1. Plot the Fermi-Dirac probability of occupation function frp(E) for T = 0, 10, 100, 200, 300 and 400K.
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- 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/OE3 The Fermi-Dirac distribution provides the fraction of electrons that can be found for a given electron energy and temperature of the material. Silicon is a widely use semiconductor for computer processors and GPUs, with a band gap of 1.11 eV at room temperature (293 K). a) What is the Fermi energy of Silicon at room temperature? b) Calculate the electron concentration (total number of electrons) at 0.6 eV above the fermi level (in the conduction band) of one mol of silicon (each silicon atom contributes 4 electrons).
- 4. Consider a simple cubic system with lattice constant a = 5 Å. Determine the atom density (atoms/cm²) for the (100), (110), and (111) planes.Plot the Fermi-Dirac probability of occupation function fFD(E) for T = 0, 10, 100, 200, 300 and 400K.4. If a kind of particles obeys the following dispersion -Dpa, what is the density of states (three dimensions)?