Determination of the quasi-Fermi-level separation in single-quantum-well p-i-n diodes

The radiative behavior of quantum-well (QW) devices depends upon the quasi-Fermi-level separation ΔEf induced in the quantum well. We present a method of obtaining ΔEf in absolute units from the emission spectra of optically or electrically biased QWs. Emission spectra are calibrated by comparison with measurements of the limiting photocurrent. A theoretical model is then used to separate out the effects of carrier generation rate and field-dependent QW absorption. We apply the method to the low-temperature photoluminescence spectra of a set of single QW p-i-n photodiodes at different electric fields. We show that modeled emission spectra agree closely with measured spectra in flatband conditions. We also observe a field-dependent loss in emission intensity—leading to a reduction in ΔEf of several meV—which we attribute mainly to carrier escape from the QW. The derived values for field-dependent nonradiative efficiency are consistent with independent measurements of low-temperature dc photocurrent, and with a simple model for thermally assisted carrier escape. We show how the method can be applied to electroluminescence spectra in order to investigate the dependence of ΔEf on applied bias.