Impurity Conduction and the Metal-Nonmetal Transition in Manganese-Doped Gallium Arsenide

Abstract

Electrical-transport measurements between 20 and 550 K demonstrate impurity conduction below 100 K in Mn-doped GaAs samples with ${N}_{a}>{10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. Of a group of samples with ${10}^{19}<{N}_{a}<3\ifmmode\times\else\texttimes\fi{}{10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ and moderate compensation ($K<0.1$), some display metallic (activationless) impurity conduction, whereas others have a finite activation energy of about 0.015 eV in the impurity-conduction range. It is concluded that this energy should be identified as ${E}_{2}$ for impurity conduction in a semiconductor with "intermediate-range" doping, and that the transition range of ${N}_{a}$ in which ${E}_{2}$ decreases before vanishing must be a narrow one. The values for ${E}_{2}$ are compatible with the models of Mycielski and of Mikoshiba for this conduction. Since the bound-state wave function for a manganese acceptor has a characteristic radius ${a}_{L}=10.1$ \AA{}, then the critical acceptor density ${N}_{c}$ for a metal-nonmetal transition corresponds with the condition ${a}_{L}{N}_{c}^{\frac{1}{3}}=0.28$. This denotes closer spacing than the Mott-Hubbard criterion because of the compact nature of the manganese wave function. Hopping conduction was not detected with samples containing less than ${10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ of Mn acceptors, and this also is to be expected from the charge distribution of the manganese bound state.