A realistic potential energy function comprising angle dependent terms was employed to describe the potential surface of the N+O2 system. The potential energy parameters were obtained from high level ab-initio results using a nonlinear fitting procedure. It was shown that the potential function is able to reproduce a large number of points on the potential surface with a small rms deviation. A literature survey was conducted to analyze exclusively the status of current small cluster research. This survey turned out to be quite useful in understanding and finding out the existing relationship between theoretical as well as experimental investigative techniques employed by different researchers. Additionally, the importance of the role played by computer simulation in small cluster research, was documented

Halicioglu, Timur

English

Three different investigations based on computer simulations were carried out. Simulation calculations were performed using model potentials with two- and three-body interactions which were represented by the Mie and the Axilrod-Teller potentials, respectively. In the first part, to analyze stability criteria for simple crystals, a parametrical investigation was performed and stability regions for five different crystalline structures were determined with respect to potential energy parameters. To simulate some of the basic surface processes such as diffusion and nucleation, in the second and third parts, silicon surfaces were considered as a specific example. In these studies diffusion of adatoms on stepped surfaces were simulated and energetics associated with the formation of kink sites were calculated

NASA Technical Reports Server

. 
cr2 SIMULATION STUDIES FOR SURFACES AND M A T E R I A L S  STRENGTH 
Semi-Annual Report 
for 
Cooperative Agreement NCC2-297 
for the period 
November 1 ,  1986 - April 30, 1987 
Submitted to 
National Aeronautics and Space Administration 
Ames Research Center 
Moffett Field, California 94305 
Computational Chemistry Branch 
Dr. David Cooper, Chief and Technical Monitor 
Thermosciences Division 
Dr. Jim Arnold, Chief 
Prepared by 
ELORET INSTITUTE 
3788 Fabian Way 
Phone: 408 730-8422 and 415 493-4710 
Palo Alto, CA 94303 
K. Heinemann, President and Grant Administrator 
Timur Halicioglu, Principal Investigator 
(tiASA-Ca-180539) I S I E U L A T I C I  SIUCIES FOR N87-22277 
SUBPACES A N D  HAIERIALS STEENG1IP Semiannual 
iieport, 1 Hov. 1466 - 30 Apr- 1987 (Bloret 
Corp.) 13 p Ava i l :  "XIS EIC AOz/HF A 0 1  U n c l a s  I CSCL 20K G3/39 007U105 
https://ntrs.nasa.gov/search.jsp?R=19870012844 2020-03-20T11:50:30+00:00Z
Three different investigations based on computer simulations were carried out 
during this period. Simulation calculations were performed using model potentials 
with two- and three-body interactions which were represented by the Mie and the 
Axilrod-Teller potentials, respectively. In the first part, to analyze stability criteria 
for simple crystals, a parametrical investigation was carried out and stability regions 
for five different crystalline structures were determined with respect to potential 
energy parameters. To simulate some of the basic surface processes such as diffusion 
and nucleation, in the second and third parts, we considered silicon surfaces as a 
specific example. In these studies diffusion of adatoms on stepped surfaces were 
simulated and energetics associated with the formation of kink sites were calculated. 
1. Stability Diagrams for Simple Crystals 
In simulation calculations structural stability of the model system is an impor- 
tant aspect. Often, it is desired that the structure of the system under consideration 
corresponds to the energetically most favorable configuration. For a given potential 
energy function, finding the most stable structure among different possible configu- 
rations is a cumbersome and time consuming procedure. This problem emerges, in 
particular, for potential energy functions involving three-body interactions which 
furnish stability regions for a large number of crystalline structures ranging from 
the close-packed (HCP or FCC) to more open (e.g., diamond cubic or p-tin) struc- 
tures. The significance of three-body interactions in calculating the energy and 
structure-related properties of simple crystals were shown in our earlier investiga- 
t ions. 
In the present study, stability regions for five different crystalline structures 
(HCP, FCC, BCC, @-tin and diamond cubic) were calculated for a wide range of 
potential parameters. Calculations were carried out in a dimensionless form using 
the Mie potential and the Axilrod Teller function to represent t w e  and three-body 
interactions, respectively. The results are presented in a graphical form in Figure 
1. This representation is found to be very useful in deciding parameters for various 
specific systems in which two-body and three-body interactions are operational. 
The stability map shown in Figure 1 represents clearly the effect of the three-body 
interaction on the stability of crystals. A potential energy function based only 
on a two-body potential is able to provide stable regions only for HCP and FCC 
structures. In analyzing Figure 1 one should remember that every point on these 
maps corresponds to the energetically most stable structures among the five dif- 
ferent crystals taken into consideration in this work. The general tendency in the 
stability of these crystals as a function of 2’ is changing as HCP-tFCCdBCC 
for small n, as HCP-FCC-t P-tin-tdiamond cubic for intermediate values of n 
1 
and as HCP-tFCC +diamond cubic for larger n values. Because of the structural 
similarities, the difference between energies calculated for HCP and FCC structures 
turned out to be very small. Within our accuracy limits the HCP and FCC struc- 
tures were considered energetically degenerate for regions denoted by HF which 
occupies large areas in the stability maps for n 5 6 (see Figure 1). 
Boundaries between the stability regions should not be taken as sharp limits. 
Due to the discrete nature of the calculations all boundaries must be regarded 
rather as somewhat broader transition regions. The map for n = 5 is interesting; 
for example for Z* = 0.825 and rn = 9 all five crystalline structures seem to have a 
common region. The @-tin structure has a narrow stability region from n = 5 to  
n = 8. 
2. Adatom Diffusion and Ledge Interactions on the Si(l l1) Surface 
Knowledge concerning the diffusion of atoms on surfaces containing ledges is 
essential for the proper understanding of crystal growth phenomena at an atomic 
level. Early studies on metal surfaces revealed the importance of adatom-ledge in- 
teractions for surface diffusion when attempting to evaluate different growth mech- 
anisms. Based on calculations of surface structure and energetics for single atoms, 
the motion of particles across an otherwise flat ideal Si(ll1) surface will occur by 
activated jumps between hole sites. These jumps will carry the atom through the 
cradle sites so that the minimum energy path for the motion of an atom from the 
hole to the cradle site will control this diffusion process. Figure 2 defines these and 
other possible adatom positions. Of course, the actual macroscopic process of sur- 
face diffusion depends on the detailed structure of the surface so that diffusion via 
this simple unit process is expected to be somewhat modified by (7 x 7), (2 x 1) or 
(1 x 1) surface reconstruction patterns and by the presence of ledges on the surface. 
In the present study, the ”Constrained Statics” method is utilized to find the 
minimum energy configuration of the surface when one adatom is constrained to  
relax only in a specific plane while all other atoms relax in all three dimensions. 
Many similar computations are performed for the specific atom in different initial 
positions and minimum energy trajectory which takes the atom from one position 
to  another is thus mapped out. The result for the hole to cradle trajectory is shown 
in Figure 3. The moving atom stayed in the vertical plane containing the two sites, 
as expected, so that it passed through the bridge site with an interaction energy of 
1.24 eV (see Figure 2), which is clearly an inflection point on the energy trajectory. 
A small additional energy hump (0.12 eV) exists between the bridge site and the 
metastable cradle site (0.99 eV). Upon analysis of overall structure when the adatom 
was near the energy maximum (1.36 eV), the energy hump was seen to be caused 
by the development of a significant local reconstruction underneath the cradle site. 
2 
The subsequent cradle to hole site energy barrier, to complete the overall hole to 
hole motion, is E,  = 0.36 eV. 
These are the absolute minimum energy changes that can be associated with 
the jump. In practice, the large local atomic reconstruction at  the cradle site is not 
likely to happen during an adatom jump so that the hole site to hole site adatom 
movement could exhibit an average maximum activation energy somewhat greater 
than 1.36 eV. Experimental estimates for the Si( 111) surface diffusion activation 
barrier range from 0.2 to 2.0 eV due to  the very indirect nature of the data which 
must be analyzed and interpreted, and because of the uncertainty of the local surface 
structure and composition. 
Adatom-ledge Interactions 
Although it is important to  study all adatom-ledge interactions, only the hole 
adatom-[211] ledge interactions are considered here. Figure 4 gives side views of the 
12111 lower and upper ledges, respectively, displaying the adatom positions tested. 
Simulation calculations were performed with ledges at 25.45A spacings. Figure 4c 
plots the hole formation energies, E f ,  using circles for the lower ledge and squares 
for the upper ledge. The data points are vertically coincident with their spatial 
positions in Figures 4a and 4b. The horizontal dashed line shows the formation 
energy for the adatom at a hole site on the flat ideal surface, labeled as E f ,  indicating 
the energy that would obtain a t  an infinite distance from the ledge. 
From our earlier study, we found that the hole adatom puts the surface further 
into compression, and that a 0.5% in-plane tensile strain caused the E f  of the hole 
adatom to decrease (become more favorable) by 0.08 eV. In Figure 4, where the 
upper ledge causes a major reduction of the surface compression, the hole E f  should 
be much lower near the edge, as Figure 4c clearly confirms. In fact, the stress effect 
is larger on the terrace above the ledge than on the lower terrace, and the E f  
is also more negative above the ledge. The increase in the adatom energies right 
next to the ledge is arguably due to the interference of short range reconstruction 
displacements of the adatoms and ledge which begin to  dominate the longer range 
stress interactions. 
The lower [211] ledge has a much smaller effect on the surface compression, but 
it still decreases it somewhat, particularly on the terrace above the ledge. However, 
in the explicit calculation of Figure 4, the hole adatom is not at all favored on the 
upper site of this ledge, and it is repulsed significantly from the terrace below the 
ledge. It may be that the shear fields may offset the otherwise favorable effect of the 
normal stresses above the ledge. The repulsion below the ledge does not have any 
obvious explanation in terms of simple stress interactions. As argued above, the 
local reconstructions interfering with one another may be the source of repulsion. 
Or, the stresses in the underlying puckered layers, which have not been extensively 
analyzed thus far, may be involved in the repulsion effect. 
3 
The only firm conclusion to be drawn from these results is that the surface 
behavior is not always so easily cast into a simple top layer stress interaction model. 
In the case of the upper ledge, where the stress effect is huge, the stress analysis 
is sufficient. For the lower ledge, where the surface compression is not a dominant 
feature, there is no simple correlation between the stress effects of the separate 
defects and their interaction energy. 
Perhaps the most important point to notice about Figure 4 is that the adsorp- 
tion energies of adatoms near the ledge are symmetrical, an assumption that has 
been used in most computations of adatom diffusion to  ledges via both the lower 
and upper terraces. Of course, these numbers are expected to change when more 
adatoms and surface vacancies are present and when the terraces reconstruct into 
distinctive patterns. 
3. Kink-Site formation Energies on the S i ( l l1 )  Surface 
A semiempirical potential energy function (PEF) has been developed for Si 
comprising both two-body and three-body effective potentials that has significant 
application to a variaty of phenomena ranging from cluster stabilities to crystal 
growth considerations. The parameters contained in this PEF were obtained from 
fits to various experimental properties. Using this PEF, as described in our earlier 
reports, more than 25 different materials properties of Si bulk, clusters and surfaces 
were successfully reproduced. The  calculated energy quantities are all within *20% 
while structural properties, such as bond distances for small clusters and the nearest 
neighbor distance in relaxed crystals, were reproduced to within 7%. However, 
quantities related to the second derivatives of energy, such as bulk modulus, elastic 
constants and vibrational properties were not predicted so well and only qualitative 
agreement is obtained for such parameters. On the other hand, surface energy 
values for the Si(lOO), (110) and (111) surfaces were predicted with good precision 
and the PEF produces the correct surface reconstruction geometry for the (2 x 1) 
Si(100) surface and for the (2 x 1) Si(ll1) surface. 
In the crystal growth, as well as in the surface reconstruction processes, energy 
values associated with the kink formation are very important. It would be very 
nice if one could make first principles ab initio calculations of surface quantities like 
ledges and kinks; however, such calculations are only possible for very small systems 
containing only a few atoms. Since long-range surface stress effects due to interact- 
ing ledges on Si(ll1) surfaces have been calculated and found to be important to 
make meaningful ledge or kink calculations with any PEF, about 500-1000 atoms 
must be taken into account. It is for this reason that one is presently limited to the 
use of semiempirical potential functions. Of the alternate semiempirical Si PEF’s 
available today none has the track record of that proposed here. Each undoubtedly 
has its strengths and weaknesses but insufficient experience is available to catalogue 
4 
their applicability in a given situation. Perhaps it is best to look at each as the 
analogue of a particular experimental technique that provides a measurement with 
a certain error bar. Refinement of the technique generally reduces the error bar. 
Such semiempirical PEF's are able to make a determination of ledge and kink en- 
ergies which is more than present experimental techniques can do. Granted, one 
does not really know the magnitude of the error bar generated by using a particular 
PEF so the number should be treated with caution until substantiated in some al- 
ternate fashion; however, it is the best path presently available to  determine some 
quantities important to crystal growth modeling. 
Using the present PEF, most recently, the structure and energetics for the 
dominant ledges on the Si(ll1) surface have been calculated. These ledges are free of 
kinks and, therefore, are not the equilibrium configuration except at 0"K. However, 
the properties of four different kind of [2ii] and [211] ledges that can be found on 
the Si(ll1) provide a necessary baseline and are an important structural basis for 
kink formation studies. These four structures are presented in Figure 5. The ledge 
energy per atom for these four structures at large ledge spacing are X = 0.24 and 
0.01 eV for [21T] lower and upper ledges, respectively, while X = 0.192 and 0.01 eV 
for (2111 lower and upper ledges, respectively. This report presents calculations of 
the kink structure and the kink energetics on these ledges. These kink properties 
are also expected to depend upon the state of surface reconstruction, either by a 
direct structural connection or indirectly through the surface stresses. Although the 
surface reconstruction problem should be attacked first and a more thorough study 
of ledges in contact with such reconstructed surfaces is needed before the nature of 
the kink sites can be studied in detail, there is pedagogical value to be gained from 
a study of kink formation on these 0°K ledges. Because of these limitations, only 
a preliminary study of a few kink sites will be presented here. 
Results for isolated kink formation on both the (ZiI] and [ Z l l ]  upper ledges 
and the [211] lower ledge at  0°K are summarized in Figure 6. Although three 
examples do not constitute a statistically significant trend, the main feature of 
interest is that the kink formation energy is low when the reconstructed ledge energy 
is high. The ledge energy is low when the reconstruction produces a large tensile 
stress component and reduces the net local stress to very small values. Thus, little 
additional stress relaxation can occur via kink formation. For those ledges that do 
not reconstruct strongly, kink formation has the opportunity of strongly relaxing 
the local compressive stress. 
Large values of Ek will lead to  a small kink density and thus slow ledge move- 
ment during crystal growth at a given driving force. Small values of Ek lead to high 
kink densities and thus rapid ledge movement during growth at  such driving force. 
Thus, although the [Zii] and [ Z l l ]  ledges will bound the terraces on the Si(l l1) 
surface at equilibrium for energetic reasons, they will be the slowest growing ledges 
and will thus also bound the terrgces during crystal growth for kinetic reasons. In 
5 
actual practice, the foregoing conclusion is always valid, however, for doped mate- 
rials interaction energies must be properly modified to obtain correct kink energy 
values. 
6 
Figure Captions 
1 )  Stability regions for five simple crystalline structures, HCP (H) ,  FCC (F) ,  BCC 
(B), ,&tin (S) and Diamond cubic (D). Parameters m and n are the repulsive and 
attractive exponents of the Mie potential, respectively, while 2' represents the 
three- body intensity parameter. 
2) Top view of postulated adatom adsorption sites on the Si(ll1) surface 
3) Minimum energy path for the motion of an adatom from the hole site to the 
cradle site. Energies are in eV measured relative to the hole site adatom formation 
energy. 
4)  Formation energies for hole adatoms near the (a) lower and (b) upper 121 l ]  ledges. 
Adatom positions are shown with filled triangles in (a and b). Energies are plotted 
directly below in (c), using circles for the lower ledge and squares for the upper 
ledge. 
5) Relaxed structures of the basic (2111 and [Zii] single height ledge on Si(ll1). 
6) Structures and energies for selected single height ledges (Aoo) and kink sites (Ek) 
on Si(ll1). 
7 
P L. 
X n 
0. 
P L. 
I 
* -. 
L. 
I 
b n  . . . . . . , . , . 
N 
d P 
I 
A Hole 
0 Cradle 
-1 Bridge 
0 Point 
FIGURE 2 
FIGURE 3 
A 
B 
0 
0 o 0  o 0  o 0  0 0  0 0 0 0 
0 0 0 0 
0 
0 
0 0 
0 
0 .. 0 0 0 
0 0 0 0 
0 0 0 
0 0 0  
0 e 0 
C 
FIGURE 4 
- 
SIDE VIEW TOP M t W  ' ( t i i )  
LEDGE 
1 
I I  O I  ~ 0 0 0 0 0  . . . . . .  
0 0 0 0 0 0  * 6 . . . . .  
LOWER 
0 0 0  
0 0 0 .O .O 
0 0 0 0 0  
0 . 0 0 .  
FIGURE 5 
i Ledge 1 
! 
I i i 
! ( z i i )  
I 
UPPER 
(211) 
UPPER 
I 
0.01 
0.01 
I 
( z i i )  I i 
LOWER 1 0.24 
i 
- 
Top View of Structure E x  I 
I 
0.75 
Y ~ O O O C )  . . . . . .  
0 0 0  
e . . . . .  
a a o 0 o t. 0 
0.73 
FIGURE 6 


Simulation studies for surfaces and materials strength

During this reporting period three investigations were carried out. The first area of research concerned the analysis of the structure-energy relationship in small clusters. This study is very closely related to the improvement of the potential energy functions which are suitable and simple enough to be used in atomistic simulation studies. Parameters obtained from ab initio calculations for dimers and trimers of Al were used to estimate energetics and global minimum energy structures of clusters continuing up to 15 Al atoms. The second research topic addressed modeling of the collision process for atoms impinging on surfaces. In this simulation study qualitative aspects of the O atom collision with a graphite surface were analyzed. Four different O/graphite systems were considered and the aftermath of the impact was analyzed. The final area of investigation was related to the simulation of thin amorphous Si films on crystalline Si substrates. Parameters obtained in an earlier study were used to model an exposed amorphous Si surface and an a-Si/c-Si interface. Structural details for various film thicknesses were investigated at an atomistic level

Halicioglu, T.

S I M U L A T I O N  S T U D I E S  F O R  S U R F A C E S  / n /  v& 
A N D  MRTEKIGSLS; S T R E N G T H  
37507 
Semi-Annual Report 
for 
Cooperative Agreement N C C 2 - 2 9 7  
f o r  the period 
M a y  1, 15'86 - October 31, 1 9 8 6  - , \ '  
Submitted to 
National Aeronautics and Space Administration 
M o f f e t t  Field, California 94305 
Ames Research Center 
Co mp u t a t i o na 1 Ch em i 5 t r y Br a nc h 
Dr. David Cooper, Chief and Technical Monitor 
Therrnosciences Division 
Dr-. Jim Arnold, Chief 
Prepared by  c 
ELORET I NST I TUTE 
1178 Maraschino Drive 
Sunnyva 1 e, CA 94087 
(phone: 408 730-8422)  
K .  Heinemann, President and Grant Administrator 
Timur Halicioglu, Principal Investigator 
https://ntrs.nasa.gov/search.jsp?R=19870002924 2020-03-20T13:39:49+00:00Z
SIMULATIOhT STUDIES FOR SURFACES AND 
MATERIALS STRENGTH 
In accordance with the original proposal, during this period the following in- 
vestigations were carried out. 
(I) An analysis of the structure-energy relationship in small clusters. This study is 
very closely related to the improvement of the potential energy functions which are 
suitable and simple enough to  be used in atomistic simulation studies. Parameters 
obtained from ab  initio calculations for dimers and trimers of AZ were used to 
estimate energetics and global minimum energy structures of clusters containing 
up  t o  15 AZ atoms. (2) Modeling of the collision process for atoms impinging 
on surfaces. In this simulation study we analyzed qualitative aspects of the 0 
atom collision with the graphite surface. Four different O/graphite systems were 
considered and the aftermath of the impact was analyzed . (3) Simulation of thin 
aEorphous S i  fi!-ms on crystalline S i  substrates. Parameters obtained in an earlier 
study were used to model an exposed amorphous Si surface and an a - S i / c  - Si 
interface. Structural details for various film thicknesses were investigated at an 
atomistic level. 
1. Structure-Energy Relationship in Small Clusters 
To calculate low energy configurations of small AZ clusters we employed a 
semiempirical potential energy function comprising two- and three-body interac- 
tions which v.7ere approximzted by the Lennard-Jones a n d  4xilrod-Teller potentials, 
respectively. Parameters for these functions were evaluated from fits to  Alp and AZg 
energies obtained from ab initio all electron calculations. The fitting procedure was 
carried out to produce the best result around the minimum regions of the potential 
energy. Assuming reduced parameters for the AZ system, the value of the dimen- 
sionless three-body parameter was found to be in the interval of 2' = 0.4 - 0.5. 
1 
For the smaller clusters (up to n = 6. where n represents the total number of 
atoms in the cluster), the ab initio results were best reproduced with a value of Z* 
around 0.5. For larger clusters ( n  > 6) it was found that the value of 2' should 
be somewhat reduced. However, this conclusion, at this stage, is rather qualitative 
because the comparison was made based solely on the ab  initio result of A113 which 
was calculated at a less approximate level than the small cluster cases. In order to 
analyze the general trends in the structure-energy relationship for relatively larger 
AZ clusters, calculations were carried out considering 2" = 0.425, as a prototype 
example. In this investigation we calculated global minimum energy configurations 
for clusters containing 7 - 15 AZ atoms. 
Minimizations were performed in two basic steps. First, a Monte-Carlo tech- 
nique was employed in connection with a damping method to  search the configu- 
rational space and find the catchment area belonging to  the lowest minimum. The 
Monte-Carlo runs were started from a randomly chosen initial configuration con- 
fined in a volume to give the correct density of the AZ crystal. We performed, 
for each case: approximately lo5 individual Monte-Carlo steps during which the 
total energy of the system was monitored continuously and the configuration cor- 
responding to the lowest energy was saved. In the second part, this lowest energy 
configuration was used as an input in a fast minimization routine to further min- 
imize the energy and obtain the energetically most favorable structure of the run. 
For each cluster, the whole minimization procedure was repeated a t  least 50 times 
(with different initial configurations) and the global minimum was chosen as the 
one with the lowest-lying energy level among all. 
The  most important conclusions drawn from this study were: (i) The  lowest 
energy structures do not always have high symmetry. (ii) Two-dimensional, as well 
as three-dimensional, structures may be the low-lying state. (iii) The potential en- 
ergy function employed in this study is flexible enough to  produce results consistent 
with ab initio calculations. 
2 
2. Modeling of the collision process for atoms impinging on surfaces 
Simulation calculations for the collision process of a free 0 atom onto graphite 
surfaces were carried out using a molecular dynamics technique based on the 
Nordsieck-Gear algorithm. In the calculation of energies and forces among the par- 
ticles we employed the Lennard-Jones and the Axilrod-Teller potentials to  represent 
two- and three-body interactions, respectively. The potential energy parameters for 
carbon were taken from an earlier study based on the same potential energy func- 
tion. Some shortcomings of these parameters (as discussed in previous reports) do 
still exist. Parameters considered for C were: c(c-c) = 5.437 eV ,  r ~ c - c )  - 1.439 
A and Zccc = 129.53 eV.A9. These parameters are able to reproduce accept- 
able cohesive energy and the first volume derivative values for graphite, but fail to 
produce correct stress tensor values in all three directions. For cross interaction 
parameters we considered: ~ ( c - 0 )  = 5.0 eV ,  T : ~ ~ ~ )  = 1.250 A and Zcco = 130.0 
eV.41’. In all cases the impact velocity of 0 was chosen to be approximately 5 
e V ,  with an initial surface temperature of 1°K.  Because of the high kinetic energy 
assigned for the 0 atom the time step was taken to be IO-’‘ sec. throughout the 
molecular dynamics runs. Calculations were performed for four different systems. 
In the first two of these cases, a n  ideal “defect free” graphite surface was assumed, 
\vhile for the other tivo cases vie considered a surface with a ledge. (i) First, the 
impinging 0 atom was chosen to collide into a hole site. In this case, 0 diffused 
through the hexagonal C-ring into the first interlayer spacing (between the first 
and second layers) and localjzed as an intercalated 0 atom. The surface damage 
was found to be minimal. ( i i )  Second, the 0 atom was assigned to  hit near the 
center between two neighboring carbon atoms located on the exposed surface. This 
collision created considerable surface damage and, as in the previous case, 0 was 
found to be trapped between the first and second layers. (iii) In the third case, the 
0 atom, on a perpendicular 
a surface carbon atom near 
was damaged. In this case, 
t~ajeztory to the surfzice i;!ane, c=!!ided head-en ~7 i th  
the ledge. As in the second case, the impact region 
however, the 0 atom bounced back from the surface 
3 
and was leaving the system (as observed during the time frame of the simulation!. 
(iv) In the last case, the 0 atom hit a ledge carbon atom with an incident angle 
of 45 degrees. As in the previous cases, the 0 atom was found to be trapped in 
the first interlayer spacing and considerable damage and disorder around the ledge 
were observed. In the last three cases, surface damage caused by the impact of 
the 0 atom was quite extensive, the local order of the hexagonal arrays in the top 
layer was lost and, probably, some degree of amorphization took place around the 
impact region. During this investigation we were unable to detect any desorbing C 
atoms leaving the system as a result of the impact. This is clearly due to the strong 
bonding which exists among C atoms at the surface layer of the graphite lattice. 
However, once the top surface layer is damaged and its ordered structure no longer 
exists, the  result of subsequent impact by 0 atoms may be quite different. 
3. Simulation of Thin Amorphous Si Films 
T h e  thin layer of amorphous silicon (a - Si) on the crystalline silicon (c - 
Si) substrate was created by melting and then quenching the surface region of a 
properly oriented silicon crystal. Simulation calculations were performed using a 
molecular dynamics technique. The code uses the Lennard-Jones and the Axilrod- 
Teller potentials to  approximate the two- and  three-body interactions. hlelting 
was achieved by raising the temperature of a thin region at  the free surface to a 
value above 1920'K which was found earlier to be the melting point of Si using 
the same potential energy function. All the Si atoms in the surface region were 
allowed to  move under the molecular dynamics code, while in the crystalline region 
below, the atoms were constrained to stay at  their lattice points. Two-dimensional 
periodic boundary conditions were applied in the directions parallel to the exposed 
surface and all possible interactions between moving and fixed atoms were included 
for calculating forces and energies. Three thousand molecular dynamics steps at 
T = 1950'K were found to  be sufficient for melting. Quenching was achieved 
by lowering the system temperature in a single step with temperature rescaling 
I 
4 
. 
(at T = 1.0'K) applied for approximately 500 steps to drain the excess kinetic 
energy from the system. The system was then permitted to  equilibrate freely and 
i t  eventually stabilized at T = 450°K. 
In this study, both Si(100) and Si(ll1) substrates were used. For the Si(100) 
case, three different film thicknesses were considered in order to investigate the 
film thickness effect on the structural features. For the Si(ll1) case, a large film 
thickness was considered to investigate the substrate orientation efIect on the struc- 
tural features. The most striking feature was found to be the presence of a "skin" 
or inordinately dense layer of atoms at the free surface of the amorphous region 
underlaid by a much less dense zone with large holes or cavities. This feature is 
present for all layer thicknesses studied. One can be reasonably assured tha t  it is 
an equilibrium phenomenon and not a film thickness artifact. This high density 
surface skin is reminiscent of the strongly compressive stress tensor found at the 
Si(ll1) free surface. A second striking feature is the a - S i / c  - Si interface void 
region for the Si(ll1) substrate compared to  the Si(100) substrate. This occurs 
because of the high atomic density and the triangular network of the (11 1) surface. 
Silicon atoms from t,he amorphous region cannot approach the crystalline surface 
as closely as they can for the (100) case with a square atomic network. Of course, 
this may be partially due to the fact that the crystalline substrate was held rigid. 
5 


Simulation studies for surfaces and materials strength

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