Power Gain Modeling of Si Quantum Dots Embedded in a SiO$_{\bm x}$ Waveguide Amplifier With Inhomogeneous Broadened Spontaneous Emission

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 Schrödinger 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
^-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.