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ECE230A_Homework-3_Solution

# ECE230A_Homework-3_Solution - ECE230A Fall 2009 Solution...

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ECE230A Fall 2009 Solution for Homework #3 1. The intrinsic carrier concentration at room temperature (300K) for Ge and Si is 2.3x10 13 cm -3 and 1.1x10 10 cm -1 , respectively. The bandgap energy Eg,Ge=0.67 eV, Eg,Si = 1.1 eV. (a) Find the intrinsic concentrations of Ge and Si at 400K. (b) If Si is doped with shallow acceptors and shallow donors: N a =2x10 15 cm -3 and N d =1x10 15 cm -3 . Calculate the Fermi energy above the valence band edge. (c) If N d > N a , derive = + kT E E N n N N n N n d c c a d a exp ) ( 2 where E d is the energy of the donor state. ANS: (a) The intrinsic carrier concentration i n ⎡− = kT E N N n g v c i 2 exp and 2 3 2 3 2 * 2 2 T h kT m N n c = π , 2 3 2 3 2 * 2 T h kT m s N p v = π For Ge, Asssume eV E E K T gGe K T gGe 67 . 0 ) 300 ( ) 400 ( = = = = Then, ) 300 ( ) 400 ( 2 3 ) 300 ( ) 400 ( ) 300 ( ) 400 ( 2 exp 2 exp 300 400 2 exp 2 exp K T g K T g K T g v c K T g v c K T iGe K T iGe kT E kT E kT E N N kT E N N n n = = = = = = ⎡− ⎡− × = ⎡− ⎡− = ) 300 ( ) 400 ( 2 3 ) 300 ( ) 400 ( 2 exp 2 exp 300 400 K T g K T g K T i K T iGe kT E kT E n n = = = = ⎡− ⎡− × × = 1

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