A Mathematical Model of the Gas-Phase and Surface Chemistry in GaAs Mocvd
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A MATHEMATICAL MODEL OF THE GAS-PHASE AND SURFACE CHEMISTRY IN GaAs MOCVD
MICHAEL E. COLTRIN* AND ROBERT J. KEE** *Sandia National Laboratories, Albuquerque, NM 87185 "**SandiaNational Laboratories, Livermore, CA 94550 ABSTRACT This paper presents a detailed mathematical model of the coupled gas-phase chemistry, surface chemistry, and fluid mechanics in the MOCVD of GaAs from trimethylgallium and arsine in a rotating-disk reactor. The model predicts steady-state deposition rates as a function of susceptor temperature and partial pressure of the reactants. Rate constants in the model have been adjusted to match experimental deposition rates from the literature. INTRODUCTION Computer modeling of the chemical vapor deposition process has been the subject of much work in this decade (see, for example, extensive reviews in Refs. [1,2]). Accurate computer models can be used to understand the complicated heat and mass transport leading to deposition. Ideally, such models can be used in the design phase of reactor development to address issues such as deposition uniformity and rate. Previously, we have developed detailed computer models of the coupled gas-phase fluid flow and chemical kinetics in the deposition of Si from SiH 4 in boundary-layer flow [3,4] and for the infinite-radius rotating disk reactor [5]. Detailed predictions of the models compared well with in situ laser-based measurements of chemical species density profiles [6,7]. Our previous models contained a relatively simple treatment of the surface chemistry in the Si CVD system, i.e., boundary conditions on the concentrations of gas-phase species (sticking coefficients). In the MOCVD of GaAs from trimethylgallium (TMG) and arsine (AsH3), details of the surface chemistry are believed to dominate the deposition process [8]. Computer modeling of this system is considerably more challenging because much less is known of the fundamental surface (and gas-phase) kinetics than in the SiH 4 system. In this paper we describe our first attempts to develop a detailed model of the coupled surface chemistry, gas-phase chemistry, and fluid flow in GaAs MOCVD. Taking advantage of a similarity transformation, we use a simple one-dimensional model of an infinite-radius rotating disk [5,9]. A similar modeling effort was recently published by Tirtowidjojo and Pollard [101, who considered 232 gas-phase and 115 surface reactions for GaAs MOCVD in an impinging-jet reactor. The level of detail in our chemistry treatment is considerably simpler than in Ref. [10]. DEFINING EQUATIONS The model solves for the coupled surface chemistry, gas-phase chemistry, and fluid flow in a rotating-disk reactor. We use the von Karman similarity transformation which results in a set of coupled, one-dimensional, ordinary differential equations, which are solved as a boundary-value problem [5,9]. The simplicity of the one-dimensional equations allows consideration of complex gas-phase and surface chemistry, at modest computational effort. The equations defining the model are as follows: du dz
dp + 2V
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