DC conductivity and mobility of a degenerate electron gas in heavily doped GaN crystals at room temperature

Abstract

We consider n-type gallium nitride crystals heavily doped with hydrogen-like donors (silicon or germanium atoms) and weakly to moderately compensated by hydrogen-like acceptors (magnesium atoms). Donor and acceptor concentrations correspond to the metallic side of the insulator–metal concentration phase transition (Mott transition). The shift of the conduction band (CB) electron mobility edge into the bandgap, caused by electrostatic fluctuations in the interaction energy between electrons and impurity ions, is taken into account. Within the relaxation time approximation for electron quasi-momentum, the dependences of stationary (DC) electrical resistivity and drift mobility on the concentration of CB electrons in n-GaN crystals are calculated. Each act of elastic Coulomb scattering of a CB electron by a donor or acceptor ion is assumed to occur within a spherical volume of the crystal matrix associated with a single ion. Electron scattering on phonons is considered according to Matthiessen's rule. The calculation results, obtained using the proposed formulas without fitting parameters, quantitatively agree with experimental data over a wide range of CB electron concentrations. From analysis of experimental data, a new approximation formula for drift mobility at room temperature is obtained. The results using the new approximation and the proposed theoretical formula are consistent.