my wife, Tiina, who has given all the love and support during these

years.

Financial support from the Academy of Finland and Magnus Ehrnrooth foundation is gratefully ac-

knowledged.

Helsinki, May 2000

Jura Tarus

28

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