Consider a doped semiconductor such as phosphorus-doped silicon. At high density, Mott assumed that the effective potent

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Consider A Doped Semiconductor Such As Phosphorus Doped Silicon At High Density Mott Assumed That The Effective Potent 1 (76.52 KiB) Viewed 24 times

Consider a doped semiconductor such as phosphorus-doped silicon. At high density, Mott assumed that the effective potential due to each hydrogenic impurity is of the form: e2 V(r) = (1) -e-dr er where is the Thomas-Fermi screening length (see, for instance, Chapter 17 of Ashcroft and Mermin), 1 = [me? (2n?n)1/3/e]1/2, and n is the electron density. Follow- ing Mott, use the variational wavefunction (r) = Aer (2) where u is a variational parameter, to show that a bound state will occur below a critical density. Find this critical density in terms of ab = €/m*e”, the Bohr radius in the semiconductor, where m* is the effective mass.