243S2008-02 - D 2 C = 1 r r r C r = C t 0 r C r = K...

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N. CHEUNG, Sp2008 EE243: ADVANCED IC PROCESSING AND LAYOUT Homework Assignment #2 (Due Feb 13, W 9:10am) Reading Assignment PGD, Chapter 6 on thermal oxidation Problem 1 Doping and orientation dependence of thermal oxidation ( Problem 6.16 of Plummer textbook) Problem 2 2-D and 3-D Deal-Grove Model (a) Show that the oxide growth rate for cylindrical geometry can be expressed as: N dx o dt = k s C i = C * 1 k s + 1 h a(t) b(t) + 1 D a(t)log b(t) a(t) Ref: Kao et al, "Two-Dimensional Silicon Oxidation: Experiments and Theory," IEDM , p.388 (1985) (b) Derive the expression for the oxide growth rate of a spherical Si sphere. Answer : N dx o dt = k s C i = k s C * 1+ a 2 k s b 2 h + k s a 2 D ( 1 a(t) - 1 b(t) ) Hints : Make sure you understand the original derivation of 1D Deal-Grove model found in most textbooks. For 2D and 3D problems, mass flow (i.e. flux times transport surface area) is conserved across boundaries
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Diffusion flux inside oxide F 2 = D C r (a) Diffusion Equation in cylindrical co-ordinates
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Unformatted text preview: D 2 C = 1 r r r C r = C t 0 r C r = K =constant (b) Diffusion Equation in spherical co-ordinates D 2 C = 1 r 2 r r 2 C r = C t 0 r 2 C r = K =constant Problem 3 Very thin oxide Growth Model Make an estimate for the additional oxide grown by using the following perturbational approach. Assume 1050 degrees centigrade, atmospheric pressure, no HCL, and no doping. Use the values for the thin oxide term in equation 6.37 on pp. 327 PDG. a) First assume k =0 in the thin oxide term and solve for the oxide thickness versus time. b) Now substitute this function for Xo in the exponential term to produce only a function of time on the right hand side. c) Now integrate the right hand side and find the integrated contribution of the additional oxide growth rate term. (It is purported to be 2.5 nm)...
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This note was uploaded on 11/02/2010 for the course EECS 243 taught by Professor Ee243 during the Spring '03 term at University of California, Berkeley.

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243S2008-02 - D 2 C = 1 r r r C r = C t 0 r C r = K...

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