6b.1. Consider a square sheet with length L, thickness D, and resistivity p and its surface resistance are given by Rsurf pL A Suppose that the minimum collision time D pL Р (LD) D and p= Tmin where vp = Fermi velocity VF Show that for a monoatomic sheet with single atom thickness has a maximum surface resistance of: ħ e² m* ne²T Rsurf Hint: Use n≈ for sheet with single atom thickness and use the momentum using the De-Broglie relation m*v = ħk such that the de-Broglie wavelength is approximately the sheet thickness D. · ~ 4.11 ΚΩ ħ m²vp == / D

The Boltzmann constant is k = 8.617 * 10-5 eV/K. For a metallic solid at room temperature (293 K), what is the probability that an electron state is occupied if its energy is 0.0400 eV above the Fermi level?

The 2DEG in (iii) is patterned to produce a clean, quasi-1D channel. The current I through the channel is = Nev, where N = the number of electrons, e the electronic charge and = the electrons' group velocity. The number of electrons N(ɛ) = f(ɛ, µ)g(ɛ), where f (ɛ, u) =Fermi-Dirac distribution = 1 and g(ɛ) density of states = dn/dɛ. 1+exp() kBT (a). Write down the dispersion relation for free electrons of mass m. What is their group velocity v? (b). Find an expression for g(ɛ) involving the group velocity. Leave your answer in terms of v.

The function F(E) shown here is 10 E-Ho 0 KT -10 0.5 → F(E) a. the Fermi function, fo(E) Ob. 1 - fo(E) Oc. 1 + fo(E) Od. kT Ofo/OE Oe.- KTOfo/OE