Calculation of carrier equilibrium effects in transition-metal doped semiconductors with application to Cr-doped GaAs

A diagram useful for representing the electronic levels arising from transition-metal impurities in tetrahedral semiconductors is proposed. Computer calculations of carrier equilibrium effects are described, highlighting the problems of including all relevant physical effects. The calculations are believed to be amongst the most complete attempted to date. Semi-insulating behaviour, conduction activation energy, relative occupations of Cr valence states, and compensation dependence of Cr solubility in Cr-doped GaAs are elucidated. The calculations suggest that the Cr levels tend to follow the valence band edge, rather than the conduction band, as temperature varies, and that the saturated solubility of the neutral species Cr III at the melting point is about 10 17 cm -3 . The calculated variation of electrical resistivity with compensation shows a structured 'resistivity edge', in the region of which the Fermi potential, fractional occupations of Cr oxidation states, and the apparent conduction activation energy all vary rapidly.