Homework_1

# Homework_1 - EE506 Semiconductor Physics Homework...

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

Homework_1 - EE506 Semiconductor Physics Homework...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online