Fully coupled electrical and optical simulation of vertical cavity surface emitting lasers.

摘要

The two-dimensional quantum well laser simulator MINILASE has been extended in several ways. First, the underlying device equations have been modified to accomodate the cylindrical geometry of vertical cavity surface emitting lasers (VCSELs). Second, an accurate band structure using the well-known k · p method, altered to include various external potentials, has been added in a fully self-consistent manner. The k · p method also yields the envelope functions within the quantum well which are used to compute the optical coupling strengths between electrons and holes in various subbands. It is shown that inclusion of an accurate bandstructure is important for obtaining correct laser output characteristics such as the modulation response. Finally, a fast new Green's function based optical solver (VMS) has been included self-consistently within MINILASE. The speed of VMS allows for direct inclusion within a Newton-Raphson iteration scheme that is performed very frequently during the simulation. VMS takes as input the change in the dielectric function computed within MINILASE and returns the optical recombination rates and net modal gain as outputs. The theory underlying VMS is presented as well as a detailed description of its coupling with MINILASE. To this end, a (quasi) photon rate equation that describes the dynamic behavior of the optical modes is derived. Finally, results related to the comprehensive coupling scheme are presented. For example, it is shown that the benefits of a tapered oxide aperture postulated to reduce threshold are negligible. Also demonstrated are the detrimental effects of spatial hole burning (an effect of minimal importance in traditional edge-emitting lasers) and vertical carrier leakage on the small signal response.