Let f(s) be the Fermi-Dirac distribution function and be the chemical potential. Obtain the expression for the derivative of f(s) with respect to eat & = μl. (a) (b) (c) (d) -18-18-14 2T 6T 4T 1 T
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- Pure silicon is used as a photon detector. An incoming photon can strike the surface and excite electrons from the valence band to the conduction band, where they can be counted. (a) Compute the number of electrons you would expect to count if a silicon detector is struck with a 1.04-MeV gamma ray produced in the decay of a 136Cs nucleus. (b) Explain why the counting of electrons should be more precise if the detector is cooled well below room temperature.xx=41 Q1. Consider an extrinsic Silicon doped with Indium atoms at a concentration of N₁ = 4×10¹6 cm³ The ionization energy for Indium is given as 0.16eV. Calculate: a) The carrier concentrations no. Po and the Fermi level E-E, at the temperature of T = xx+60 °K. 40+ xx 100 b) The temperature at which Po N₁ cm, for xx<50 60+xx N₁ cm³, for xx 250 100 (Ex: xx = 00 → Po=0.4N₁ -1.6x10¹ cm³; xx=99 Po=1.59N, -6.36x10¹ cmCopper metal can be well-described by assuming that the electrons inside are free, with a den- sity ne = 8.47 × 1028 m-³. Calculate the Fermi energy EF.
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- 3. (a) Use the two-dimensional density of states expression P(e) = Am/2nh² to obtain the chemical potential m of a non-interacting two-dimensional Fermi gas of N femions occupying an area A at temperature T = 0 K. (b) For T > 0 K, show that the chemical potential is given to a good approximation by H= 8p- kgTln (1+ exp (-)).Assume a temperature of 300 K and fi nd the wavelength of the photon necessary to cause an electron to jump from the valence to the conduction band in (a) germanium, (b) silicon, (c) InAs, and (d) ZnS.If you know that the average energy of an electronic gas when T>0 is given by the relationship (e) = N e f(e)g(e)de When substituting for the Fermi function and the density of cases, (广 e3/2 de V (e) = 00 2m 3/2 h2 e(e=ep)/kT + 1 Prove in detail the product of the integration above is [3 (e) = Ef(0) n? (T %3D