ECE230A_Homework-2

# ECE230A_Homework-2 - eigenvalue(energy E Note that in this case the effective mass of electron in InGaAs and InAlAs is different a ‐ b InGaAs(m 1

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ECE230A Homework #2 Homework due: October 22, 2009 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 a 1-D crystal with a lattice constant of 3 Å. The periodic potential can be written as V(x) = V o 0 < x < 1Å = 0 1Å< x < 3Å (a) Find the expression of the effective mass away from the zone boundary. (b) Find the effective mass of the lowest band at k= π /30 (Å -1 ) and V o = 2 eV. (c) Find the first three bandgap energies for V o = 2 eV. 3. 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 Schordinger equation in regions I and II. (b) Write the boundary conditions that allow us to solve the coefficients and the

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Unformatted text preview: eigenvalue (energy) E. Note that in this case, the effective mass of electron in InGaAs and InAlAs is different. a ‐ b InGaAs (m 1 ) InAlAs (m 2 ) I II V o 4. This question was created by one of our students in Homework #1. Consider the following XRD pattern for Aluminum (FCC crystal), which is collected using CuK a radiation ( l = 1.540562Å). Please index this pattern and determine the lattice constant. Note that the first number in the parenthesis associated with each peak is the value of 2 θ where θ is the incident angle of the x-ray wrt the diffraction plane. 5. Create our own question related to energy band theory, effective mass, and the concepts of electrons and holes. Provide a solution to your question....
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## This note was uploaded on 10/09/2010 for the course ECE 230 at UCSD.

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ECE230A_Homework-2 - eigenvalue(energy E Note that in this case the effective mass of electron in InGaAs and InAlAs is different a ‐ b InGaAs(m 1

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