Theoretical Analysis of Threshold Characteristics in Electrically-Driven GeSn Lasers

GeSn lasers have emerged as a promising solution for on-chip lasers in silicon photonics. This study systematically investigated the threshold characteristics of electrically-driven Ge<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1–<i>x</i></sub>Sn<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> lasers on Si operating at room temperature, focusing on Sn content and defect density. Theoretical models were developed to calculate band structure, carrier occupation, free-carrier absorption (FCA), and threshold current density. The results indicate that at low Sn contents, where the GeSn active layer is an indirect bandgap material, increasing Sn content decreases the energy difference (Δ<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ΓL</sub>) between indirect and direct conduction band edges, thereby reducing transparent carrier density. Conversely, when the GeSn active layer is transformed into a direct bandgap material with a sufficiently high Sn content, the transparent hole density is minimally affected by further Sn increases. Additionally, increasing defect densities increases FCA, suppressing net gain, highlighting the need for high material quality in Ge<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1–<i>x</i></sub>Sn<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> with defect densities below <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</b>×<bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10⁷cm</b><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−</sup><bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">²</b> for efficient lasing. Moreover, while increasing Sn content initially reduces threshold current density, further increments lead to higher Auger recombination current at longer lasing wavelengths, limiting continuous decrease. Therefore, an optimal Sn content of 13% achieves the lowest threshold current density. This study provides valuable guidelines for developing efficient electrically-driven Ge<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1–<i>x</i></sub>Sn<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>x</i></sub> lasers for practical room-temperature applications.