Analysis of Threshold Current Behavior for Bulk and Quantum-Well Germanium Laser Structures

Abstract

We analyze the optical gain of tensile-strained, n-germanium (n-Ge) material taking bandgap narrowing (BGN) for heavily doped Ge into account. Both the direct bandgap and indirect bandgap are narrowed by 60 meV. Our new modeling explains the wide lasing spectrum of 1520-1700 nm in electrically pumped Ge lasers. The calculated materials gain can reach 1000 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> when the injected carrier density is ~mid-10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">19</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> with a combination of 0.25% tensile strain and 4.5×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">19</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> n-type doping. The threshold current density is estimated to be 0.53 kA/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> for an optimized edge-emitting double-heterojunction Ge device, comparable to bulk III-V lasers. We also review current progress on Ge quantum-well (QW) structures. The threshold current density of most Ge QW structures is similar to bulk Ge. Only tensile-strained QWs show reduced threshold currents.