DEPOSITION UNIFORMITY, PARTICLE NUCLEATION, AND THE OPTIMUM CONDITIONS FOR CHEMICAL-VAPOR-DEPOSITION IN MULTIWAFER FURNACES

A second-order perturbation solution describing the radial transport o f a reactive species and concurrent deposition on wafer surfaces is de rived for use in optimizing chemical vapor deposition process conditio ns. The result is applicable to various deposition reactions and accou nts for both diffusive and advective transport, as well as both ordina ry and Knudsen diffusion. Based on the first-order approximation, the deposition rate is maximized subject to a constraint on the radial uni formity of the deposition rate. For a fixed reactant mole fraction, th e optimum pressure and optimum temperature are obtained using the meth od of Lagrange multipliers. This yields a weak one-sided maximum; depo sition rates fall as pressures are reduced but remain nearly constant at all pressures above the optimum value. The deposition rate is also maximized subject to dual constraints on the uniformity and particle n ucleation rate. In this case, the optimum pressure, optimum temperatur e, and optimum reactant fraction are similarly obtained, and the resul ting maximum deposition rate is well defined.