The Application of Gain Theory to Vertical-Cavity Surface-Emitting Lasers
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The Application
of Gain Theory to Vertical-Cavity Surface-Emitting Lasers
Weng W. Chow and Hans Christian Schneider Abstract The development of vertical-cavity surface-emitting lasers (VCSELs) relies on an understanding of gain-medium physics, more so than in edge-emitting lasers. An important tool in the investigation of semiconductor gain behavior is a theory that provides a systematic account of the interaction between the laser field and the electron–hole plasma, the influence of the band structure, and the many-body effects due to Coulomb interactions among carriers. This article describes a semiclassical approach that is based on the semiconductor Bloch equations, with carrier correlation effects described at the level of quantum kinetic theory. To illustrate its application, we discuss research activities involving the development of gain media for longwavelength VCSELs. Keywords: many-body theory, optoelectronic materials, semiconductors, vertical-cavity surface-emitting lasers (VCSELs).
Introduction An understanding of gain-medium physics is important in the development of vertical-cavity surface-emitting lasers (VCSELs). The most apparent reason is the more than three orders of magnitude reduction in the gain length relative to edge-emitting lasers, which places drastic demands on maximizing active-medium performance. There are complications of a more fundamental nature as well. Because VCSEL optical-cavity resonances are narrow and widely spaced, laser performance strongly depends on the alignment of the gain peak to one of these resonances. This alignment sensitivity is influenced by the detailed spectral shape and carrier-density dependence of the laser gain. In addition, a knowledge of gain-medium behaviors at the microscopic level allows one to selectively perform band-structure and gainregion engineering so that VCSEL structures can be tailored to meet specific performance criteria. For example, when one is selecting MRS BULLETIN/JULY 2002
quantum-well structures for operation at a desired wavelength, a microscopic theory allows the screening of the usually large number of possible quantum-well width and alloy-composition combinations. Calculations of semiconductor gain are performed at different levels of sophistication.1 A very simple but often useful laser model is already obtained at the phenomenological rate equation level, where one keeps only carrier density and laser intensity as dynamical variables. More sophisticated is the treatment based on the free-carrier theory, where the laser gain is computed microscopically but the Coulomb interaction between the charge carriers is ignored. Even by including the Coulomb interaction, one has to make approximations at some level, since the interacting system leads to an infinite hierarchy of coupled equations. Depending on the truncation scheme, one obtains different variants of the many-body approach.
To date, the most predictive gain model for semiconductors uses a truncation scheme that leads to the semiconductor Bloch equations1 with collisi
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