Quantum box fabrication tolerance and size limits in semiconductors and their effect on optical gain
Lower and upper limits on size are established for quantum boxes. The lower limit is shown to result from a critical size below which bound electronic states no longer exist. This critical size is different for electrons and holes. The optical gain of arrays of quantum boxes is computed taking into account the inhomogenous broadening of the gain spectrum resulting from fabricational variations in quantum box size and shape. The dependence of maximum possible gain on an rms quantum box roughness amplitude is determined. For high gain operation a medium composed of quantum boxes does not offer significant advantages over a conventional bulk semiconductor unless quantum box fabricational tolerances are tightly controlled. For low gain operation, however, arrays of quantum boxes may offer the unique advantage of optical transparency at zero excitation. This property does not require excellent fabricational control and may make possible ultralow threshold semiconductor lasers and low noise optical amplifiers.