Numerical model of capacitance in vertical-cavity surface-emitting lasers

In this paper we present a model of impedance and modulation time constants for vertical-cavity surface-emitting lasers (VCSELs) operating above threshold current. A 3D numerical model of potential distribution in the device under a constant bias is used to determine resistances and capacitances of an appropriate equivalent circuit. The model has been verified by comparing the theoretical and measured impedance as a function of frequency Z(f). The measured Z(f) is determined from S-11 small signal modulation experiments. The comparison has been performed for frequencies up to 40 GHz and a wide range of above threshold currents, for two oxide-confined VCSELs of different aperture diameters. We obtained a very good quantitative agreement for frequencies up to about 15 GHz and qualitative agreement over the entire range of currents and frequencies.