Physics 871 (Solid State Physics)

Physics 871: Problem set 5

A certain material is heated until it thermionincally emits electrons.
(a) What is the velocity distribution f(v→) of the emitted electrons? You can calculate this straightforwardly in the Sommerfeld (free-electron) model. (The number of electrons having velocity within d³v of v→ is proportional to f(v→)d³v.)
(b) Show that the average energy per emitted particle is (E/N) = 2k_BT. Discuss this result in the context of thermodynamic equilbrium.
A certain alkali halide has static dielectric constant ε(0) = 5.9 at ω = 0. In the near infra-red it has a non-disperesive dielectric constant ε(∞) = 2.25. The reflectivity of the crystal vanishes at wavelength λ = 30.6 μm. Calculate and sketch the reflectivity coefficient r(ω).
M & A problem 27.5.
A certain insulator has a single parabolic conduction band and single parabolic valence band. Calculate the energy density (per unit volume) for the electrons in the conduction band. What is the deficit of energy from the holes in the valence band?
A tetragonal crystal of intrinsic semiconductor with a diagonal conductivity tensor (of course) has the property σ_xx = σ_yy ≠ σ_zz.
(a) Show that for an applied voltage in the x - y plane the current parallels the electric field.
(b) Confirm whether or not this is the case for the x - z plane.
A slab of a certain cubic intrinsic semiconductor has a single conduction band with energies E(k→) = E_C + (ħk)²/2m^*. One end at z = a is held at a temperature ΔT higher than the other end at z = 0. This temperature difference is small enough that you can ignore the variations of τ and μ with temperature.
(a) What is the current density in the slab in terms of the electron density n, τ, etc?
(b) What is the resulting energy flux in the slab?
(c) How would this change for a heavily doped n-type material?
(d) What is the thermal conductivity in (c)?
(e) Notice that your answer in (d) and its complementary answer for p-doping cannot be summed to give the correct answer for the intrinsic case. Why not?