Description of the trends for rare-earth impurities in semiconductors

Substitutional rare-earth impurities in semiconductors are studied by a self-consistent tight-binding Green’s-function technique previously devised for transition-metal impurities. The 4f states are treated as a frozen core and the 5d states are found to interact so strongly with the neighbors that there are no 5d-derived gap states. The 4f occupancy levels are then calculated and found to be resonant in most cases, leaving $3^{+}$ as the only oxidation state except for a few possible exceptions. These results provide a good overall understanding of the experimental information.