Power Gain Modeling of Si Quantum Dots Embedded in a SiO Waveguide Amplifier With Inhomogeneous Broadened Spontaneous Emission

摘要

The small-signal power gain of Si quantum dots embedded in a Si-rich SiO $_{x}$ (SiO$_{x}$:Si-QD)-based ridge waveguide amplifier with an inhomogeneously broadened spontaneous emission is analyzed and simulated. The small-signal power gain and the direct bandgap radiative recombination rate of SiO$_{x}$ :Si-QD waveguide amplifier are linked by correlating the rate equation of semiconductor amplifier (SOA) with the finite-potential-well Schr?dinger equation based on a zero-phonon assisted recombination model. Due to the increased momentum overlapping probability of an electron–hole pair in Si-QDs, the radiative lifetime of Si-QDs is abruptly decreased from 6.3?μs to 83?ns by shrinking the average Si-QD size from 4.3 to 1.9?nm. Furthermore, the differential gain and transparency carrier density of SiO$_{x}$ :Si-QD amplifier have been estimated by simulating the small-signal power gain with rate equation of SOA and zero-phonon assisted recombination model, which are mandatory for designing the Si-QD-based optical amplifier. The small-signal gain coefficients of the SiO$_{1.24}$:Si-QD and SiO$_{1.42}$:Si-QD based amplifiers are determined as 9.6?cm $^{-1}$ at 785?nm and 2.3?cm $^{-1}$ at 650?nm, respectively. The differential gains of 6?×?10 $^{-15}$ and 4?×?10- formula formulatype="inline"> $^{-15}$ cm$^{2}$ with the transparency carrier density of 6?×?10$^{18}$ and 2?×?10 $^{18}$?cm$^{-3}$ are determined for the SiO$_{1.24}$:Si-QD and SiO $_{1.42}$:Si-QD.