Computer simulation of relaxation process of deposited films

496

Journal of Crystal Growth 99 (1990) 496—501 North-Holland

COMPUTER SIMULATION OF RELAXATION PROCESS OF DEPOSITED FILMS Y. SASAJIMA, S. NAKAGAWA, E. MIYAMOTO and M. IMABAYASHI Faculty of Engineering Ibaraki University, Hitachi 316, Japan

The relaxation process for deposited films has been simulated by the molecular dynamics (MD) method. The system calculated was that involving a monatomic layer of fcc(111) on a bcc(110) substrate. For simplicity, the inter-atomic potential was assumed to be a morse function and only the lattice constants were fitted to the experimental values. The systems with lattice constant ratios of 1i, ~ 4/3 and ~ were constructed and relaxed by the MD method. The kinetic and potential energies of the system were 2/s monitored during the calculation. The relaxed structures strongly depended upon the depths of the interaction potentials. Some systems showed coherent interfaces under the strong effects of the substrate potential. These systems showed some definite epitaxial relationship when the strength of interaction potentials of the deposit—substrate and that of the deposit—deposit were comparable.

1. Introduction It is essential to understand the epitaxial growth mechanism in order to control the thin film structure on an atomic level. From many experiments, two kinds of epitaxial relationship have been found in the fcc(1 1 1)/bcc(1 10) interfaces: Nishiyama— W assermann ([2111 fcc//El 101 bec) and Kurdjumov—Sachs ([iiO]fcc//EillIbcc) [1]. These interfacial structures are shown in fig. 1. In this paper, the epitaxial relationship is represented by the rotational angle between
make heterogeneous interface was simulated by the MD method.

2. Methods of calculation The initial structures of the simulated systems were generated in the following way. The six atomic planes of bcc(11O) were generated in cylindrical shape as the substrate. Each layer contained about 300 atoms. The four kinds of one atomic disk of fcc(111), which contained about 60 to 100 atoms, were set on the substrate. The lattice constants of the deposited fcc 4disks were selected to make 6’s of 2/i/i, \/37~, /3 and V~. The interacting potentials were assumed to be Morse functions:

~

=D(e2

_ro)2

e°(’~’0)),

(1)

where r is the atomic distance measured by the first neighbour distance of the bcc substrates. Three sets of the parameters D, a and ,~ should be determined for the fcc—fcc, bcc—bcc and fcc—bcc interactions. Two sets of values of D were examined in our simulation; (i) 0.2 eV for all the interactions and (ii) 0.4. eV for the fcc—fcc interaction and 0.2 eV for the other, a was fixed as 6.0 for the three types of interactions. The values of r 0 were determined to reproduce the lattice constant

Y. Sasajima et a!.

/ Computer simulation of relaxation process of depositedfilms

Nishiyama-Wassermann

method. The three types of orientational relationship, 0°, KS and NW were set for the initial structure of the heterogeneous interface. The initial velocities, of which the directions were randomly chosen, were given to the film atoms and then the trajectry of each atom was calculated deterministically. The temperature of the system was not kept constant and it was evaluated from the mean kinetic energy of the film atom, Eklfl, as follows:

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s-Fe 0-Ni

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Fourier transformation of the interfacial structures,

s-Fe

-

.

0-N,

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I(q)= J~exp(—iq.~)I2,

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,,~

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.s

(2) T= 2Ekjfl/3kBN, where kB is Boltzmann constant and N is the number of the film atoms. In the case that the values of D were the same for all types of the interaction, we also performed the more realistic simulation: the substrate atoms were allowed to move and their velocities were reset periodically according to the Maxwell distributjon function. The structures obtained were compared to those calculated by the previous method. The onentational relationship of the initial and relaxed interfaces were determined from the 2D

8=24.740

-

_________

‘-

b

Fig. 1. Two types of epitaxial relationships for the fcc(111)/ bcc(110) interface; (a) Nishiyama—Wassermann (NW) and (b) Kurdjumov—Sachs (KS). Closed and open circles represent bce Fe and fcc Ni atoms, respectively.

(3)

where r are the 2D coordinates of the interfacial atoms viewed from the stacking direction and q is the scattering vector. The relaxation was performed up to 500 MD steps and the relaxed atomic structure was obtained as averaged coordinates during the last 50 steps, where 1 step is the time interval in the order of 1015 s.

3. Results and discussion of each bulk structure for the homogeneous atomic interactions. For the heterogeneous interaction, r 0 was evaluated as the arithmetic mean of the values for the homogeneous interactions, For reduction of the Central Processor Unit (CPU) time, the substrate atoms were fixed and only the deposited atoms were relaxed by the MD

Table 1 shows the orientational relationships of the relaxed structures. At first, the results for the case that the values of D were 0.2 eV for all the interactions that are represented. For the system with 6 = ~ and the initial structure KS, the trajectries of the deposited atoms are shown in fig. 3a. The film atoms rotated

498

Y. Sasajima eta!. Ni/Li

/ Computer simulation

of relaxation process of deposited films

Ni/W Cu/WAI/Li -

Ag/Cr~Au’Fe

I

~

NW’ I

o,29

Pb(T~

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~Fe

I

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28

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o

~26

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~ 25

I\

.0_I

1.0

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At/1a 2~’ Cu/Fe ~. ~AutW ~giw..~\ tKS: 1’2’~~~ 1~3 4’~ 1.’4~~

1~5~

6

(afCC/abCC) Fig. 2. Preferred orientational relationships of fce(111)/bcc(110) interface predicted by the geometrical theory 131. Rotational angle between (101>,~and <110> ~_ represents the epitaxial relationship; 30° and 24.74* represent NW and KS, respectively. Essentially the same figure can be found in ref. 121.

systematically to make the NW relationship which is a metastable interfacial structure. The relaxed film structure is not single crystal; It contained line defects. In this relaxation process, the change of orientational relationship was observed. This is clearly shown in the 2D Fourier transformation of the system (figs. 3b and 3c). The results suggest that the epitaxial growth is the relaxation process of the deposited atoms to form the metastable interface. The same system, but with the initial

structure NW, did not show the change of the orientational relationship. The fact that the NW relationship is energetically stable for this system supports the validity of the geometrical theory to predict the epitaxial relationship. In case of the initial structure 0°,the system with 6 = ~f~J showed the temperature dependance in the relaxation process. The system was relaxed into the metastable interface with 0° orientation at relative low ternperature (260 K) but into that with NW at high

Table 1 The relaxed structures of fcc deposited atoms on the bce substrate; numbers in parentheses represent the system temperature (in K) and C means coherent structure Prediction by geometrical theory NW 4/3

2/Vi

Depth of

Initial structure

fcc—fcc

00

KS

NW

potential [eV} 0.2

(260) (918)

NW

(608)

NW

(513)

NW

C KS

(611) (803)

00

KS

0.2 0.4

C 0°

(705) (226)

C KS

(551) (753)

KS

0.2 0.4

C 00

(980) (724)

C KS

(758) (1053)

C C

(1010) (768)

0.2 0.4

C C

(919) (1479)

C C

(904) (1108)

C C

(1002) (803)

NW

Y. Sasajima et a!.

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Computer simulation of relaxation process of depositedfilms

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Fig 3 Relaxation process of fcc film of the system with ~ -

‘~

~‘-~“:

~

‘

4

and initial structure KS (a) trajectones of the deposited atoms

I

2D transformation of (b)structures. initial and (c) relaxed interfacial

temperature (918 K). This is an interesting demonstration to show that the epitaxial orientation depends on the system temperature. However, this was not clear in the other simulated systems. The systems with 6 = 4/3, .~/i7~ and 2/ V~were relaxed into the coherent interface. Fig. 4 shows the relaxation process of the system with 6 = and initial structure 00. The Fourier transforma-

tion of the relaxed interface (fig. 4c) shows that the deposited film was strained to make a coherent interface with the bcc substrate, In the preceding simulation, the depth of the deposit—deposit interaction was deepened to twice that of the deposit—substrate interaction. The systems with 6 = 4/3 and ~/~i7~ were relaxed into the incoherent interface with some definite epi-

500

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Computer simulation of relaxation process of depositedfilms

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taxial relationships, except for the case of 6 =~ and initial structure NW. The epitaxial relationship of these systems are predicted as KS by the geometrical theory. It is also confirmed from the fact that these systems with initial KS orientation were metastable in the present calculation. In contrast to the above-mentioned case, the system with 6 = 2/ %fi was relaxed into the coher-

Fig 4 The same as fig 3 but with structure 0°.

~ %/~i7~and =

initial

ent structure and the change of growth mode was observed. The side view of the relaxed film structure is shown in fig. 5. The form of the film changed from 2D layered structure to 3D island structure. This can be attributed to the strengthening of the film atom interaction, which make a change of the growth mode from Frank—van der Merwe to Volmer—Weber.

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/ Computer simulation of relaxation process of depositedfilms

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CD

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Fig. 5. The side view of the relaxed film structure for the system with 2/V~and initial structure 00. The depth of fcc—fcc interaction is 0.4 eV. The circles and triangles represent the substrate and deposited atoms, respectively.

The more realistic simulation in which the substrate atoms were allowed to move was also performed but the interface structures obtained were the same as those calculated by the above men ioned method. It suggests that our simple calculation simulates the relaxation process of the film atoms fairly well.

4. Summary

(ii) Three factors, initial structure, system temperature and depth of interaction potentials are essential to determine the interfacial structure of thin film.

References [1] E. Bauer, Appi. Surface Sci. 11/12 (1982) 479. [2] U. Dalimen, Acta Met. 30 (1982) 63.

13) The relaxation process of deposited fcc atoms on the bce substrate was simulated by the MD method and followtng conclusions were obtained. (i) The interfacial structures predicted by the geometrical theory are energetically stable.

W. Bollmann, Crystal Defects and Crystalline Interfaces (Springer, Berlin, 1970).

(4) i.E. Black and P. Bopp, Phys. Rev. B34 (1986) 7410. [51M. Schneider, A. Rahman and 1K. Schuller, Phys. Rev. Letters 55 (1985) 604. [61M. Schneider, 1K. Schuller and A. Rahman, Phys. Rev. B36 (1987) 1340.