Mater. Res. Soc. Symp. Proc. Vol. 1 © 2013 Materials Research SocietyDOI: 10.1557/opl.201 .4

Multiscale Modeling of CdTe Thin Film Deposition Process

Alexey Gavrikov1, Andrey Knizhnik1, Dmitry Krasikov1, Boris Potapkin1, Svetlana Selezneva2, Timothy Sommerer2

1 Kintech Lab Ltd., 1, Kurchatov Sq., Moscow 123182, Russia 2 GE Global Research, Niskayuna, NY 12309 U.S.A.

ABSTRACT Deposition of semiconductor films is a key process for production of thin-film solar cells,

such as CdTe or CIGS cells. In order to optimize photovoltaic properties of the film a comprehensive model of the deposition process should be build, which can relate deposition conditions and film properties. We have developed a multiscale model of deposition of CdTe film in close space sublimation (CSS) process. The model is based on kinetic Monte Carlo method on the rigid lattice, in which each site can be occupied by either Cd or Te atom. The model tabulates the energy of the site as a function of its local environment. These energies were obtained from first-principles calculates and then approximated with analytical formulas. Based on determined energies of each site we performed exchange (diffusion) processes using Metropolis algorithm. In addition the model included adsorption and desorption processes of Cd and Te2 species. The results of the model show that a steady-state structure of the surface layer is formed during film growth. The model can reproduce transition from film deposition to film etching depending on external conditions. Moreover, the model can predict deposition rates for non-stoichiometric gas compositions.

INTRODUCTION

CdTe is a very promising material for low-cost solar cells. Solar cells based on CdTe have been able to reach efficiencies as high as 18.3% [1]. Close space sublimation is a relatively inexpensive technique for deposition of polycrystalline thin-films due to the moderate operating pressure (0.01–15 Torr) and simple configuration [2], [3]. This has created much interest in using CSS for deposition of low-cost polycrystalline CdTe solar cells. The method is able to deposit at very high rates (up to ~15 µm/min) [2]. The combination of high growth rates and simple equipment creates an opportunity to use the CSS large-scale production of low cost solar cell.

For CSS growth technique, some models were proposed for diffusion-limited and sublimation limited cases [4]. However, these models do not take into account the stoichiometry of gas phase. But to control of the intrinsic defects concentration the gas phase composition may be essential; besides the difference in gas diffusion coefficient may give rise to deviation from P(Cd)/P(Te2)= 2/1 ratio both at source and substrate surface. Therefore, there is a need for a model that describes CdTe growth/evaporation in nonstoichiometric conditions. This article presents such growth/evaporation model built from the first principles. CdTe (111) surface orientation is often observed in CdTe films grown by CSS technique, for example [2], [3]. So the present work mainly deals with CdTe (111)B surface.

FIRST PRINCIPLES STUDY

Chemical processes on the surface of CdTe (111)B, such as diffusion, adsorption and desorption of Cd and Te2 were investigated using the Perdew-Burke-Ernzerhof (PBE) functional [5] in the frame of density functional theory (DFT) [6], with core electrons replaced

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by pseudopotentials, and valence states described by a plane wave basis set as implemented in the VASP code [7]. Plane augmented wave pseudopotentials [8] were used for all the atomic species. We have used hexagonal supercell with dimensions 16.23x16.23x40Å (2x2x1 k-points grid was used) with 6 layers of CdTe (111) and 17Å vacuum gap.

It was found that calculation with PBE functional overestimates experimental Te2 binding energy (2.7 eV [9-11]) by about 0.8 eV, so a step should be taken to correct this error. Our calculations have shown that MP2 method [12, 14-Laikov] gives correct value of Te2 binding energy while CCSD [13, 14] method underestimate it by about 0.4 eV.

131 possible surface structures were investigated for CdTe (111)B. To estimate the relative stability of these structures we calculated the excess surface energy Es = (Etot – NCd*μCd-NTe*μTe)/A, where μ is the chemical potential of species, A is the cell surface area and N – is the number of corresponding atoms. Equilibrium condition which determines the CdTe stability region is μCd + μTe = μCdTe . Structures with lowest excess energies are shown in Fig. 1. Using RHEED technique, Tatarenko at al. [15] have observed that at 235-260oC under moderate flux of either of component CdTe (111)B surface has (1x1) reconstruction. After cutting off the component flux, surface evolves through (2x2) to (2√3x2√3)R300 reconstruction. Structures Cd3Te2 with 1/4 monolayer coverage (Fig. 1a) and Te2 with 1/4 monolayer coverage (Fig. 1c) have (2x2) reconstruction, and structure “VCd+3VTe” 1/12 monolayer coverage (Fig. 1b) has (2√3x2√3)R300 reconstruction. So it is likely that structure in Fig. 1b corresponds to RHEED diffraction pattern observed under vacuum conditions.

(a) (b) (c)

Fig. 1. Lowest energy CdTe (111)B surface structures. From left to right, structures are ordered from Cd rich to Te rich. See text for description.

Binding energies of Cd and Te adatoms decrease with increase of their concentrations (see Fig. 2). For concentration above 0.25 ML formation of adatom associates (dimer, chains, clusters, etc.) becomes more favorable than isolated adatoms.

Fig. 2. Average(Eav), and partial, dE/dΘ, adsorption energy of Cd (left) and Te (right) adatoms on CdTe (111)B surface. “S2” and “mono” are the sites for Cd and Te atoms, “poly” is the cluster structure of Cd atoms, “dimer” is the dimer Te2 structure on the surface.

KINETIC MONTE CARLO SIMULATION

To study the kinetics of CdTe growth/evaporation we employed kinetic Monte-Carlo technique. This technique allows a proper description of influence of local environment on the rate of individual chemical process. We made our own surface lattice kinetic Monte Carlo code (SLkMC). Surface lattice kinetic Monte Carlo model is based on a rigid lattice with face-centered cubic (fcc) grid, in which each node can be void or contain Cd, Te or CdTe, thus representing regular CdTe bulk and vacancy defects.

Energy of each node depends on what it contains and on its nearest neighbor environment. Dimers and other aggregates are taken into account implicitly, by energy parameterization.

System energy is parameterized in form

( ), , ,N

CdTe Cd Tetot i i i i i

i

E E S N N N=∑ (1)

where Ei is the site energy, which depends on species occupying given site iS , and numbers of species in the nearest neighbor sites ( , ,CdTe Cd Te

i i iN N N ). Energies are tabulated using first principles data. Energy of each site environment is fitted to the database of parameters obtained from the first principles. Fitting database includes 131 CdTe (111)B surface structures, 14 CdTe(110) surface structures, 23 CdTe(355) surface structures, 45 bulk defect structures and 21 small CdTe clusters. It should be noted that the size of our fitting database is smaller than the number of energy parameters. Therefore the values of many parameters were interpolated.

In our SLkMC code, the model is periodic in two dimensions. The surface lattice is formed by 32x32x128 node’s grid, and the simulations start with 32768 CdTe units (32 layers with flat surface) in lower part of the supercell (with height 490 Å and width 150 Å).

Three types of events are modeled: (i) Cd/Te atomic jumps between nearest neighbor sites; (ii) adsorption of Cd and Te2 on the surface; (iii) desorption of Cd and Te2 from the surface. Adsorption/desorption is possible only for the site connected with the upper vacuum region. At each time step one and only one chemical reaction is chosen based on its rate and the total rate of all chemical reactions (i,l are site indexes, k,j are reaction indexes) with probability:

, expl j

l ik ak j ji

ji j

r Ep rr kT

ν ⎛ ⎞= = −⎜ ⎟

⎝ ⎠∑∑ (2)

Activation energies for kMC events are calculated as , 0,

, 0.b

ab

dE E if dEE

E if dE+ >⎧

= ⎨ ≤⎩ (3)

where dE is the energy change in the event. Eb is the energy barrier and it is parameterized as a function of reaction site environment in order to reproduce calculated with first principles activation energies for adatoms diffusion on the surface and vacancies diffusion within bulk. We introduce three separate pre-exponential factors vj for diffusion, Cd desorption and Te desorption; they can be considered as fitting parameters.

We analyzed the sensitivity of CdTe sublimation rate to variation of some parameters (Table 1). It was found that the difference in diffusion and desorption preexponential factors and the error in the DFT value of Te2 molecule energy considerably affects the sublimation rates.

Table 1. Sensitivity test of CdTe (111)B sublimation rate (SR) to the variation of preexponential factors for diffusion (kD) and for atoms desorption (kCd, kTe) and to the energy of Te2 molecule. Sublimation rates extrapolated from [15] are 12.99 ML/s, 406.90 ML/s for 775 and 875 K respectively.

kD, THz kCd, THz kTe, THz ½ E(Te2), eV SR(775 K),

ML/s SR(875 K),

ML/s 1.0 10 20 -2.071 56.0 672 1.0 5 20 -2.071 62.6 693 0.5 10 20 -2.071 35.5 484 1.0 10 20 -1.971 18.1 198 1.0 5 20 -1.971 10.8 211 0.5 10 20 -1.971 10.7 109 0.5 5 20 -1.971 9.54 106 1.2 2 20 -1,971 17.0 236 1.2 1.2 20 -1.971 18.5 230 1.2 0 20 -1.971 20.0 305 1.0 1 1 -2.433 7.60 86

Results of CdTe growth/evaporation simulation at 775K and 875K (kD = 1.0 THz, kCd = 1.0 THz, kTe

= 20 THz) are presented in Fig. 3. It is seen that transition from evaporation to growth occurs not far from the position of thermodynamic equilibrium [16], [17] shown by the solid curve. Thus, these results show that direct prediction of film growth kinetics based on first-principle data can be achieved with the given approach.

Fig. 3. CdTe (111)B growth/evaporation rate as a function of Cd and Te fluxes at different temperatures. Solid curves indicate thermodynamic equilibrium position. Growth rate 1 μm/min corresponds to the flux 44.5 ML/s.

To understand what happened with CdTe surface under different conditions we look at the surface composition. At 875K under equimolar and Te-rich conditions, the surface is almost flat, with up to 40% Te adsorbed, however in Cd-rich condition there are few adsorbed atoms. Instead a large (up to 5 layers) surface roughness develops there. Increased roughness under high Cd/Te ratios can explain the acceleration of evaporation.

CONCLUSIONS

Elementary processes of CdTe film growth in from Cd and Te2 precursors were investigated using first-principles methods. Rigid-lattice kinetic Monte Carlo model for CdTe deposition was developed and fitted to the results of first-principles calculations. It was found that direct prediction of film growth kinetics is possible, but due to typical errors of first-principles methods

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