An Evaluation of Simplified Models for Surface Kinetics in Movpe Processes
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AN EVALUATION OF SIMPLIFIED MODELS FOR SURFACE KINETICS IN MOVPE PROCESSES MAX TIRTOWIDJOJO AND RICHARD POLLARD Department of Chemical Engineering, University of Houston, Houston, TX 77204 ABSTRACT A general MOVPE model has been used to assess the applicability of simplified representations for surface kinetics. With the general model, predictions for GaAs deposition on (111 )Ga using trimethylgallium and arsine show excellent agreement with observed growth rates. However, if Langmuir-Hinshelwood kinetics is assumed, the model only matches the deposition rates over a narrow range of operating conditions, even when several rate-limiting steps are included. This limitation arises because combinations of equilibrium constants and local partial pressures often do not give reasonable approximations for the surface concentrations of reactive intermediates. The form of the Langmuir-Hinshelwood relation(s) and the parameter values can be fitted empirically to experimental data, but this could lead to erroneous conclusions concerning process behavior and the model would have limited predictive capabilities. An alternative approach is to use surface reaction probabilities, but they can only be applied in an empirical fashion and their magnitudes depend on gas flow rate, inlet composition, and reactor pressure as well as surface temperature. INTRODUCTION A mathematical model for metalorganic vapor phase epitaxy (MOVPE) of GaAs has recently been developed [1,2]. The analysis considers multicomponent heat and mass transport, the kinetics of reactions in the gas phase and at the deposition surface, and fluid flow for impinging-jet and rotating-disk reactors. A unique feature of the model is that it considers many plausible reactions, and the rate constants for each elementary process are estimated from statistical mechanics, transition-state theory, and bond dissociation enthalpies. With this approach, dominant reaction pathways are predicted rather than assumed, and species compositions and deposition rates are determined without adjusting the value for any kinetic parameter. The theoretical predictions show quantitative agreement with available experimental data [1]. A total of 79 species and 347 elementary processes are included in the model for homoepitaxial formation of GaAs from Ga(CH 3)3 (TMG) and AsH 3 on (111)Ga substrates [1,2]. However, theoretical calculations over a wide range of operating conditions indicate that many of the intermediate species and their reactions do not have an appreciable effect on the system behavior. Therefore, the process can be described accurately with only 19 species and 25 reactions (1,2]. In the model, the forward and backward rates of each surface reaction include the fractional occupancies 0m, of reactant and product species adsorbed on active sites of type m [1]. The finite rates of adsorption and desorption processes are also treated, and steady-state material balances are used to determine the values for 0.m. This approach can be contrasted with previous models of epitaxial chemical
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