Effects of electron-hole energy transfer on the small-signal modulation response of semiconductor lasers

In this work, without assigning an arbitrary time constant and thus obscuring the role of electron-hole energy transfer, we calculate the electron energy relaxation rate due to electron-hole scattering from first-principles, and derive an explicit formula from this calculation. From our result, we define the electron energy relaxation time due to electron-hole scattering. We incorporate the effect of this electron-hole energy transfer into the rate equations of semiconductor lasers. We perform a small-signal analysis on these rate equations, and, without any approximation in our derivations, we obtain the modulation response function. Our result indicate that the nonlinear gain coefficient due to carrier heating defined in the small-signal modulation response of semiconductor lasers is no longer a simple sum of the term due to electron heating and that due to hole heating