Contributions of Franz–Keldysh and Avalanche Effects to Responsivity of a Germanium Waveguide Photodiode in the $\hbox{L}$-Band

Abstract

When driven with a high-voltage reverse bias of 15 V, a germanium photodiode with a silicon waveguide exhibits responsivity of over 1.14 A/W in the entire <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\hbox{C}$</tex> </formula> -and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\hbox{L}$</tex></formula> -bands. The high responsivity in the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\hbox{L}$</tex></formula> -band is due to Franz–Keldysh (F-K) and avalanche effects. We prove by numerical calculation that the high responsivity under high bias driving is due to both effects. For accuracy in the calculation, we consider a change in the thickness of depletion layer in the germanium mesa with bias voltage. Calculation results, considering the contributions of both effects, show good agreement with measurement results. Considering the contributions of both effects to minimum detection limit, we discuss optimization for dark current and the electric field applied to Ge.