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The small-signal power gain of Si quantum dots embedded in a Si-rich SiOx (SiOx: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 SiOx: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 SiOx: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 SiO1.24:Si-QD and SiO1.42: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 cm2 with the transparency carrier density of 6 × 1018 and 2 × 1018 cm-3 are determined for the SiO1.24:Si-QD and SiO1.42:Si-QD.