Energy-band diagrams of p-i-n heterostructures for single quantum-well lasers

The variations of energy-band diagrams with forward bias voltages for step separate-confinement-heterostructure single quantum-well lasers operated below threshold are investigated by numerically solving the semiconductor device equations with two band parameters described by the generalized Einstein relation and with various position-dependent parameters for the materials. The effects of band-gap shrinkage are included. By examining band diagrams, it is found that the potential profiles of the quantum wells with respect to the centres of the wells are symmetric at high injection, tilted at low injection, or almost flat with reasonable injection. In the intrinsic regions, the difference of the quasi-Fermi potentials can be well approximated by the applied voltage. At high injection, the current density of the I-V characteristic and the current injection efficiency of the device may be overestimated by using the Boltzmann statistics when compared with the Fermi-Dirac statistics