Unformatted text preview: ' , n ! )F / # q & + k B TL
. n0 = N C e!F " !F = ln ( n0 N C ) = #5.78 (non
degenerate semiconductor) Assume ! n = 2 kBTL (non
degenerate, constant mfp) S = ! ( 86 )[ 2 + 5.78 ] = !669 µV/K S = !669 µV/K 2c) Estimate the number of conduction channels per cm2. Make reasonable assumptions, but clearly state them. Solution: ! = n0 q µn = 2q2
M
h " #M= h!
2q2 " ! = n0 q µn = 12.8 S/cm h!
12.8
M= 2
= 13 # 10 3
= 4.2 # 1010 cm 2 2q "
40 # 10 $7
M = 4.2 ! 1010 cm 2 ECE
656 2 Fall 2013 Mark Lundstrom 3) 10/30/13 It is tempting to estimate the momentum relaxation time, ! m , from the mobility and then to multiply by a velocity to get the mean
free
path. Give the correct expression for the mfp for backscattering in 2D – in terms of ! m as extracted from the measured mobility. You may assume a non
degenerate semiconductor. Solution: Dn = !T " = 2 k BT
k T q #m
µn = B
q
q
m* #m ! = 2 k BT
"T ! = "
" ! = " #T $ m * m = 2" k BT
m* 2 k BT
m* #m =" #m $ m*
2 k BT
2 k BT
" m* = #m 2$ k BT
m* (i) # m (ii) (iii) The above expression relates the mean
free
path for backscattering (the “Landauer mean
free
path”) to the transport average scattering time. 4) The purpose of this homework assignment is to solve the Boltzmann Transport Equation for a particle with charge +Zq, where Z is an integer > 1. This may occur in problems like the flow of ions through channels in cell walls or the flow of ions inside a battery. 4a) Solve the BTE in the relaxation time...
View
Full Document
 Fall '14

Click to edit the document details