EASSP

Which quantities equalize when we create a p-n junction? 

• chemical potential
• electrochemical potential
• impurity level energies
• charge carrier densities (n,p)

Where is the chemical potential in a lightly doped n-type semiconductor at so high T that there are much more thermally excited electrons than donor atoms? Assume the CB and VB effective masses (their absolute values) are similar.  

• near the centre of the gap
• on the donor levels
• between the donor levels and E_C
• in the CB

In a nearest-neighbour Heisenberg model on a 2D square lattice with J<0: at low temperature (kT<<J) what do we expect?  

• ferromagnetism (nonzero M magnetisation)
• antiferromagnetism (zero net M but ordered spins)
• paramagnetism (M=0 without H field, and M=χH with χ>0)
• diamagnetism (M=0 without H field, and M=χH with χ<0)

An electron at the top of a valence band in germanium at k_0=0 is excited to near the bottom of the conduction band by a photon. How does its new momentum (k) relate to the typical size of the Brillouin zone, ~pi/a? Help: consider the minimum photon energy, and conservation of energy and momentum.

• much smaller
• comparable
• much larger

When do we talk about a diamagnet? χ is the magnetic susceptibility.

• χ>0
• χ<0
• χ=0

In a doped semiconductor operating in the extrinsic regime, how do we define majority and minority charge carriers? 

• n-doped: h majority, e minority     /   p-doped: e majority, h minority
• n-doped: e majority, h minority    /    p-doped: h majority, e minority

The distribution function f of non-interacting electrons in thermal equilibrium is described by the Fermi function. But let us start with a system out of equilibrium where the distribution function is f(E)=0.5=constant up to a given E_limit value, and zero above. What is the minimum requirement to reach thermal equilibrium? 

• Ballistic behaviour (no interaction with anything else, either: completely free electrons)
• Ballistic behaviour reacting to constant external E, B fields
• Elastic scattering
• Inelastic scattering

What does the Hubbard model predict on a square lattice for the x=1 case (1 e / site on average) if U=0? 

• Insulator
• metal

Which of the following is required for G=2e^2/h conductance in a single-channel ideal quantum wire? Please select the best suited answer. 

• 2D wire with free electrons (parabolic dispersion relation).
• Both 2D or 3D (cylindrical) wires, but only if the free electron picture is valid.
• Either 2D or 3D wire with arbitrary dispersion relation, since the specific form of the dispersion relation at the Fermi energy cancels in the calculation