In the fabrication of solid state devices the growth of silicon dioxide on a silicon wafer...
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In the fabrication of solid state devices the growth of silicon dioxide on a silicon wafer by oxidation is an important step. This is accomplished by exposing a flat silicon wafer to oxygen for a fixed amount of time so that a suitably thick layer of oxide is formed. The reaction is Si + O2→ SiO2. It is believed that the external mass transfer is rapid, and that the process rate is governed by product layer diffusion of molecular oxygen and interfacial reaction at the Si – Sio, interface. Assume that the interfacial reaction is first order in oxygen and the rate of consumption of oxygen per unit area at this interface is ksC where, C is the local concentration of oxygen. It is given that the product layer diffusion coefficient of oxygen is D, the surface concentration of oxygen at the SiO2 – oxygen interface is Co, and the molar density of silicon is ß. Derive an expression for the thickness of the SiO2 layer as a function of time t. Express your answer in terms of D, Co, t, B, and ks only. Assume that the thickness of the product layer formed is the same as that of the silicon reacted. In the fabrication of solid state devices the growth of silicon dioxide on a silicon wafer by oxidation is an important step. This is accomplished by exposing a flat silicon wafer to oxygen for a fixed amount of time so that a suitably thick layer of oxide is formed. The reaction is Si + O2→ SiO2. It is believed that the external mass transfer is rapid, and that the process rate is governed by product layer diffusion of molecular oxygen and interfacial reaction at the Si – Sio, interface. Assume that the interfacial reaction is first order in oxygen and the rate of consumption of oxygen per unit area at this interface is ksC where, C is the local concentration of oxygen. It is given that the product layer diffusion coefficient of oxygen is D, the surface concentration of oxygen at the SiO2 – oxygen interface is Co, and the molar density of silicon is ß. Derive an expression for the thickness of the SiO2 layer as a function of time t. Express your answer in terms of D, Co, t, B, and ks only. Assume that the thickness of the product layer formed is the same as that of the silicon reacted.
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Related Book For
Fundamentals of Momentum, Heat and Mass Transfer
ISBN: 978-1118947463
6th edition
Authors: James Welty, Gregory L. Rorrer, David G. Foster
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