Calculate the probability that an energy state in the valence band at E-E-kT is empty of an electron at T=280 k. assume the Fermi energy is 0.3 eV above the valence band energy.
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- Why does the horizontal Line in the graph in Figure 9.12 suddenly stop at the Fermi energy? Figure 9.12 (a) Density of state for a free electron gas; (b) probability that a state is occupied at T = 0 K; (c) density if occupied states at T = 0 k.To obtain a more clearly defined picture of the FermiDirac distribution, consider a system of 20 FermiDirac particles sharing 94 units of energy. By drawing diagrams like Figure P10.11, show that there are nine different microstates. Using Equation 10.2, calculate and plot the average number of particles in each energy level from 0 to 14E. Locate the Fermi energy at 0 K on your plot from the fact that electrons at 0 K fill all the levels consecutively up to the Fermi energy. (At 0 K the system no longer has 94 units of energy, but has the minimum amount of 90E.) 1 Microstate8 others? One of the nine equally probable microstates for 20 FD particles with a total energy of 94E.At what temperature, in terms of Tc, is the critical field of a superconductor one-half its value at T = 0 K?
- In a Si semiconductor sample of 200 am length at 600 K the hole concentration as a' function of the sample length follows a quadratic relation of the form p (x) = 1 x1015x, at equilibrium the value of the electric field at 160 jum will be: O 1.935 V/cm O 3.250 V/cm O 5805 V/cm O 55.56 V/cm O 6.450 V/cmThe 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.Assume that the Fermi energy level is 0.25 eV above the valence band energy. Let T = 300 K. %3D Determine the probability of a state being empty of an electron at E = E,-3kT/2 %3D Note: Boltzmann Constant is 8.61 x 10 eV/K
- The probability that a state at Ec+kT is occupied by an electron is equal to the probability that a state at Ey-kT is empty. Determine the position of the Fermi energy level as a function of Ec and Ey.The concentration of acceptor silicon atom is 5x10^21 m^-3 at 300 ° K . How far from the edge of the valence band the fermi level if mh = 0.6 m .Prove that mean energy of the electrons at absolute zero <E> = 3.Ef/5 where Ef is the Fermi energy. Show also that <v^2>/<v>^2 = 16/15
- For a spin 1/2 Fermi gas. where is the Fermi – Dirac distribution function a)What is the defination of Fermi energy (Ef), and Fermi temperature (Tf) b) Find Ef in terms of N and V c) What is for Aluminium d) What is the total energy of the Fermi gas at T=0 K. e) What is the pressure at tje Fermi gas at T=0 K.Statistical mechanics-physicsCu Assume that the crystal structure of metallic copper (Cu) results in a density of atoms p = 8.46 × 10²m 3. Each Cu atom in the crystal donates one electron to the conduction band, which leads, for the 3-D Fermi gas, to a densityu of states g(ɛ) = 2 x = ( 2 m ² ) ² 1/2 where m is the effective mass of the conduction electrons. In the low temperature limit (i.c. T = 0 K), find the Fermi energy E, in units of eV. You may assume m* to be equal to the free electron mass mConsider a sample of GaAs at 300 K in which the Fermi level is 0.40 eV below the bottomof the conduction band. For the following questions, the Boltzmann approximation isvalid.a) What is the probability the energy state Ec is occupied by an electron?b) What is the probability a state E = 0.20 eV above the valence band is empty?c) What is the carrier concentration of electrons in this sample? Holes?