PHZ3400-11 Problem Set 5

Problem 1.

a) Derive the expressions for the Fermi energy, Fermi velocity, and electronic density of states for a two-dimensional free electron gas.

b) A 2D electron gas formed in a GaAs/AlGaAs quantum well has a density of $2{\rm {x}}10^{11}cm^{-2}$. Assuming that the electrons there have the free electron mass, calculate the Fermi energy and Fermi velocity.