A Calculation Method of the Deposition Profiles in Chemical Vapor Deposition Reactors Using Basis Functions
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1024-A06-13
A Calculation Method of the Deposition Profiles in Chemical Vapor Deposition Reactors Using Basis Functions Takahiro Takahashi, Ken Kawamura, and Yoshinori Ema Department of Electrical and Electronic Engineering, Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, 4328561, Japan ABSTRACT In this paper, we introduced a novel calculation method to reproduce deposition profiles in various types of Chemical Vapor Deposition (CVD) reactors. Robust and accurate calculations along with reduced computing cost were achieved by the method. Boundary value problems for estimating diffusion-reaction equations by iterations of numerical integrations were changed into problems of finding the linear combinations consisted of a few "basis functions", which are inherent in the reactors. The coefficients of the linear combinations were optimized by Genetic Algorithms (GA). We could demonstrate the validity of the proposed method using various examples of the reaction mechanisms and conditions. INTRODUCTION CVD is one of the most important manufacturing processes used in the semiconductor industry. Fast and accurate calculation of the predicted results of CVD is helpful to the highthroughput optimization of the CVD processes. However, a huge calculation cost for estimating the predicted results by solving difficult (stiff) diffusion-reaction equations obstructs the practical use of the high-throughput optimization. Therefore, we proposed a novel calculation method using GA to estimate the deposition profiles in the CVD reactor [1]. Although we successfully demonstrated the validity of the method, the application of the method was limited to the specific type of the reactor, that is, a macroscopic cavity (macrocavity) [1]. Therefore, in this study, we developed and generalized the calculation method in order to deal with the various types of the reactors. In additions, we investigated the validity of the method by calculating the deposition profiles in the batch-type reactor with round-shaped substrates as an example of the reactor. THEORETICAL DETAILS In this study, the reaction model consists of deposition species, films, gas-phase reactions with values of the rate constants and surface reactions with values of the rate constants. All of the reactions in the model are the first-order reactions of the species. We assigned the number to the deposition species and the reactions. The number 1 indicates the source gas and all other numbers indicate intermediate species. [2] For the deposition reactor, we used the batch-type reactors with round-shaped substrates corresponding to semiconductor wafers. (Fig. 1) We assumed the axisymmetric profiles to the direction of the gas flow, that is, z-axis.
z R
w
r
θ
Diffusion Flow
Figure 1. Schematic structure of the batch-type reactor with round-shaped substrates. (r: distance from the center of the substrate, R: radius of the substrate, w: interval between the substrates) Under isobaric and isothermal conditions in the reactor, the deposition profiles w
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