Presentation 6 diffusion_I

Presentation 6 diffusion_I - Diffusion •Diffusion...

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Unformatted text preview: Diffusion •Diffusion Mechanisms • Substitutional • Interstitial Particle flux J is proportional to the negative of the gradient of the particle concentration J = − D ∂ N ∂ x D = diffusion coefficient Fick’s First Law Diffusion ∆ C ∆ x F out F in in J out J N ∆ Eqn. Continuity with Law First Combine flux particle the of divergence the of negative the to equal is ion concentrat of increase of Rate : Flux Particle for Equation Continuity x N D J ∂ ∂ − = x t x J t t x N ∂ ∂ ∂ ∂ ) , ( ) , ( − = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ = x t x N D x t t x N ∂ ∂ ∂ ∂ ) , ( ) , ( ion! concentrat of t independen be to assumed D 2 2 ) , ( ) , ( x t x N D t t x N ∂ ∂ ∂ ∂ = Fick’s 2nd Law Diffusion ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ = x t x C D x t t x C ∂ ∂ ∂ ∂ ) , ( ) , ( Fick’s 2nd Law (1) Pre-deposition diffusion Phosphorus Silicon "Predep" controlled dose Drive-in constant dose Phosphorus pre- deposition diffusion (2) Driven-in diffusion Driven-in diffusion Diffusion (1) Pre-deposition diffusion Phosphorus Phosphorus pre- deposition diffusion ( ) ( ) Function Error ary Complement = erfc t Coefficien Diffusion ion Concentrat Surface 2 , : Dose Total 2 , : ion Concentrat = = = = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ∫ ∞ D N Dt N dt t x N Q Dt x erfc N t x N π ⎟...
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This note was uploaded on 10/27/2009 for the course ENGR MSE 401 50 taught by Professor Drwang during the Fall '09 term at LA Tech.

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Presentation 6 diffusion_I - Diffusion •Diffusion...

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