and where VT is the temperature-corrected gas velocity, DT is the reactant diffusion coefficient at temperature T, and b0 is the initial channel height above the susceptor. The exponential variation can be nullified by tilting the susceptor at an angle, 9c (3 to 5°), such that:

2 dO

bovo fT V

where D0 is the diffusion coefficient of the precursor molecule measured at room temperature (TO), Ta is the average temperature of the gas above the susceptor, and V0 is the initial horizontal gas velocity at T0 in front of the susceptor. Low-pressure MOCVD (~10 kPa, or 0.1 atm) increases V0, allowing sin(9c) to approach zero.

The rigorous simulation of mass transport in epitaxial systems involves solving the mass continuity equation and the Navier-Stokes equation of momentum conservation, according to the appropriate boundary conditions set by the geometry of the reactor, the heating method, and gas inlet and outlet flow (Ref 68). With the rapid advances in computation speed and memory over the last decade, numerical models have expanded from simple boundary-layer descriptions, to two-dimensional models, to three-dimensional descriptions of horizontal reactors (Ref 55).

The numerical modeling effort has focused on different reactor cells, such as return cells (Ref 69, 70), horizontal reactors (Ref 71, 72), and recirculation cells in the vertical reactor configuration (Ref 73, 74). The influence of inlet flow rate, pressure, and geometry on the flow pattern has been studied to understand the origin and nature of mixed-convection flows. Two-dimensional simulations of flow patterns have been generated for both horizontal and vertical reactor configurations (Ref 73, 74, 75).

The modeling of three-dimensional flow patterns for the growth of GaAs using TMGa and AsH3 has been reported (Ref 55). The following boundary conditions were used to simplify the solution of the partial differential equations:

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