Effect of minority-carrier injection on Schottky-barrier heights that approach the semiconductor band gap

Abstract

A guideline for interpretation of capacitive and photothreshold Schottky-barrier energies has been set forth for metal–semiconductor systems which have barrier energies approaching or exceeding the band gap energy. For such systems the measured apparent barrier energies are always less than the true barrier energy if minority-carrier injection controls the incremental field at the interface. For very strong inversion the apparent barrier energy reaches a maximum value independent of the true degree of inversion. However, when the electric field penetration into the metal dominates over the effect of minority-carrier injection, the capacitively measured apparent barrier energies are greater than the true barrier energy and can be greater than the band gap energy without true surface inversion. An approximate universal relationship between the apparent and the true barrier energies has been found for Schottky barriers with a minority-carrier effective density of states Nv greater than 100× the dopant concentration Ns. Then we know the true barrier energy only when the observed capacitive barrier energy is more than one kT from the maximum possible apparent barrier energy predicted by the relationship for a given Nv/Ns. When Nv?100Ns, characterization of C–V data for Schottky barriers requires individual calculations of the detailed relationship between the apparent and the true barrier energies. Existing C–V data for barrier energies close to the band gap energies were interpreted: (1) true barrier energies of the Au–n-GaSb barrier measured by Mead and Spitzer are less than 26 meV greater than 0.61 eV at 298 K and there is no correction for the reported barrier energy, 0.75 eV, at 77 K, (2) bearing in mind all the existing data for Au–p-InAs Schottky barriers we suggest the true barrier energy should be specified as 470±20 meV in the temperature range 4.2 K to 77 K, (3) there appears to be no surface inversion under operating conditions for the Pb–p-PbTe and Sn–p-PbTe Schottky barriers measured at 77 K by Walpole and Nill, despite the fact that the apparent C–V barrier energy for the Sn–p-PBTe barrier exceeds the band gap energy. Finally we have shown that in the presence of strong minority-carrier injection the observed photothreshold barrier energy is greater the greater the applied bias or the higher the dopant concentration, contrary to the tendency expected by the effect of image force alone.