A Mathematical Model for LPCVD in a Single Wafer Reactor

Abstract

A mathematical model for low‐pressure chemical vapor deposition (LPCVD) in a single wafer reactor of the impinging jet type has been developed. The model includes the partial differential equations describing the balance of mass, momentum, heat, and species concentration, Stefan‐Maxwell equations for multicomponent diffusion, multicomponent thermodiffusion, multiple surface reactions, and variable gas properties. Gas‐phase chemistry is neglected. The equations are solved numerically in two‐dimensional, axisymmetric form, using a control‐volume‐based finite difference method. The model is applied to silicon LPCVD from silane. It is shown that in single wafer LPCVD modeling, the coupling of the flow equations to the species concentrations is very important, as are thermodiffusion effects. Multicomponent diffusion phenomena can be modeled accurately using Wilke's approximation in many cases. In some situations, however, the Stefan‐Maxwell equations should be used. The model is used to optimize both reactor geometry and process conditions, in order to obtain uniform deposition on large wafers at high growth rates. A series of parameter variations is presented, illustrating the power of the model as an aid in such an optimization study.

Visualization of Vortex Flow Patterns with a Uniformly Perforated Showerhead in a Model Lamp Heat, Single‐Wafer Thermal Processor

“…Moreover, as the gas enters the reactor through a single-inlet tube, the recirculation cell could be eliminated by increasing the inlet gas flow rate. [19] For low pressure CVD in a single-wafer reactor, Kleijn et al [20] reach a similar conclusion in their numerical computation of the gas flow. Patnaik et al [21] also showed that operating at a pressure of 0.2 atm gave good epilayer uniformity and interface abruptness for GaAs-AlGaAs growth in metal-organic (MO)CVD.…”

Comparison of Coupling Methods for Linking Between Reactor and Feature Scales

“…The reactor geometry of the test cases presented in this study was that of an impinging jet reactor. The reactor-scale geometry, grid, flow rate, reaction model, temperature, and pressures were all based on test case 3 from Kleijn et al [9] The conditions for this test case are an inlet flow rate of 0.2 slm, a wafer temperature of 1000 K, a pressure of 133 Pa, and an inlet gas temperature and wall temperature of 300 K. The composition of the inlet gas is 45 mole percent (m/o) hydrogen, 45 m/o nitrogen, and 10 m/o silane. This case was selected because it provided concentration profiles for verification of the reactor-scale results.…”

“…This made the increased surface area provided by the presence of features more important to the reaction rate than if the reaction rate had been diffusion limited. The chemistry of this test case was also simple, consisting of a one-step reaction model for the hydrogen reduction of silane used by Kleijn et al [9] This resulted in Equation 1.…”

Development of a spatially controllable chemical vapor deposition reactor with combinatorial processing capabilities

“…Their simulation study examined the relationship between the growth uniformity and tilt angle of the susceptor, giving the optimal setting for this reactor geometry parameter. Another example of rigorous modeling and simulation was performed by Kleijn et al (1989). Their mathematical model was used to show the significance of thermal diffusion and its effect on growth uniformity and gas-phase reactant species distribution.…”