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Homework09_solution - Homework 9 Solution Problem 1 Compute...

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1 Homework # 9 - Solution Problem # 1 . Compute the concentration of electrons and holes in an intrinsic semiconductor InSb at room temperature (E g =0.2eV, m e = 0.01 m and m h = 0.018 m ). Determine the position of the Fermi energy. For an intrinsic semiconductor the concentration of electrons and holes are equal and given by ( 29 3/2 3/ 4 / 2 2 2 2 g E kT e h kT n p m m e π - = = . Substituting T =300K and the given values of E g , m e and m h , we obtain n = p 8.1·10 20 m -3 The Fermi energy is determined by 3 ln 2 4 v c h e E E m kT m μ + = + . At T =300K we obtain 0.011 2 v c E E eV μ + + . So the position of the Fermi energy is 0.011eV above the middle of the energy gap. Problem # 2 . Indium antimonide has E g = 0.23 eV; dielectric constant ε = 18; electron effective mass m e = 0.015 m . Calculate the donor ionization energy and the radius of the ground state orbit. At what minimum donor concentration will appreciable overlap effects between the orbits of adjacent impurity atoms occur? This overlap tends to produce an impurity band - a band of
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