Luminescence and Recombination through Defects inp−nJunctions

We have developed simple expressions for the recombination current occurring in the space-charge region of a $p-n$ junction at high temperatures. The current passing through a defect state in the forbidden gap is shown to vary approximately exponentially with applied voltage as $I\propto \exp \left(\frac{\mathrm{eV}}{\beta \mathrm{kT}}\right)$, where $\beta =1, 2, >2\mathrm{}$ depending on the bias voltage relative to two "kink" voltages $V_k$ and $V_d$. The energy $e{V}_k$ is given approximately by twice the energy of the center as measured from midgap, while $V_d$ is determined by the gap energy and carrier effective masses and by the ratio of the capture cross sections of the center for holes and electrons. These effects are shown to explain the kinks appearing in curves of light intensity versus voltage for electroluminescent diodes. When used to analyze emission peaks from copper-doped GaAs junctions they provide values for the cross-section ratios and identify the center producing the 0.97-eV emission as a donor lying in the upper half of the energy gap.