Spontaneous emission in multilayer semiconductor structures

Abstract

Abstract-A theoretical analysis of spontaneous emission from a quantum well in dielectric multilayer structures, especially the influence of dielectric geometry on the relative intensities of guided and radiation modes and on polarization, is presented. We first discuss a relatively simple three-layer case, and subsequently a technologically more interesting five-layer structure that has been proposed for a high-power laser. The expression for the partia,l as well as total, emission rates is derived within a broader framework of coupled Heisenberg equations of motion for charge carriers and the quantized electromagnetic field. Thereby, explicit mode decomposition of the Green tensor is avoided. Still, the beta factor for individual guided modes, which is a relevant quantity for the lasing threshold of a device, can be identified and a competition between modes is shown to exist in specific cases.Index Terms-Multilayer structures, spontaneous emission rate.

Quantum theory of spontaneous emission in multilayer dielectric structures

“…Such a characterization, however, is not unique. introduced by Carniglia and Mandel [39] for the quantization of the electromagnetic field in a dielectric interface, is orthonormal and complete [42] and it has been widely employed to characterize the radiative states in structures like dielectric waveguides [18,21] and planar dielectric microcavities [25,35].…”

“…Refs. [10,11,35,36]. In a generic multilayer structure, the normal set of modes, i.e., a complete and orthonormal set of solutions of Maxwell equations for the considered structure, is well known [37] and consists of a continuous spectrum of radiative modes and a discrete one composed of guided modes, defined for both transverse electric (TE) and transverse magnetic (TM) polarizations [38].…”

High-efficiency semiconductor resonant-cavity light-emitting diodes: a review

“…It is thus clear that the finesse of the FP mode has an optimal value, such that the peak resides well in the extraction cone, and above which value increases only marginally. With the resonant peak given by (22), an approximate criterion can be deduced (26) or , with the reflection coefficient that gives rise to a factor as defined in (26). Secondly, practical cavities have absorption losses.…”

“…Finally, due to the nonzero natural linewidth of the dipole source (the emitting material intrinsic spectrum), improving extraction efficiency at some wavelengths occurs at the expense of other wavelengths, which can cause a decrease of the spectrally integrated efficiency. If is lower than (see (26)), it is of no use to enlarge the finesse of the cavity, that is , with corresponding with . In semiconductors, the relative intrinsic spectral width tends roughly to scale with the wavelength due to thermal motion of carriers (27) Hence short wavelength RCLEDs [e.g., InGaP red RCLED (see Section V)] do not suffer from the linewidth penalty.…”

“…The first series is a quantum-mechanical description based on quantization of the electromagnetic field and mode density. These methods can become complex and their application is restricted to simple, ideal media [9], [26]. The second series is based on a classical approach valid in the so-called weak-coupling regime, which is the working regime of practical planar RCLEDs.…”