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

Abstract

The small-signal power gain of Si quantum dots embedded in a Si-rich SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> (SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> :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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> :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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> :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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.24</sub> :Si-QD and SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.42</sub> :Si-QD based amplifiers are determined as 9.6 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> at 785 nm and 2.3 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> at 650 nm, respectively. The differential gains of 6 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-15</sup> and 4 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-15</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with the transparency carrier density of 6 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">18</sup> and 2 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">18</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> are determined for the SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.24</sub> :Si-QD and SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.42</sub> :Si-QD.