On the dimensionality of optical absorption, gain, and recombination in quantum-confined structures

The purpose of this paper is to explore the dimensionality of the optoelectronic properties of quantum-well and dot systems by expressing carrier distributions in the confinement directions in terms of envelope functions rather than assuming that carriers are localized to the geometrical extent of the confining potential. The conclusions apply to an ideal two-dimensional (2-D) system or a structure where only the n=1 electron and hole subbands are populated. We show that optical absorption normal to the plane of a QW cannot be expressed as an absorption coefficient but should be specified as a fraction of light transmitted or absorbed per well. The modal gain for light propagating along the plane of a QW does not scale with well width and the variation of the material gain inversely proportional to the well width is a consequence of the definition of the confinement factor and has no independent physical significance. Coupling to the optical mode can be specified as a mode width without the need to assume the gain medium is localized in the well. Optical absorption and gain by quantum dots should be expressed as a cross section per dot. The radiative recombination current should be expressed in terms of a two-dimensional recombination coefficient and use of an equivalent three-dimensional coefficient introduces an artificial dependence on well width which can lead to errors in the comparison of QW systems. We provide an analysis of experimental data for optical absorption in GaAs wells and show that, using the correct dimensional forms, it is straightforward to use this to estimate modal gain and the recombination coefficient.