Diffusion of Ga Vacancies and Si in GaAs
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DIFFUSION OF Ga VACANCIES AND Si IN GaAs K.B. KAHEN, D.J. LAWRENCE, D.L. PETERSON, and G. RAJESWARAN, Corporate Research Laboratories, Eastman Kodak Company, Rochester, NY 14650-2011 ABSTRACT Using the Si-pair diffusion formalism of Greiner and Gibbons, a new Si diffusion model is developed based on the dominant diffusion species being Si0 ,+ - VG.- pairs, where VGa is the Ga vacancy. In the model, the unknown parameters are the pair diffusion coefficient (Dp) and the equilibrium constant, which are fitted to the experimental data. Dp is also derived to be equal to one-half the Ga vacancy diffusivity. To verify this relation, an experiment to determine the VGa diffusivity, Dr, is performed. A relation for Dv of the form 0.962 exp(-2.72 eV/kT) cm 2/s is obtained, and it is shown that the fitted Dp values are indeed approximately equal to 0.5 D,. I. INTRODUCTION
For a number of years, the accepted model for the diffusion of Si in GaAs has been the Si-pair diffusion theory of Greiner and Gibbons [1]. Their proposal is that at high Si concentrations, the dominant diffusing species are SiGa+ - SiA4 - nearest-neighbor pairs. Using two adjustable parameters, the pair diffusion coefficient, Dp, and the pair equilibrium constant, KP, their model can predict the available Si diffusion data [1,2]. In this paper, a model for Si diffusion will be presented based on combining the pair diffusion formalism of Greiner and Gibbons [1] with the notion of the dominant diffusion species being SiGa' - VGa- pairs. An advantage of our model is that the pair diffusion coefficient can be shown to be a simple function of the VGa diffusivity, D,. Because of the lack of experimental values for Dv, an expression for D, is also derived. The basis for the derivation is the observation that capping superlattice samples with SiO2 enhances the rate of thermal interdiffusion [3]. Assuming this enhancement originates from an increased Ga vacancy distribution inside the sample and that the vacancies diffuse in from the surface, a procedure for determining Dv can be derived. II. Si DIFFUSION MODEL The pair diffusion model [1] is slightly modified when the dominant diffusing species are SiGa+ - VGa" pairs. The major assumption of this model is that the high electrical compensation of Si in GaAs for large Si concentrations and high temperatures results mainly from the production of additional Ga-vacancy acceptors [4,5]. The starting point of the model is the following relation which defines the equilibrium pair concentration, P [6]: ([SiGa+] - P)([VGa-I - P) = KP P
(1)
where [ ] denotes concentration and KI is given by Kp = N / Z exp(-EB / kT).
(2)
In the above N is the molecular density of GaAs, Z is the number of configurations of the pair (Z = 12), and EB is the binding energy of the pair, which is taken to be the Coulombic interacMat. Res. Soc. Symp. Proc. Vol. 163. ©1990 Materials Research Society
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tion energy between the pair at the second nearest-neighbor distance, aD. In terms of Dp, [Si], and P, Greiner and Gibbons [1] derived a relati
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