ECE230A_2009Fall_Quiz_3_Sol

ECE230A_2009Fall_Quiz_3_Sol - c c f c d c f c d c f N N kT...

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ECE230A Fall 2009 Solution for Quiz #3 1 1. A semiconductor is doped with acceptors (N a ) and donors (N d ). (a) Assuming the degeneracy factor is 2 for donors and 4 for acceptors. N d >> N a , p 0 , and N d is 75% ionized, find the approximate electron concentration. (b) Find the Fermi level in terms of the basic parameters E c , N d , N c , and T. (c) Find the donor ionization energy Ed in terms of the basic parameters E c , N d , N c , and T. ANSWER a) d d N N 75 . 0 = + From charge neutrality, + + = + d a N p N n a N p + = d N n N d >> (both N a and p 0 ) , so and are negligible , so . d d N N 75 . 0 = + d N n 75 . 0 = N d is 75% ionized , so . Thus = E E N n c f c exp (b) d N n 4 3 = kT and from (a) = + =
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Unformatted text preview: c c f c d c f c d c f N N kT E E N N kT E E N N kT E E 3 4 ln or 4 3 ln 4 3 ln d d f d d N kT E E g N N 4 3 exp 1 = + = + (c) The degeneracy factor is 2 (g=2), so 6 1 exp 3 4 exp 2 1 = = + kT E E kT E E d f d f ( ) ) 6 ln( ln 1 6 + = = E kT E E f f d By using the result of (b), 2 9 ln or 9 2 ln ) 6 ln( 3 4 ln + = + = c d c d c c d c c d N N kT E N N kT E kT N N kT E E...
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