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Homework_1 - EE506 Semiconductor Physics Homework...

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EE506 Semiconductor Physics Homework Assignment #1 Prof. Steve Cronin Due Sept. 13, 2011 Electronic Bandstructure: 1.) Empty Lattice Approximation: Consider a two-dimensional rectangular lattice: a. The real space lattice vectors are given by R i,j = ( ia, jb ). Write an expression for the reciprocal lattice vectors, G n,m . b. Draw the Brillouin zone for the two dimensional square lattice, and label the high symmetry points, Γ = (0, 0), X = ( π /a, 0) and L =( /a , /b ). Indicate the area enclosed by the irreducible Brillouin zone. c. Write a general expression for the E n,m (k) relations for the empty lattice ( i.e ., V(r) = 0) for a two dimensional rectangular lattice in terms of the reciprocal lattice vectors. ( Hint: use parabolic dispersion relation for a free electron. ) d. Make a table of the momenta and energies at the high symmetry points: ( n,m )| ( G k + ) Γ | E Γ | ( G k + ) X | E X | ( G k + ) L | E L | where ( n,m )=(0,0), (1,0), (0,1), (-1,0)…etc. e. Find E(k) explicitly along Γ - X and X - L for the lowest 3 energy levels, indicating the degeneracies of each level. Plot E(k) for these levels (preferably using MATLAB). f.
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Homework_1 - EE506 Semiconductor Physics Homework...

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