Development of an analytical model of erbium doped silicon laser diode

Abstract

An analytical model is developed for laser operation from erbium doped silicon. The mechanism of erbium excitation through Shockley-Read-Hall (SRH) recombination process in silicon is analyzed for conditions of achieving the lasing threshold. Stimulated and spontaneous emission and the stimulated absorption of light by erbium under different conditions are determined. The effects of erbium concentration, background doping, erbium lifetime, loss coefficient, cartier lifetime etc. are investigated on the light output. Enhancement of the absorption coefficient of light with the increase of carrier injection is studied. Rate equations for the excited erbium atom and photon density are solved for determining the dynamic characteristics of laser. The steady state values for excited erbium atom and photon density are determined as a function of the excitation current. Sinusoidal small signal variation is added to the steady state current density and modulation transfer function is determined to evaluate the frequency response characteristics and 3-dB cutoff points. It is found that bandwidth of erbium doped silicon laser is of the order of hundred MHz range, which increases with the output power level. Numerical solution of the rate equations for large signal is done for studying the transient behavior and tum-on time of the laser. The laser tum-on time is found to reduce with the increasing excitation level.