Effect of impurity correlation in modulation-doped quantum wires

A theory is given of the electronic properties of modulation-doped quantum wires which undergo a thermal treatment, taking into account the Coulomb interaction among ionized impurities in the sample preparation. It is pointed out that the correlation among impurities weakens their field and is enhanced when elevating the doping level, lowering the freezing temperature for impurity diffusion, and reducing the size of the impurity system. The screening of the ionic correlation by charge carriers in the sample growth is of minor importance. In the limiting case of a one-dimensional impurity system, the correlation may totally suppress the random field at any doping level, so that a finite electron mobility is governed by other scattering mechanisms than impurity doping, e.g., interface roughness and alloying. It is found that the ionic correlation changes the electron mobility of quantum wires as regards not only its magnitude but its dependence on the doping conditions as well. For impurity systems of a small size, the mobility may be increased by up to more than one order of magnitude at a doping level of ${10}^6{\mathrm{cm}}^{-1}.$