Determination of the Scattering Length (Γ → L) by the Electrically Pumped Germanium Zener Emitter

This letter presents a theoretical analysis and experimental validation of the scattering length of direct electrons <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{\mathrm {dn}}$ </tex-math></inline-formula> in the Germanium Zener Emitter, a promising candidate for integrated low-temperature optical pump sources on the silicon platform. With the increasing demand for stable quantum photonic integrated circuits, efficient optical pump sources operating at cryogenic temperatures are essential. Experimental results demonstrate that reducing the n+ Ge thickness <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d_{\mathrm {n-Ge}}$ </tex-math></inline-formula> to 50 nm enhances the optical power density <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P_{\mathrm {opt}}$ </tex-math></inline-formula> by a factor of 9. These findings highlight the potential of the Germanium Zener Emitter to address the need for efficient, cryogenically compatible optical sources in quantum photonic integrated circuits.