F f px 0 ii

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Unformatted text preview: approximation assuming a constant relaxation time, and a small electric field, but no concentration gradient. Use the result to derive an equation for the drift current. Solution: BTE: !f !f !f $f + "x +F =# !t !x ! px %m ECE ­656 3 (i) Fall 2013 Mark Lundstrom 10/30/13 steady ­state, spatially uniform, constant scattering time: !f #f =" ! px $0 (ii) (iii) (iv) % $f ( ! f = " ' # 0 Zq E $ px * x & ) (v) (vi) F ! f = "# 0 F $f $ px F = + ZqE x % $f ( f = f0 + ! f = f0 " ' # 0 Zq E $ px * x & ) This is a displaced Maxwellian with the displacement in momentum being: pdx = (! 0 Zq )E x (vii) (viii) The average drift velocity is pdx # q" 0 Z & = E = µE x , m* % m* ( x $ ' so the mobility of these charged particles is: !x = " q! % µ = Z $ *0 ' , #m & (ix) (x) and the drift current is J nx = nZq ! x = n Zq µE x J nx = n ( Zq ) µE x " q! % µ = Z $ *0 ' #m & 4b) Solve the BTE in the relaxation time approximation assuming a constant relaxation time, and a small concentration gradient, but no electric field. Solution: In this case, the steady ­state BTE becomes: ECE ­656 4 Fall 2013 Mark Lundstrom !x 10/30/13 "f $f =# "x %0 ! f = "# 0$ x % f0 %x (xi) 4c) Use the result from 4b) to derive an equation for the diffusion current. Solution: J nx = ( 'f + 1 1 " ( Zq )# x$ f = ! " ( Zq )# x * %& 0# x ' x0 - ! ! !k ) , k J nx = !...
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This document was uploaded on 01/15/2014.

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