Mesoscopic Scale Modeling of Microloading during Lpcvd

This paper discusses a model designed to deal with pattern dependencies of deposition processes. It is a mesoscopic scale model in the sense that it deals with spatial scales on the order of 10 ?3 m to 10 ?2 m, which is intermediate between reactor scale and feature scale. This model accounts for the eeects of the microscopic surface structure via suitable averages obtained by a homog-enization technique from asymptotic analysis. Two studies on the LPCVD of silicon dioxide from tetraethoxysilane are presented to demonstrate the meso-scopic scale model. The rst study shows the eeects of microloading in regions of higher feature density. The second study shows the eeects of varying operating conditions on loading and introduces a generalized Damkoehler number, which includes information about the surface patterns, to quantify the degree of transport limitations. Some thoughts on how this model can be used to bridge reactor scale and feature scale models are presented. INTRODUCTION The trend towards single wafer reactors (SWR) for deposition and etch processes in the microelectronics industry is expected to continue as wafer size continues to increase. In order to make single wafer reactors more economically attractive, deposition and etch processes are being run at high rates to maintain reasonable throughputs.High rates can lead to nonuniformities on the wafer scale because of depletion of reactants and transport limitations. Reactor scale models (RSM) for ow, heat transfer, and chemical reactions are well developed for single wafer reactors used for thermally driven chemical processes and susceptor based heating. In fact, reactor scale modeling and simulation have been used to help design reactors and establish operating conditions which provide acceptable wafer state uniformities for speciic processes 1]. 1 Although not central to the purpose of this paper, the single wafer reactor considered is assumed to be radially symmetric and in stagnation point ow. The wafer rests on a heated susceptor in the center of the reactor chamber, and the reactant gases are introduced through a shower head at the top. A schematic cross-section with a rough sketch of the ow pattern is shown in Figure 1. High deposition rates can also lead to nonuniformities on the feature scale, even in the absence of wafer scale nonuniformities; i.e., the lm thickness may not be uniform inside features. This loss of conformality is well understood and feature scale models (FSM) and simulators are fairly well developed for thermally driven deposition processes …