Magnified image of a computer chip 05mm 1 deposit p

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magnified image of a computer chip 0.5mm 1. Deposit P rich layers on surface. silicon Chapter 6 - ENME 382 Spring 2010 Section 0201 9 3. Result: Doped semiconductor regions. silicon light regions: Si atoms light regions: Al atoms 2. Heat it. Adapted from chapter-opening photograph, Chapter 12, Callister & Rethwisch 3e.
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Diffusion How do we quantify the amount or rate of diffusion? ( )( ) s m kg or s cm mol time area surface diffusing mass) (or moles Flux 2 2 = J Measured empirically Make thin film (membrane) of known surface area Impose concentration gradient Chapter 6 - ENME 382 Spring 2010 Section 0201 10 J slope dt dM A l At M J = = M = mass diffused time Measure how fast atoms or molecules diffuse through the membrane
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Steady-State Diffusion dC - = Fick’s first law of diffusion C 1 C 1 Rate of diffusion independent of time Flux proportional to concentration gradient = dx dC Chapter 6 - ENME 382 Spring 2010 Section 0201 11 dx D J C 2 x C 2 x 1 x 2 D diffusion coefficient 1 2 1 2 linear if x x C C x C dx dC - - = Δ Δ
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Example: Chemical Protective Clothing (CPC) Methylene chloride is a common ingredient of paint removers. Besides being an irritant, it also may be absorbed through skin. When using this paint remover, protective gloves should be worn. If butyl rubber gloves (0.04 cm thick) are used, what is the diffusive flux of methylene chloride through the Chapter 6 - ENME 382 Spring 2010 Section 0201 12 glove? Data: – diffusion coefficient in butyl rubber: D = 110x10 -8 cm 2 /s surface concentrations: C 2 = 0.02 g/cm 3 C 1 = 0.44 g/cm 3
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Example (cont). 1 2 1 2 - x x C C D dx dC D J - - - = D t b 6 2 l = glove C 1 C 2 skin paint remover x x Solution – assuming linear conc. gradient D = 110x10 -8 cm 2 /s C = 0.44 g/cm 3 Data: Chapter 6 - ENME 382 Spring 2010 Section 0201 13 s cm g 10 x 16 . 1 cm) 04 . 0 ( ) g/cm 44 . 0 g/cm 02 . 0 ( /s) cm 10 x 110 ( 2 5 - 3 3 2 8 - = - - = J 1 2 C 2 = 0.02 g/cm 3 C 1 = x 2 – x 1 = 0.04 cm
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Diffusion and Temperature Diffusion coefficient increases with increasing T . D = D o exp - Q d R T Chapter 6 - ENME 382 Spring 2010 Section 0201 14 = pre-exponential [m 2 /s] = diffusion coefficient [m 2 /s] = activation energy [J/mol or eV/atom] = gas constant [8.314 J/mol-K] = absolute temperature [K] D D o Q d R T
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