8.4 Elastic Scattering From Ionized Impurities

Establishing a method to control electrical conductivity in semiconductors is essential for many practical device applications. The performance of transistors and lasers depends critically upon flow of current through specific regions of a semiconductor. An important way to control the electrical conductivity of a semiconductor is by a technique called substitutional doping.

Substitutional doping involves introducing a small number of impurity atoms into the semiconductor crystal. Each impurity atom replaces an atom on a lattice site of the original semiconductor crystal. In the example, we will be considering a density n of Si donor impurity atoms that occupy Ga sites in a GaAs crystal. At each impurity site, three of the four chemically active Si electrons are used to replace Ga valence electrons. At low temperatures, the remaining Si electron is bound by the positive charge of the Si donor impurity ion. In a GaAs crystal, this extra electron has an effective electron mass of = 0 .07 m ₀ and is in a hydrogenic s-like electronic state (Table 2.1). The coulomb potential seen by the electron is screened by the presence of the semiconductor dielectric which is characterized by dielectric permittivity ?. The screened coulomb potential and the low effective electron mass in the conduction band of GaAs increases the Bohr radius (Eq. (2.69)) characterizing a hydrogenic state from

to an effective Bohr radius given by

where the use of the low-frequency relative dielectric...