7.1

Calculate the coherence length l _? for an electron traveling with a velocity of 3 10 ⁴ m/s in a bulk GaAs semiconductor material. Assume that the lifetime (time between two successive inelastic collisions) is 1.0 ps. What would be the coherence length in GaAs quantum wells and quantum wires?

7.2

A Hall-effect device is fabricated from GaAs bulk material with d = 0.5 mm, W = 3 mm, and L = 10 mm. The electric current is I _x = 5 mA, the bias voltage is V _x = 2.5 V, and the magnetic field is B _z = 0.1 T, The Hall voltage was measured to be V _H = -3.0 mV. Calculate the majority carriers, the mobility and the resistivity. What is the conductivity type?

7.3

The filling factor v is defined as the number of Landau levels lying below the Fermi energy level. Show that this factor is given by v = n _sh/( eB). Assume that Landau levels are spin and valley degenerate.

7.4

Derive Eq. (7.34) and show that for the steady-state case, the magneto-conductivity tensor is give by Eq. (7.35).

7.5

Show that the magnetoresistivity tensor is given by Eq. (7.38).

7.6

A Shubnikov-de Haas experiment was performed on a GaAs/AlGaAs single quantum well. Two consecutive minima in ? _xx were observed at B _z = 1.56 and 2.34 T. Calculate the density of...