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Plot the Fermi function Vs. Energy at the temperature of 500 K, when EF = 2 eV
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- An atom’s nucleus is a collection of fermions— protons and neutrons. (a) In calculating the Fermi energy in a nucleus, the protons and neutrons must be considered separately. Why? (b) Find the Fermi energy of (i) the protons and (ii) the neutrons in a uranium nucleus, which has a radius of 7.4 x 10-15 m and contains 92 protons and 146 neutrons.Q3/ An experiment was conducted to find the relationship between the specific heat of potassium metal and the temperature, and it was found that this relationship takes the following formula at low temperatures 2.08 +2.57 T2 What is the value of each of: (1) the fermi temperature of potassium? (b) Debye temperature of potassium? Note that specific heat is measured in units of mj / mol / K.Silicon atoms with a concentration of 7× 1010 cm3 are added to gallium arsenide GaAs at T = 400 K. Assume that the silicon atoms act as fully ionized dopant atoms and that 15% of the concentration added replaces gallium atoms to free electrons and 85% replaces arsenic to create holes. Use the following parameters for GaAs at T=300 K: N. = 4.7 x 1017cm-3 and N, = 7 × 1018cm-3. The bandgap is E, = 1.42 eV and it is constant over the temperature range. The hole concentration?
- Silicon atoms with a concentration of 7x 1010 cm3 are added to gallium arsenide GaAs at T = 400 K. Assume that the silicon atoms act as fully ionized dopant atoms and that 15% of the concentration added replaces gallium atoms to free electrons and 85% replaces arsenic to create holes. Use the following parameters for GaAs at T = 300 K: N. = 4.7 x 1017 cm-3 and N, = 7 x 101cm-3. The bandgap is E, = 1.42 eV and it is constant over the temperature range. The donor concentration?O:22) Use fermi approximation to determine the number of softballs that can fit in a 1 meter cube. Calculate the free space in a 1 meter cube box that is filled with softballs. State all assumptions.Silicon atoms with a concentration of 7× 1010 cm³ are added to gallium arsenide GaAs at T = 400 K. Assume that the silicon atoms act as fully ionized dopant atoms and that 15% of the concentration added replaces gallium atoms to free electrons and 85% replaces arsenic to create holes. Use the following parameters for GaAs at T = 300 K: N. = 4.7 × 1017 cm-³ and N, =7 × 1018cm-3. The bandgap is E, = 1.42 eV and it is constant over the temperature range. The electron concentration ?
- Suppose we have an ideal fermion gas of identical particles in a "box" at T = 0 K. Which of the following statements are true? a. The multiplicity of the gas is =1 b. The multiplicity of the gas is =N! C. If the gas consists of electrons with densities that correspond to the typical densities of conduction electrons in metals, only a part of the electrons can contribute to the heat capacity of the system as the temperature rises. d. If the gas consists of electrons with densities corresponding the typical densities of conduction electrons in metals, all electrons can easily contribute to the heat capacity of the system as the temperature rises.Plot the Fermi-Dirac function f(E) versus the energy ratio E/EF at room temperature T=300oK.(Assume EF independent of temperature.)If EF=5ev, determine the energy values at which f (E)=0.5.0.7.0.9 and 0.95?Using the Fermi function, estimate the temperature at which there is a 1% probability that an electron in a solid will have an energy of 0.5 eV above the Fermi energy.
- 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.1. a) Use the Fermi-Dirac distribution function with no approximations to determine the probability than an energy level at E = EF + 5kT is occupied by an electron. b) Use the Boltzmann approximation to determine the probability than an energy level at E = EF + 5kT is occupied by an electron. c) The % difference between a value R and a reference value Rf is determined by the following equation; % D (R-Rf) x 100% Rf Calculate the % difference between results obtained in a) and b) above using the result without the approximation as the reference value. d) Is the Boltzmann approximation valid when E - EF = 5kT? 1.0 Fermi-Dirac function Boltzmann approximation EF Figure 3.35 | The Fermi-Dirac probability function and the Maxwell-Boltzmann approximation.Question 5 Suppose the temperature is T = 300 k. Determine the probability that a state 3kt above the Fermi energy level is occupied by an electron.