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- Which statement about the intrinsic carrier concentration in a semiconductor material is FALSE? The intrinsic carrier concentration is exponentially dependent on the inverse of the temperature of the semiconductor material. In an intrinsic semiconductor material, the concentration of electrons in the conduction band is equal to the concentration holes in the valence band. The intrinsic carrier concentration of a semiconductor material at a constant temperature depends on the Fermi energy. The intrinsic Fermi energy is positioned near the center of the bandgap for an intrinsic semiconductor.Gold has an atomic mass of 197 u, a density of 19.3 x 10^3 kg/m^3, a Fermi energy of 5.54 eV, and a resistivity of 2.04 x 10^-8 ohms. Estimate the mean free path in atom spacings between collisions of the free electrons in gold under the assumption that each gold atom contributes one electron to the electron gas.A silicon p-n junction (ni = 1010 cm3, Na = 1017 cm-3 and Nd = 4 x 1016 cm 3) is biased with an applied voltage Va = -5 V. Calculate the built-in potential, the depletion layer width and the depletion capacitance. Take the temperature as 27°C.
- K: Estimate the ratio of the electron densities in the conduction bands of silicon (Eg 1.14 eV) and gallium arsenide (Eg = 1.42 eV) at 400 K.Consider a pure semiconductor material of silicon. At 300 K, the electron concentration in the conduction band is 1016 cm 3 and the hole concentration in the valance band is 107 cm3. Assume that the electron and hole concentrations vary as T2. Calculate the intrinsic carrier concentration in silicon at T = 350 K. Note: energy gap of silicon = 1.12 ev Boltzmann constant = 8.61x10-5 eV/KIn a certain semiconductor, the valence band can be approximated by the function E(k) = Eo ak² and the conduction band can be described by the function E(k)= E₁ + 3k². Here E(k) is the electron energy and k is the wavevector. Plot E(k) for the two bands. What is the bandgap of this semiconductor? Is this a direct or indirect bandgap semiconductor?
- Given the fermi energy and electron concentration 7.00 eV and 8.0×10²6 e¯/m³ respectively of a Copper of resistivity 1.7×108 2-m, calculate the mean free path. (a) 3780 nm (b) 5000 nm (c) 4100 nm (d) 7000 nmThe Fermi energy of a doped semiconductor is different from that of a pure semiconductor. Consider silicon, where the energy difference between the top of the valence band and the bottom of the conduction band is 1.11 eV. At a temperature of 300 K the Fermi energy of pure silicon lies approximately between the bottom of the conduction band and the top of the valence band. (a) Calculate the probability of occupying a state at the bottom of the conduction band. Consider now that the silicon has been doped with donor atoms that introduce a state at 0.15 eV below the conduction band background. Doping also caused the Fermi level to be shifted to an energy 0.11 eV below the bottom of the conduction band. (b) Under these conditions, calculate the occupancy of the lower end of the conduction band. (c) Calculate the probability that the level introduced by the donor impurities is occupied. JUSTIFY ALL ANSWERS.A pure semiconductor has a band gap of 1.25 eV. The effective masses of electron and hole are 0.1me and 0.5me respectively, where me is the free electron mass. The carrier scattering time is 0.2 ps (Pico seconds). Find the following at a temperature of 300 K(a) Concentration of electrons and holes(b) Fermi energy(c) Electron and hole mobilities(d) Electrical conductivity
- Consider the semiconductor crystal at 300 K. Where n, 1.8 x 10^6 cm. a- In a sample containing only 2.5x10^15 cm* ionized donors, where is the Fermi level (E-E;) in e.v ? b- In a sample containing 2x10^15 cm* ionized donors and 9 x 10^14 cm ionized acceptors, where is the Fermi level (Er-E;) in e.v ?The Fermi energy of a doped semiconductor is different from that of a pure semiconductor. Consider silicon, where the energy difference between the top of the valence band and the bottom of the conduction band is 1.11 eV. At a temperature of 300 K the Fermi energy of pure silicon lies approximately between the bottom of the conduction band and the top of the valence band. (a) Calculate the probability of occupying a state at the bottom of the conduction band. Consider now that the silicon has been doped with donor atoms that introduce a state at 0.15 eV below the conduction band background. Doping also caused the Fermi level to be shifted to an energy 0.11 eV below the bottom of the conduction band. (b) Under these conditions, calculate the occupancy of the lower end of the conduction band. (c) Calculate the probability that the level introduced by the donor impurities is occupied.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.