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ECE495N-F08-Exam_2_practice - 1 ECE 495N EXAM II Wednesday...

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1 ECE 495N EXAM II: Wednesday, Nov.5, 2008, ME118, 1130A-1220P CLOSED BOOK PRACTICE EXAM II Problem 1 [p. 2, 3] 8 points Problem 2 [p. 4, 5] 8 points Problem 3 [p. 6, 7] 9 points Total 25 points Useful Relations: These will be provided in the exam. 1 ( ) Fermi function 1 exp( ) / f E E kT µ = + 1 exp( ( ) / ) Law of equilibrium P E N kT Z α α α µ = [ ( )] [ ]exp( .( )) Bandstructure nm m n m h k H ik d d = ( ) ( ( )) Density of states k D E E k δ ε = ( ) ( ) ( ( )) Density of modes x k v k M E E k L π δ ε = Problem 1: A channel has four energy levels all with the same energy ε , but the interaction energy is so high that no more than one of these levels can be occupied at the same time. What is the average number of electrons in the channel if it is in equilibrium with chemical
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