PHZ3400-09 Problem Set 6

Problem 1.

Aluminum is trivalent with atomic weight of 27 and a density of 2.7 $g/cm^{3}$. At room temperature the mean free time between electron collisions is $4{\rm {x}}10^{-14}$ s.

a) Calculate the resistivity of aluminum at room temperature.

b) If a 2-V voltage is applied to the ends of an aluminum wire 10 m long and with a cross- sectional area of $1mm^{2}$, what is the current flowing through it?

Problem 2.

The resistivity of a certain material at room temperature is 0.02 Wm and the Hall coefficient is $5{\rm {x}}10^{-4}$ $m^{3}/C$. An electric field of 1 V/m is applied across it. Deduce all the information you can think of about this material.

Problem 3.

a) Sketch a setup used to measure the Hall effect. Label each part.

b) A semiconductor crystal is 5 mm long, 4 mm wide, and 2 mm thick. A 40mA current flows across the length of the sample after a 2-V battery is connected to the ends. When a 0.1T magnetic field is applied perpendicular to the large surface of the specimen, a Hall voltage of 15mV develops across the width of the sample. Determine the i) conductivity, ii) carrier density, iii) mobility, iv) Fermi velocity, for this semiconductor.

Problem 4.

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.