Assignment_5

Assignment_5 - C 4 exp 2 Ï€ âˆ âˆž âˆ’ = = Dt x u s s du e...

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Assignment 5. Due on July 7 (Wednesday) before class. The first 4 problems 5 points each, the last one 10 points. Note: for part C, you can assume uniform doping so you don’t need to look at the Irvin’s curves. For diffusion coefficient D, please give the values both by graph (D vs. 1000/T) and by equation (D=D o e^(-E/kT)), but use the D by equation for the calculation of dose and junction depth. For Gaussian profile, calculate the dopant concentration at x= (Dt), and the x value for C(x)=1/2C(0); do the same for erfc profile. You can find the table for erf and erfc from the textbook or from http://www.eas.uccs.edu/wickert/ece3610/lecture_notes/erf_tables.pdf ( ) = Dt x Dt Q t x

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Unformatted text preview: C 4 exp , 2 Ï€ ( ) âˆ« âˆž âˆ’ = = Dt x u s s du e C Dt x C t x C 2 2 2 2 erfc , Show that a Gaussian profile remains Gaussian after further diffusion. That is, If : (-âˆž < x < + âˆž ) Then after additional time t at the same temperature: Please use the method similar to below for derivation. Here apparently C is not a constant â€“ it is a function of x i as C(x i ,t ) ( ) âˆ’ = 2 4 exp 2 , Dt x Dt Q t x C Ï€ ( ) + âˆ’ + = + ) ( 4 exp ) ( 2 , 2 t t D x t t D Q t t x C ( ) ( ) âˆ‘ = âˆ’ âˆ’ âˆ† = n i i i Dt x x x Dt C t x C 1 2 4 exp 2 ,...
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Assignment_5 - C 4 exp 2 Ï€ âˆ âˆž âˆ’ = = Dt x u s s du e...

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