Week12HWSolutions

0 k bt q 0 k bt q m q z m

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Unformatted text preview: ( Zq )" 0 %f * 1 d'1 &$ x2 % x0 = ! ( Zq )" 0 dx ) # &$ x2 f0 , ! # k! ( + k 2 ! x " ! 2 3 (spherical symmetry) J nx = ! m*$ 2 ) ) 1 d&1 2 ( Zq )" 0 d & 1 Zq )" 0 ( %$ 2 f0 + = ! f ( % 3 dx ' # k! 3 m* dx ( # k! 2 0 + * ' * We can recognize: m*" 2 $3 ' 1 # 2 f0 = n & 2 k BT ) , ! k! % ( so the drift current is (assume constant temperature) J nx = ! k BT ( Zq )" * m 0 dn dn = ! ( Zq ) Dn dx dx (xii) (xiii) where Dn = k BT ! 0 k BT " q! 0 % k BT " µ % = = q $ m* ' q $ Z' #& m* # & dn dx k BT # q" 0 & Dn = q % m* ( $ ' J nx = ! ( Zq ) Dn ECE ­656 5 Fall 2013 Mark Lundstrom 10/30/13 4d) Find the Einstein relation for these charged particles. Solution: Using (ix) and (xiii) D Dn = k BT ! 0 m* k BT = = µ Zq Z q! 0 m* ( ) D Dn = k BT ! 0 m* k BT = = µ Zq Z q! 0 m* ( ) D k BT = µ Zq 5) A Hall effect experiment is performed on a n ­type semiconductor with a length of 2.65 cm, a width of 1.70 cm, and a thickness of 0.0520 cm, in a magnetic field of 0.5 T. The current in the sample along its length is 200 µA. The potential difference along the length of the sample is 195 mV and across the width is 21.4 mV. 5a) What is the carrier concentration of the sample? Solution: Recall that in 2D: ! ! !! E = ! S J n + ( ! S µ n rH ) J n " B E y = ! S J y " ( ! S µ n rH ) J x Bz = " ( ! S µ n rH ) J x Bz #1 & #r & VH = !WE y = ( " S µ n rH ) I x Bz = % µ n rH ( I x Bz = % H ( I x Bz $ nS qµ n ' $ qnS ' which is the same as eqn. (4.110) in FCT r VH = H Bz I qnS ECE ­656 6...
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This document was uploaded on 01/15/2014.

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