assp e1

What is the total angular momentum J of an Fe^3+ ion (in units of ℏ)? See the figure.  (Note: both 4s electrons are removed, and one 3d.)

• 6
• 2
• 3/2
• 5/2

In an extrinsic semiconductor where the binding energy of electrons on donor levels is 10 meV, roughly at what temperature range are extrinsic electrons excited to the conduction band? (k_B = 1.38e-23 J/K , e=1.6e-19 C)

• 1 K
• 10 K
• 100 K
• 1000 K

The charge accumulation in a planar p-n junction corresponds to a local electric field E and electrostatic potential Φ. The Poisson equation is d^2 Φ / dz^2 = - ρ/ε, where ρ is the signed charge density and ε is the dielectric constant. Assuming box-like ρ(z) profiles near the interface (and zero elsewhere), what is the shape of –e*Φ? 

• constant
• constant outside the centre (ρ≠0) region, and smoothly increases inside by ~E_g
• constant outside the centre (ρ≠0) region, and smoothly decreases inside by ~E_g

In graphene, a 2D system with linear dispersion relation ( E ~ |k − K_1,2 |) the Fermi surface is comprised of two circles in k-space around points K_1,2, unlike the single circle in a GaAs based 2DEG. Assuming ballistic and phase coherent transport, what is the first conductance plateau of a graphene based quantum point contact?

• 1 e^2/h
• 2 e^2/h
• 3 e^2/h
• 4 e^2/h

What condition should be satisfied if we wish to perform ballistic transport experiments in a nanocircuit? (E.g. electron focusing).  Please select the best suited condition. (Note: these are idealized conditions, not perfectly achievable.)

• 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.

How can we describe magnetic order in iron?

• Itinerant (from conduction electrons) magnetism
• Heisenberg ferromagnetism
• Mott antiferromagnetism

Consider a quantum wire with an elastic scattering center in the middle. When an electron is reflected, what can we say about the occupation number N here (x = L/2) at the initial and final k state?

• ∂N(kinitial>0,t) / ∂t=0
• ∂N(kfinal<0,t) / ∂t=0
• Both of the above
• Neither

A single electron in an otherwise unoccupied band (see picture) is placed in a constant electrostatic field E. Assuming there is no scattering, how does its group velocity evolve in time long after the E field is turned on?

• It increases linearly.
• It oscillates.
• It is nonzero with the same sign as E.
• It is nonzero with an opposite sign as E.

What condition should be satisfied if we wish to perform ballistic transport experiments in a nanocircuit? (E.g. electron focusing).  Please select the best suited condition. (Note: these are idealized conditions, not perfectly achievable.)

• 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.

Imagine an interface of two different semiconductors. Without contact, the conduction band edge is higher in the right half (closer to vacuum energy), and the default chemical potential is lower (dashed lines). How do the bands align in the vicinity of the interface?

• No slope, no relative shift
  (red)

• Positive slope, no relative shift (green)

• Positive slope, the right side is shifted lower at the interface relative to the left (blue)

• Positive slope, the right side is shifted higher at the interface relative to the left (yellow)