We have seen in class that the electron concentration in a crystal is n = Ne:-E;)/kT...

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We have seen in class that the electron concentration in a crystal is n = Ne:-E;)/kT where Ec and EF are the conduction band edge and the Fermi level, and No is the effective density of states. For a crystal with an isotropic electron effective mass mn*, N = 2 2mkT h 3/2 In silicon there are six conduction bands minima along the X- directions of Si, namely two minima on each of the three <100> directions in the k-space. (a) Considering the six minima write the effective density of states Nc. (b) Consider now that each minima has an anisotropic effective mass. Looking at the ellipsoid-shaped constant energy surface below, there is a longitudinal effective mass (mi) along one direction (z) and a transverse effective mass (mt) along the other two axes (x and y). Calculate the effective density of states in this case, considering both the six conduction band minima and the anisotropic density of states. Conduction band 1kz m -ky We have seen in class that the electron concentration in a crystal is n = Ne:-E;)/kT where Ec and EF are the conduction band edge and the Fermi level, and No is the effective density of states. For a crystal with an isotropic electron effective mass mn*, N = 2 2mkT h 3/2 In silicon there are six conduction bands minima along the X- directions of Si, namely two minima on each of the three <100> directions in the k-space. (a) Considering the six minima write the effective density of states Nc. (b) Consider now that each minima has an anisotropic effective mass. Looking at the ellipsoid-shaped constant energy surface below, there is a longitudinal effective mass (mi) along one direction (z) and a transverse effective mass (mt) along the other two axes (x and y). Calculate the effective density of states in this case, considering both the six conduction band minima and the anisotropic density of states. Conduction band 1kz m -ky