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329sp10hw5sol - ECE 329 Spring 2010 Homework 5 Solution Due...

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Unformatted text preview: ECE 329 Spring 2010 Homework 5 - Solution Due: Feb. 23, 2010 1. a) According to Page 2 in Lecture 11, the mobility is de ned as mobility = qτ m = q mν . Although mν is not explicitly given in the problem, it is related to N e and σ by (see Page 3 in Lecture 11) σ = N e q 2 mν , or mν = N e q 2 σ , therefore, mobility = q mν = q N e q 2 σ = σ N e q = 5 . 8 × 10 7 8 . 45 × 10 28 × 1 . 6 × 10- 19 = 4 . 3 × 10- 3 ( m 2 / ( s · V ) ) , where the unit is derived from v = qτ m E . b) R = l σ · πr 2 = 1000 5 . 8 × 10 7 × π × (1 . × 10- 3 ) 2 = 5 . 5 (Ω) . c) On the one hand, J = I πr 2 . On the other hand, J = σE. ∴ E = J σ = I σ · πr 2 = 1 5 . 8 × 10 7 × π × (1 . × 10- 3 ) 2 = 5 . 5 × 10- 3 ( V/m ) . d) The velocity of an electron is v = qτ m E = mobility · E = 4 . 3 × 10- 3 × 5 . 5 × 10- 3 = 2 . 4 × 10- 5 ( m/s ) , so the time to drift from one end to the other is t = l v = 1000 2 . 4 × 10- 5 = 4 . 2 × 10 7 ( s ) ....
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