Find the position of the Fermi energy level relative to the intrinsic level of the Si semiconductor at 300 K in units of eV if the probability of finding holes in energy states at Ey – 2kT is equal to 0.6.
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- For free electrons in a solid with Fermi energy EF and temperature T, find the energy for which the probability that a state at that energy is occupied is 0.33.(a) If EF equals Eo, calculate the Fermi probability of a state being occupied at E=E₂+kT. (b) If EF equals Ev, determine the probability of a state being empty at E=E,-kT. (c) Find the probability that an energy level is occupied by an electron when the state is positioned above the Fermi level by 5kT. (d) Determine the probability that an energy level is occupied by an electron when the state is positioned above the Fermi level by 10kT. Utilize Fermi-Dirac statistics with a temperature of T=300K.A non-pure semiconductor has an energy gap of 1ev and a hole density of 1022m−3 at 300K and an electron density of 1016 m−3. Find the Fermi Level location at 500k.
- The Fermi energy for copper is EF = 7.00 eV. For copper at T = 1020 K, (a) find the energy of the energy level whose probability of being occupied by an electron is 0.911. For this energy, evaluate (b) the density of states N(E) and (c) the density of occupied states No(E).A solid with electrons localized on lattice sites is often modeled by so- called "tight-binding" model. In this 1D model the dispersion relation is E(k)= -2Eo cos(ka), where a is the lattice constant. Starting from the effective equation of motion, describe how the electron moves in such a model under the influence of the constant electric field. Assume you measure electrical current as a function of time without any scat- tering. You will find an oscillatory behavior for the current. What is the frequency of this current? This is not observed in practice because scattering will exist.for an intrinsic semiconductor having band gap 0.7eV,calculate the density of holes and electron at room temperature =(27 degres)
- The carrier effective masses in a semiconductor are mn*= 1.21 m0 and mp*= 0.70 m0. Determine the position of the intrinsic Fermi level with respect to the center of the bandgap at T= 300 K.Consider a 100 Ǻ GaAs/AlGaAs quantum well where the electron effective mass is 0.067 m0. There are 2 x 1012 electron/cm2 in the well. At low temperatures, calculate the magnetic field at which the Fermi level just enters the third Landau level of the ground state sub-band.If the Fermi energy EF is in the middle of the GaN band gap, what is the probability of finding an electron, (or equivalently, the probability of a state being occupied), at an energy kbT above the conduction band absolute minimum?
- 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 = 16/15What will be the majority and minority carrier concentrations in a P-Type Semiconductor, if the intrinsic concentration at 300 K is 1.45 x 1010/ cm3, and the dopant acceptor atom concentration is 1015/ cm3?