ECE230AHomework2 - Å , V o in the conduction band is 0.3...

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ECE230A Homework #2 Homework due: October 26, 2010 1. For the Kronig Penny model, show that (a) v g =0 at the band edge. (b) ) sin( ) ) sin( ) cos( ( ) cos( 2 2 2 2 a a a a a P ka a dk d β = where h h ϖ m mE 2 2 = = (c) Find the effective mass assuming P=3 π /2, ka= π, and β a =3π/2 . Indicate the band this effective mass refers to. 2. For the 1-D InGaAs/InAlAs superlattice, the effective mass for InGaAs and InAlAs are denoted as m 1 and m 2 , respectively. (a) Find the general solution of the Schrodinger equation in regions I and II. (b) Write the boundary conditions that allow us to solve the coefficients and the eigen value (energy) E. Note that in this case, the effective mass of electron in InGaAs and InAlAs is different. 3. For a GaAs/AlGaAs superlattice, a=b=50
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Unformatted text preview: Å , V o in the conduction band is 0.3 eV. For simplicity, you can assume the electron effective mass for GaAs and AlGaAs is 0.067m o where m o is the free electron mass. (a) Calculate and plot the conduction band subband structure of the superlattice using Kronig Penny model. (b) Calculate bandgap energies between the subbands from the Kronig Penny model. (c) Calculate the bandgap energies between the subbands using the nearly free electron model. Compare your results with the results from (b). For all your plots and calculations, use eV as the unit for energy and 1/cm as the unit for k. a ‐ b InGaAs (m 1 ) InAlAs (m 2 ) I II V o...
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This note was uploaded on 01/08/2011 for the course ECE ece230a taught by Professor Ece during the Fall '10 term at UCSD.

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