In-class exercises

These exercises are presented to the class about half way through a lecture. They take 5 to 10 minutes to complete. Students work in pairs using either a white board or chalk board.

1Estimate free carrier density in Al.
Estimate the Fermi wavelength in Al
2Sketch Re{Ψ(x)} for an electron in the n=1, k=π/4a state of a 1d chain of H atoms
4Estimate v_F in Al (application of semiclassical dynamics
5Estimate the energy of highest energy phonon in a typical crystal (starting point: Typical cohesive energy is 1 eV per atom)
61d subbands: Draw 3d k-space and mark the allowed states when the confinement potential is long and skinny
8Show that conservation of canonical momentum gives same result as Lorentz force when a charged particle moves through a magnetic field
9Find the phonon scattering length given a plot weak localization data
10Use the Thomas-Fermi screening constant to find the carrier density such that K_s is equal to the effective Bohr radius for dopant atoms in semiconductor
11Estimate the typical wavelength of an electron in the conduction band of a lightly n-doped semiconductor at room temparture
12Draw I_tunnel(V_bias) for an STM experiment based on a specific D_tip(E) and D_sample(E)
13Given T_c = 7.2 K in lead, estimate the superconducting condensation energy per unit volume at T = 0 using the BCS result Δ(T = 0) = 1.7 kT
14Estimate B_crit for lead, using info from previous excerise.

Other ideas

  • Graphene is to be used as a transparent top contact of an LED. Choose a typical sheet density of charge and calculate lateral resistance for a square of graphene assuming mobility of 10,000. (It needs to be < 10 Ohm for breakthrough applications).