The computer simulation of thin film nucleation and growth, which was previously performed for the case of single monolayer, was modified to include multilayer growth via the Volmer-Weber mechanism. The simulation results show that: (1) the kinetics of multilayer film growth is nearly identical to that of monolayer growth; (2) when no reevaporation takes place, the cluster density resulting from multilayer growth is higher at high coverage than that resulting from monolayer growth; (3) when reevaporation does take place, the cluster density resulting from multilayer growth is nearly identical to that resulting from monolayer growth. This is not due, however, to similarity in microstructure

Ghose, H. M.

Salik, J.

English

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NASA Technical Memorandum 86%8
(NISA -Tm- E6968) A COMPUTE & SIMULATION OF	 N85-21264
THIN FILM NUCUATICb AND GIC47H: THE
VCLME&-M112H CASE (NASA)	 12 p HC A02/11F A01
	
CSCL 07A	 Unc? as
G3/1 23	 14531
`	 A Computer Simulation of Thin
Film Nucleation and Growth
The Volmer-Weber Case
Joshua Salik
Lewis Research Center
Cleveland, Ohio
and
Hiren M. G3.1ose
Cuyahoga Community College
Cleveland, Ohio
Prepared for the
12th International Conference on Metallurgical Coatings
sponsored by the American Vacuum Society
+	 Los Angeles, California, April 15-19, 1985
^'^0 5
mss ^''^'n'
i
*NRC-NASA Research Associate.
A COMPUTER SIMULATION OF THIN FILM NUCLEATION AND GROWTH -
THE VOLMER-WEBER CASE
Joshua Salik*
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135
and
Hiren M. Ghose
Cuyahoga Community College
Cleveland, Ohio 44115
SUMMARY
The computer simulation of thin film nucleation and growth, which was
previously performed for the case if single monolayer, was modified to include
multilayer growth via the Volmer-Weber mechanism. The main conclusions drawn
from the simulation results are:
1. The kinetics of multilayer film growth is nearly identical to that of
monolayer growth.M
N	 2. When no reevaporation takes place, the cluster density resulting from
LL,	 multilayer growth is higher at high coverage than that resulting from monolayer
growth.
3. When reevaporation does take place, the cluster density resulting from
multilayer growth is nearly identical to that resulting from monolayer growth.
This is not due, however, to similarity in microstructure.
INTRODUCTION
Most studies of thin film nucleation and growth by means of computer sim-
ulation reported in the literature (refs. 1 to 3) are limited to a single mono-
layer, i.e., to the early stages of growth b,,
 the Frank-van der Merwe and
Stranski-Krastanov mechanisms. In these two m":hanisms a monolayer of the
deposited material is formed before multilayer growth takes place. Only one
study (ref. 4) which deals with multilayer growth has been published, and no
comparison of the growth behavior under these two different modes of growth has
been reported.
Multilayer growth is, however, very common and has been observed in many
cases (see for example ref. 5). In fact, it constitutes one of the three basic
modes of film growth, namely the Volmer-Weber mechanism, whereby multilayer
^	 }... 37
growth takes place from the very beginning. Thus, a study of the growth behav-
ior via this mechanism, and especially comparison with the other mechanisms,
seems to be warranted.
DESCRIPTION OF THE MODEL
In order to allow comparison between the results obtained earlier (ref. 3)
for the case of monolayer growth and those of the present study, the model
employed here was made as similar as possible to the one employed there. Thus,
the sample lattice selected for this study was a square lattice, and most of
the basic assumptions are identical, namely:
1. Only single atoms impinge on the surface
2. Only single atoms (i.e., atoms which do not have any nearest neighbors)
are capable of migrating on the surface.
3. Mobile (single) atoms migrate on the surface by means of jumps to
nearest-neighbor sites and the jump frequency is constant.
4. A cluster is formed by two or more atoms occupying adjacent lattice
sites.
5. Only nearest-neighbor interactions are taken into account.
6. No decomposition of clusters takes place.
7. Only single atoms can reevaporate from the surface.
B. The substrate surface is free from sites of preferred nucleation, e.g.,
defects or impurities.
9. The boundary conditions taken are of an infinite potential barrier,
i e., atoms cannot cross the boundary.
For a discussion of these assumptions see reference 3.
PROCEDI1RE
the simulations were carried out on a microcomputer. A sample lattice of
400 (20 by 20) points was used. Some test runs were also done on a 1600 (40
by 40) point lattice, in order t3 check the effect of sample size. The results
obtained in these test runs fell within the error range of the results obtained
with the 400 point lattice.
The x and y coord'nates of the sites at which atoms impinge on the
substrate surface were chosen by means of a random number generator with homo-
geneous distribution. An atom can jump in four possible directions on a two-
dimensional square lattice. The actual direction of each jump was also chosen
by means of a random number generator. In cases involving reevaporation, the
following procedure was used to determinQ whether a given (single) atom reevap-
orates at a given time: a random number in the iniarval (0,1) was generated.
2
If this number was smaller than the preassigned reevaporation probability, that
atom was 'erased."
Eight simulation runs were carried out for each case studied, and the
average as well as the standard deviation were calculated. In order to check
the sufficiency of the number of runs, 16 simulation runs were performed for
some cases. The results were within the error range obtained with eight runs
and no reduction in standard deviation resulted.
RESULTS AND DISCUSSION
In order to study the effect of each of the processes involved on the
overall growth behavior, the simulation was done for each of the following
cases.
Impingement
First, the case when the only process taking place is impingement of atoms
on the surface was studied. This corresponds to the physical situation that
exists when a film is deposited on a very cold substrate. The three-dimensional
microstructure resulting from this process on a 40 by 40 point lattice is rep-
resented in figure 1 for four values of the coverage. The percentage of atoms
bound in clusters out of the total number of impinged atoms is given, as
function of coverage, in figure 2, where the results obtained for the monolayer
growth are also given for comparison. It can be seen that the kinetics of
growth in these two modes is nearly identical, although at coverage lower than
0.4 a slightly higher fraction of the impinged atoms is bound in clusters in
the case of multilayer growth.
This is not true, however, for the cluster density. From the results
presented in figure 3, it is seen that at coverages higher than 0.2 the cluster
density resulting from the multilayer growth is substantially higher than that
resulting from monolayer growth. Thus, although these two mechanisms to not
differ much in their kinetics, they do differ in the resulting microstructure.
Impingement Combined with Surface Migration
Next, the case when impingement is combined with surface migration was
studied. This represents the situation when a film is deposited on a substrate
which is hot enough to allow surface migration, yet is too cold to allow reevap-
oration of deposited atoms. The micrrstructure resu'cing from this combined 	 i
process on a 40 by 40 point lattice is presented in figure 4. The kinetic
results presented in figure 5 display a behavior similar to that obtained for
the case of impingement, namely the kinetics of growth in the multilayer mode
is almost identical to that of the monolayer mode. Again, as in the case where
only impingement takes place, this is not true for the cluster density. The
results presented in figure 6 show that at a high coverage multilayer growth
results in higher cluster density than that resulting from the monolayer mode.
3
Combined Impingement, Surface Migration, and Reevaporation
Finally, the process of reevaporation of atoms from the substrate surface
is also introduced. This represents the situation when a film is deposited on
a very hot substrate. For the sake of clarity, the results of only one such
case, namely when the probability of each single atom reevaporating at any
given time is 0.5, are shown here. The microstructure resulting from this
process on a 40 by 40 point lattice is presented in figure 7. The growth
kinetics is given in figure 8, and, as in the former two cases, it is found to
be almost identical for the two modes of growth.
Unlike the former two cases, however, the cluster density resulting from
these two growth mechanisms, which is given in figure 9, is also similar. This
similarity in cluster density is not due, however, to similarity in microstruc-
ture, since, as can be seen in figure 7, a considerable fraction of the atoms
are located in "multilayer" positions.
CONCLUSIONS
The main conclusions of this study are:
1. The kinetics of film growth in the multilayer mode is nearly identical
to that of the monolayer mode.
2. When no reevaporation takes place, the cluster density resulting from
multilayer growth is substantially higher, at high coverages, than that result-
ing from the monolayer mode of growth.
3. When reevaporation does take place, the cluster density resulting from
the two modes of growth are very similar. This is not due, however, to simi-
larity in microstructure.
REFERENCES
1. F.F. Abraham and G.M. White, J. Appl. Phys., 41, 1841-1849, (1970).
2. A.C. Adams and K.A. Jackson, J. Cryst. Growth, 13-14, 144-147 (1972).
3. J. Salik, (to be published in the Journal of Applied Physics.)
4. R.C. Feber, L.D.F. Allen and D. Grimmer, J. Vac. Sci. Technol. 8, 397-402
(1971).
5. E. Bauer and H. Poppa, Thin Solid Films, 12, 167-185 (1972).
4
^j	 4
UK4,'S V. ,	.	 .
f figure 1. - hUcrostructure resulting form direct impingement,
100
Wso
d
a `0
H W
H
0
W 40
U7Z
20
0.10
0.08
^! 0. 06N
N
OC
iy
N
0. D4
0.02
e	 i
is
i	 1
GROWTH MODE
0	 0.2	 0.4	 0.6	 0.8	 1.0
COVERAGE
Figure 2. - Percent of atoms nucleated directly upon 	 4
Impingement as a function of covera<e.
0
	 0.2	 0.4	 0.6	 0.8	 1.0
COVERAGE
Figure 3. - Cluster density due to impingement as a function of coverage.
a
,j ,	 c.1
9 - 0.5	 r7 = r.L
Figure 4. - Microstructure resultinglror iripin „rr^^rr.v.:rL^r^	 „^^^ „ri,,. - r')iyratron.
J
1W
80
U
a'
60
N
D
v
z
20
I{
W 
GROWTH MODE
0
J
40	 60	 80	 100	 120
TIME
Figure 5. - Percent of nucleated atoms upon impingement combined
with surface migration. Impingement rate, 2.5x10 - atoms /(site x
time unit); Jump frequency, 1 per time unit
0.06
^ 0.04N
N
y1'
v 0.02
0
	
80	 160	 240	 320	 400
TIME
Figure 6, - Cluster density due to Impingement combined with surface migration.
Impingement rate, 2.5x10 - stomcl(site x time unit); Jump frequency, 1 per time
unit
J
OF POOR Q6ALW';
0. 0.°
B • 0.5
	
0 • 1.0
F figure 7. - lAicrog ructure resulting from combined impingement, surface migration, and reevaporativ
0. 02 r- _	 GROWTH MODE
w
N
tY
N 0.01
N
U
1.0 GROWTH MODE
--- MONOLAYER
MULTILAYFR
T
0.8 -
N
0.6 TOTAL NUMBER OFIMPINGED ATOMS
0
0.4
z
oc /W
m
zZ
0.2
0	 200	 400	 600	 am
TIME
Figure 4 - Percent of nucleated atoms upon combined Impinge-
ment, surface migration, and reevaporation. Impingement
rate, 2.5x10-3
 atomsllsite x time unit); jump frequency,
1 per tlrre unit- reevaporation sobebiflty, 0.5,
0	 201,	 400	 600	 B00
TIME
Figure 9. - Cluster density due to combined impingement, sgrfece
migration, and reevaporation. Impingement rate, 2.5x10
-1 atoms l
(site x time unit); jump frequency, 1 per time unit; reevapontlon
probability, 0.5,
I


A computer simulation of thin film nucleation and growth: The Volmer-Weber case

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