Week2HWSolutions

M is the longitudinal effective mass and my mt is y

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Unformatted text preview: is the number of states per unit area. Now map these states onto energy: D2 D ( E ) dE = 1 1 N ( k ) dk = kdk A π Note that by convention, D2 D ( E ) dE is the number of states per unit area. Solve for D2 D ( E ) : D2 D ( E ) = 1 dk 1 dk N (k ) =k A dE π dE (*) (**) The bandstructure is: 2k 2 2 E +αE = 2 m* ( 0 ) Differentiate with respect to k: 2 dk 1 + 2α E = * k m ( 0 ) dE k * dk m ( 0 ) = (1 + 2α E ) dE 2 Now insert (**) into (*) to find: D2 D ( E ) = m* ( 0 ) π 2 (1 + 2α E ) ECE- 656 9 Fall 2013 Mark Lundstrom 8/24/2013 ECE 656 Homework 2 (Week 2) (continued) 6) Derive an expression for the 2D density of states for one of the conduction band ellipsoids in silicon. ky * mDOS = ? kx HINT: You may find he discussion in P...
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