Numerical optimization procedure of operating conditions and reactor shapes for a uniform epitaxial layer has been developed for vertical and horizontal reactors. Boundary conditions at the inlet for vertical reactors, and the shape of the horizontal reactor are optimized in the present study. The objective is to minimize the cost function which is defined as the spatial nonuniformity of the growth rate. Followings are incorporated to achieve the aforementioned goal; The cost function is linearized by sequential linear programming to overcome the nonlinear relation between the cost function and the design variables; The design variable for the linearized problem is sought by the random search technique. The sensitivity of the cost function on a design variable is estimated directly from the relation between the growth rate and the reactant concentration distribution. The Navier-Stokes equations that govern the fluid motion, temperature and concentration are solved by a SIMPLE based finite volume method on a nonorthogonal grid. Also adopted is the reduced basis method that gives an approximate optimal solution to save computation time.
The optimization method is applied to find an improved inlet boundary condition for the vertical reactor. The optimization is effective for high Reynolds number flows while it becomes less effective for low Reynolds number flows since any characteristic distributions at inlet is nullified by the strong diffusion. Optimized inlet velocity profile is shown to suppress the buoyancy driven recirculation and increase the uniformity successfully.
For the horizontal reactor, optimizing the reactor geometry is found to be an effective parameter for uniformity. The uniformity is proportional to the Reynolds number regardless of the reactor shape. The relative improvement in uniformity appears to be more pronounced for the horizontal reactors than for the vertical ones. The recirculating flow has adverse effects on uniformity for horizontal reactors; A properly designed reactor can completely remove the recirculation and grow epitaxial layers with perfect uniformity.
