assp e2301

A single electron in an otherwise unoccupied band (see picture) is placed in a constant electrostatic field E. How does its group velocity evolve in time, assuming there is no scattering?

• It increases linearly.

• It oscillates.

• It is constant with the same sign as E.

• It is constant with an opposite sign as E.

Which of the following is true of an n-MOSFET when a positive voltage higher than the threshold is applied to the gate? 

• Current flows from Gate (G) to Source (S)
• Current flows from Gate (G) to Drain (D)
• Charge carriers under S,G,D are e,e,e
• Charge carriers under S,G,D are e,h,e

For U >> t (on-site interaction >> hopping) and exactly 1 e on each site of a square lattice, we get the Mott insulating state at T=0 temperature. Here the conductivity is zero: σ=0. How much energy is required to get an electron moving (remove an electron from its original position)?

• t
• U
• z t^2 / U, with z coordination number
• U^2/t

What is χ = dM/dH (H-->0)  of a ferromagnet like for 0 < T < T_C, if the magnetic field ( B = µ_0 * H) is aligned parallel to the nonzero magnetization M?

• positive
• negative
• zero
• infinite, in other words the question does not make sense

Let us imagine two electrodes (Left and Right) with different temperatures (T=0 on the left and T>0 on the right) but equal electrochemical potential µL=µR=µ at the time t=0. The nanowire that connects them has a transmission probability T(E) with a step-like increase at µ. Assume the density of states is constant. Electron current contributions are highlighted (purple/green). The contacts are parts of a closed circuit with zero resistance. What happens over time?

• µL=µR do not change, and neither does the current.
• µL will be > µR and the current decays to 0 over time
• µR will be > µL and the current decays to 0 over time
• µL=µR, but TL and TR equalize, and the current decays to 0 over time

Which of the following is required for the operation of a solar cell made of a p-n junction?

• forward bias
• reverse bias
• a band gap < = than the photon energy
• thermal energy k_B*T comparable to the photon energy

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

For U >> t (on-site interaction >> hopping) and exactly 1 e on each site of a square lattice, we get the Mott insulating state at T=0 temperature. Here the conductivity is zero: σ=0. How much energy is required to get an electron moving (remove an electron from its original position)?

• t
• U
• z t^2 / U, with z coordination number
• U^2/t

An electron’s spin ↑ is flipped when scattering on a magnetic impurity (to ↓), while k is unchanged. Does this process contribute to the collision integral in Boltzmann’s equation?

• Yes, since an electron appears in the specific k point with ↓.
• No, since position r and momentum k do not change.

What condition should be satisfied, if we wish to perform coherent electron transport experiments in a nanocircuit? (E.g. Aharonov/Bohm interferometry.)  Please sign the best suited condition.

• There should be no inelastic scattering in the sample along the electron trajectory.
• There should be no elastic scattering in the sample along the electron trajectory.
• There should be absolutely no scattering in the sample along the electron trajectory.