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International Journal of Recent Trends in Engineering, Vol 2, No. 2, November 2009. 85 ... Abstract—We have developed atomic scale simulations of thin film growth .... applied periodic boundary conditions on both lateral directions. The first ...
LETTERS International Journal of Recent Trends in Engineering, Vol 2, No. 2, November 2009

Atomic Scale Simulation of Thin Film Growth by Kinetic Monte Carlo Method A. Ali Messaoud1, A. Chikouche1, 2, A. Estève3, 4 , G. Landa3 , 4 and M. Djafari Rouhani3, 4 1

Saad Dahlab University /Sciences Faculty, Blida, Algeria Email: [email protected] 2 Unity for Development of Solar Equipments, Bou Ismail, Tipaza, Algeria Email: [email protected] 3 CNRS ; LAAS ; 7 avenue du colonel Roche, F-31077 Toulouse, France 4 Université de Toulouse ; UPS, INSA, INP, ISAE, LAAS ; F-31077 Toulouse, France Email:{aesteve, georges.landa, djafari}@laas.fr

Abstract—We have developed atomic scale simulations of thin film growth using Kinetic Monte Carlo (KMC) method. We have applied the method to the two extreme cases of GaAs(100) growth and to the dry oxidation of Si(100), observing similar features. We show that these features are characteristics of molecule-surface interactions We consider that the molecules As2 and O2 are first adsorbed in the physisorbed state before dissociation in a chemisorbed state. to exceed to the chemisorbed state. Up-to-date, no model of simulation has taken the energetic model for the physisorbed state of the arsenic or the oxygen into account. The existence of the physisorbed state and its further diffusion along the surface are certainly at the origin of the reported features.

results with the experimental data [4, 6 7]. In section II, we describe briefly the simulation process. Section III is devoted to the enumeration of energetic parameters used in the simulations and the presentation and discussion of the results. These concern mainly the influence of some physical parameters on the growth mode and surface morphology. II. MODELLING AND SIMULATION The Kinetic Monte Carlo method [2-5] allows us to describe the time evolution of the system when the probabilities of occurrence of elementary events are known. For GaAs/GaAs(100) growth, we consider the adsorption, diffusion, evaporation and incorporation of As2 molecules. For Silicon dry oxidation, chemical reactions of O2 molecule on the surface, adsorption of SiO on Si(100) and reconstruction of the surface according to SiO2, are taken into account. A sequence of random times, sampled according to occurrence probabilities, determine the temporal evolution of the surface configuration. With these assumptions, the growth simulation of our systems proceeds as follows. The adsorption of atoms and molecules from the gas phase onto the surface occurs at random positions and time according to the Poisson distribution and kinetic gas law (Eq. 1).

Index Terms—Crystal growth, Computer simulation, Monte Carlo Kinetic method, Thin film, GaAs/GaAs(100), SiO2/Si(100)

I. INTRODUCTION Interest in the growth of semiconductors layers goes back to the seventies soon after computers were made available. The Kossel approximation [1] (Solid On Solid) was the guideline for the first simulations. In the S.O.S model, the adsorbed atoms were given the cubic shape. In an effort to develop it, Madhukar and his collaborators [2] have introduced, in the eighties, the essential features of growth, involving surface molecular reactivity. More recently, motivated by the general trend in microelectronics to reduce device sizes, a new model of dry silicon oxidation has been proposed by several workers[3-5], using the kinetic Monte Carlo (KMC) simulation technique in different experimental conditions of temperature and pressure. Our work concerns first the modelling of the growth of GaAs(100) based on chemical reactions suggested by Arthur and subsequently by Foxon and Joyce [6, 7]. Then, we present the results of our model for dry silicon oxidation before comparing them with GaAs/GaAs(100) growth simulations and show the agreement between coverage profiles. Note that, in terms of elementary event and energetic model, no modelling of the physisorbed state of the molecules As2*(p) and O2*(p), is available today. That is why we incorporate this precursor state in our model in order to compare our

ti =

3.513.10 23 P S

ln Z i =

1 ln Z i . R

(1)

Where Zi is a random number distributed uniformly in the [0, 1] interval, P is the pressure of the gas (in Torr), M the molecular weight of the gas, T the temperature and S the area of the impact site. R represents the total atomic or molecular impingement rate per atomic site of the surface. The time of occurrence of events on the surface are determined according to Arrhenius law and Poisson probability (Eq. 2).

t = i

dE K T −e B S R 0

lnZ . i

(2)

Where KB is the Boltzman constant, TS is the substrate temperature, R0 represents the constant of reaction and dE the activation energy. The activation energy dE of an

Corresponding author: [email protected] Tel/Fax: 00 (213) 25 433642 or 00 (213) 25 431164

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− MT

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LETTERS International Journal of Recent Trends in Engineering, Vol 2, No. 2, November 2009 atom (or molecule) in its adsorbed state represents the energy barrier of that the atom (or molecule) has to overcome in order to perform an event. The knowledge of the local configuration of the surface, for both the initial state and the intermediate state during the occurrence of an event, is needed for the calculation of dE. Once all times for all possible events are calculated, the event corresponding to the minimum time is performed and the surface configuration is updated accordingly. For the next simulation step, only the times corresponding to events whose probabilities are modified are calculated. According to fundamental chemical considerations and the experimental observations [2, 5], we have considered that the incoming gallium (Ga) atoms are directly adsorbed in the chemisorbed state Ga*(c) if the favourable site is vacant. This is not the case for the incoming arsenic molecules (As2) on GaAs(100) and oxygen molecules (O2) on Si(100) whose adsorption mechanisms are shown on Fig. 1.

As2 Flux

0.14

[6, 7]

As2-Ga

0.13

[6, 7]

As2- As2

0.006

[9, 10]

Type of Events Chemisorption

K0 (s-1) 106

Evaporation

109 10-4 5. 107

SiO*+ O*(c)―

[2, 8]

Observation From Physisorbed state (As2*(p)) Atomic form (Ga) Physisorbed state (As2*(p)) Chemisorbed state As*(c)

―> O2*(p)

E (ev) 6.9

Observation O2/Si(100)_2x1

4.6

O2/Si(100)

2.3

Desorption event

0.07

Surface reconstruction

SiO2*

The intensity of the incident flux has been fixed in the range of [1013-1015] atom.cm-2. The substrate temperature is taken in the range [600K-900K]. Because of their high activation energies, two events are only considered when the substrate temperature is higher than 650K. The first one is the dissociation reaction of physisorbed molecules, leading to the chemisorbed state of arsenic or oxygen. The second event is the evaporation from the surface of chemisorbed atomic species, arsenic or oxygen, in their final molecular form, as shown in Fig. 1. This event implies the transition of atomic species to molecular physisorbed state and the subsequent evaporation of the physisorbed molecules. The interaction energies between second neighbour atoms are estimated to EGa-Ga = EAs-As = 0.14 ev. This value is in conformity with the interaction energies used in previous simulations [2, 6, 8, 9]. Fig. 2 represents the coverage of GaAs(100) substrate surface by Ga atoms and As2 molecules, as a function of time. Similarly, Fig. 3 shows the evolution the coverage of Si(100) by O2 molecules. The curves represented in Figs. 2 and 3 are in agreement with the theoretical expression for the time t dependent coverage c :

2 O*(c) R3

O2(v) Figure 1. Synoptic diagram showing the several possible reaction pathways for the incorporation of As2 on GaAs(100) [3, 5] and the O2 on Si(100)[4-7].

III. RESULTS AND DISCUSSIONS The process described in section II has been simulated by the KMC method, using square lattices ofvarious sizes, never less than 30x30 atomic sites. We have applied periodic boundary conditions on both lateral directions. The first monolayer of GaAs is grown on the ideal arsenic terminated (100) surface. It is therefore a Ga layer. The input parameters are the interaction energies (Tab.1) and the constants of reactions (Tab. 2). The input data used for the growth of SiOx/Si(100)_2x1 are the reaction energies (Tab. 3).

c =1 − e

−t w

(3) 1

With

⎡ ⎤3 1 w =⎢ ⎥ 3 . 14 r g v r ⎦ ⎣

(4)

Where g is the nucleation rate; r is the number of sites per unit of the substrate and vr is the radial velocity of two dimensional nuclei.

TABLE 1. ENERGIES USED IN COMPUTER SIMULATION OF HOMO EPITAXIAL SYSTEM GROWTH

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[2, 8]

As-As

2O(c)

R2 R1

0.14

Reactions O2*(p) ― 2O*(c) O*(c)+Si ―> SiO*(c)

As2(v)

O2*(p)

Ga-Ga

TABLE 3. BASIC REACTIONS USED IN COMPUTER SIMULATION OF DRY OXIDATION

K3

O2 Flux

References

Diffusion

2 As*(c) K1

E (ev) 1.0

TABLE 2. CONSTANTS OF REACTIONS USED IN COMPUTER SIMULATION OF HOMO EPITAXIAL SYSTEM GROWTH

K2

As2*(p)

Interaction Ga-As

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LETTERS International Journal of Recent Trends in Engineering, Vol 2, No. 2, November 2009

Figure 4. The growth coverage of atomic system Ga/GaAs and molecular system As2/GaAs, taken each one alone. The thermodynamic input parameters are T=850K and JAs2 = JGa. Figure 2. The arsenic and gallium layers coverage in the GaAs/GaAs(100) homoepitaxial growth. The substrate temperature is T=850K and the flux ratio JAs2/JGa is unity.

We conclude from Fig. 4 that, in the initial state, the molecular evolution growth is faster than the atomic growth. This should be due to the fact that, in the As2/GaAs (or O2/Si (100)) system, the vacant sites are occupied by pair of atoms at each impingement. At the end section of the curve, the growth rate of an atomic system is higher than for a molecular system. This result can be justified by the presence of isolated sites, which cannot be occupied by molecules. This case cannot occur in the presence of an atomic flux (Fig. 5). (a) Atomic coverage evolution

Figure 3. The oxygen coverage evolution on Si(100) during oxidation. The substrate temperature is T=850K and the incorporation rate of oxygen is R-1=0.5s.

t =1s

The mode of the build up of GaAs coverage is, therefore, the continuous growth mechanism. At this stage, our results are similar to that obtained from the CDRI (Configuration Dependent Reactive Incorporation) atomic model suggested by Madhukar and Ghaisas [2] for the GaAs/GaAs(100) growth. An analysis of the build up profiles (Figs. 2 and 3) shows that the evolution of the GaAs layer (Fig. 2) and the oxide layer (Fig. 3) goes over three distinct states which are, respectively, the progressive and uniform growth phase which corresponds to the initial state of growth, the transition state and the saturation state which corresponds to the end of growth. These three states are influenced by experimental parameters such as the structure of the adsorbed species, the intensity of the incoming flux and the substrate temperature. In the following, we concentrate on the influence of the first two parameters. Fig. 4 shows the evolution of the GaAs(100) surface when the flux one species, Ga or As2, is turned off. Figs. 2 and 4 show clearly the difference between the two growth processes.

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t =5 s

(b) Molecular coverage evolution

t =1s

t =5 s

Figure 5. The morphology of the surface at t=1s and t=5s, end of simulation, (a)Ga/GaAs(100), (b)As2/GaAs(100) or O2/Si(100). The dark colour is the substrate: GaAs(100) or Si(100) and the light one is the chemisorbed species at the substrate temperature of T=850K

It is clear that the whole coverage of the surface is obtained in a short interval of time when the flux is more intense (Fig. 6). Then, by drawing in Fig. 7 the intensity

87

LETTERS International Journal of Recent Trends in Engineering, Vol 2, No. 2, November 2009 of the incoming flux against the inverse of the monolayer (ML) growth time, we find the linear relation: Time = 63.10 14 . 1 J As 2 .

many types of phenomenon observed experimentally or suggested theoretically during growth [9, 4]. The results reported here show explicitly that numerical simulations using spatially random atomistic kinetic processes and surface diffusion of gallium and arsenic, in the case of GaAs/GaAs(100), and oxygen, in the case of SiOx/Si(100), as an atomistic Arrhenius activated hopping process, can control the real growth of thin films under realistic experimental conditions. We have been able to assess the quality of the growing interface in the two extreme cases of perfectly lattice matched III-V system of GaAs/GaAs(100) and the lattice mismatched system of SiO2/Si(100). These results should prove useful for scientists and engineers interested in understanding the physical and chemical nature of interfacial structures and their formation mechanisms [5, 12].

(5)

One can deduce from this relation that the time for the monolayer completion corresponds to one second when the intensity of the incoming flux is close to 6.3 1014 molecules/cm2 s. This result obtained from our work is in agreement with chemical kinetics theory [2, 11]. R-1 =0.5 s

R-1=1.5 s

ACKNOWLEDGMENT We acknowledge Dr. D. Estève from Laboratory for Analysis and Architecture of Systems (LAAS-CNRS) for guiding our work to completion.

Figure 6. The Morphology of the surface layer coverage in the case of molecular incoming flux: As2/GaAs(100) or O2/Si(100), with different rates R of incoming gas species at the substrate temperature of T=850K and after 12s simulation.

JAs2 (1023 molecules/ cm2. s)

REFERENCES 7

[1] W. Kossel, Noehr Ges wiss gotting, 1927, pp. 135. [2] A. Madhukar and S. V. Ghaisas, App. Phys. Lett. 47 vol. 3, pp. 247-249, August 1985 [3] A. Estève, M. Djafari Rouhani, Ph. Faurous, D. Estève, Materials Science in Semiconductor Processing vol. 3, pp. 47-57, 2000. [4] N. Richard, A. Estève, M. DjafariRouhani, Comp. Mat. Sci. vol. 33, pp. 26-30, 2005. [5] A. Ali Messaoud, A. Hemeryck, A. Estève, M. Djafari Rouhani, G. Landa, Mater. Res. Soc. Symp. Proc. vol. 996E, 2007 [MRS Spring Meeting in Electronic and Magnetic Materials, 2007, USA]. [6] C.T. Foxon, B. A. Joyce, Surface Science. vol. 50, pp. 434450, 1975. [7] C. T. Foxon, B.A. Joyce, Surf. Sci. 64, pp. 293-304. 1977. [8] Sing and K. K. Bajaj, J. Vac. Sci. Technol. B2 (2), pp. 276279, 1984. [9] Sing, K. K. Bajaj, J. Vac. Sci. Technol. B2 (3), pp. 575-58, 1984. [10] D. M. Young, A. D. Crowel, «Adsorption physique des gaz» Bibliothèque Sciences et Techniques Nucléaire, 1967, traduit 1991. [11] F. Arnaud D’avitaya , «MBE-CBE» [1st Summer School on the Film Processing and Characterization Marseille, 1994. [12] A. Estève, M. Djafari Rouhani, D. Estève, “(100) Silicon oxidation: first principle investigation of basic mechanism”, Journal of Non-Crystalline Solid, 245, pp. 150, 1999.

6 5 4 3 2 1 0 0

0,02

0,04

0,06

0,08

1/Time (s) Figure 7. The relationship between the flux intensity and the inverse of the time for one atomic layer completion at T=850K.

IV. CONCLUSION The KMC simulation of growth of thin films of both GaAs/GaAs(100) and SiOx/Si(100) has been performed using atomic and molecular gas flux. The experimental data of the chemical reactions of adsorbed As2 and O2 with GaAs(100) and Si(100) surface, respectively, have been used. The energetic model for both the physisorbed and chemisorbed states of As2 and O2 has been taken into account. At this stage of simulation, we believe that by including various kinetic processes, we have been able to focus on

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