  There is an increasing need for silicon-compatible high bandwidth
extended-short wave infrared (e-SWIR) photodetectors (PDs) to implement
cost-effective and scalable optoelectronic devices. These systems are
quintessential to address several technological bottlenecks in detection and
ranging, surveillance, ultrafast spectroscopy, and imaging. In fact, current
e-SWIR high bandwidth PDs are predominantly made of III-V compound
semiconductors and thus are costly and suffer a limited integration on silicon
besides a low responsivity at wavelengths exceeding $2.3 \,\mu$m. To circumvent
these challenges, Ge$_{1-x}$Sn$_{x}$ semiconductors have been proposed as
building blocks for silicon-integrated high-speed e-SWIR devices. Herein, this
study demonstrates a vertical all-GeSn PIN PDs consisting of
p-Ge$_{0.92}$Sn$_{0.08}$/i-Ge$_{0.91}$Sn$_{0.09}$/n-Ge$_{0.89}$Sn$_{0.11}$ and
p-Ge$_{0.91}$Sn$_{0.09}$/i-Ge$_{0.88}$Sn$_{0.12}$/n-Ge$_{0.87}$Sn$_{0.13}$
heterostructures grown on silicon following a step-graded
temperature-controlled epitaxy protocol. The performance of these PDs was
investigated as a function of the device diameter in the $10-30 \,\mu$m range.
The developed PD devices yield a high bandwidth of 12.4 GHz at a bias of 5V for
a device diameter of $10 \,\mu$m. Moreover, these devices show a high
responsivity of 0.24 A/W, a low noise, and a $2.8 \,\mu$m cutoff wavelength
thus covering the whole e-SWIR range.
