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86 2 578 669 vk s 669 vk 2c estimate

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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...
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