Electrical characterization of heterostructure lasers

An improved phenomenological model of the electrical and optical characteristics of semiconductor heterostructure injection lasers is analyzed with emphasis on the nonlasing-to-lasing phase transition. The model includes both radiative and nonradiative carrier recombination, as well as electron-photon coupling. Recently developed approximations of the Fermi-Dirac integral are used, and they allow closed-form solutions of the electron and photon rate equations to be obtained—even though the carrier populations are highly degenerate near lasing threshold. Because of the detailed information which harmonic-voltage amplitudes provide, calculation of the functional forms of the voltage derivatives of the devices is emphasized, and expressions for the height and width of the second-derivative peak, and for the slope at threshold of the first derivative, are obtained. The effects of carrier degeneracy and of nonradiative recombination are explicitly displayed, and both are found to be important in modifying the values of the parameters entering the traditional form, i=ir exp(qV/mkT), of the forward-conduction current-voltage relation. In (Al,Ga)As stripe-geometry lasers values of m?2 are found to be reasonable.