  Achieving high crystalline quality Ge$_{1-x}$Sn$_{x}$ semiconductors at Sn
content exceeding 10\% is quintessential to implementing the long sought-after
silicon-compatible mid-infrared photonics. Herein, by using sub-20 nm Ge
nanowires as compliant growth substrates, Ge$_{1-x}$Sn$_{x}$ alloys with a Sn
content of 18\% exhibiting a high composition uniformity and crystallinity
along a few micrometers in the nanowire growth direction were demonstrated. The
measured bandgap energy of the obtained Ge/Ge$_{0.82}$Sn$_{0.18}$ core/shell
nanowires is 0.322 eV enabling the mid-infrared photodetection with a cutoff
wavelength of 3.9 $\mu$m. These narrow bandgap nanowires were also integrated
into top-gated field-effect transistors and phototransistors. Depending on the
gate design, these demonstrated transistors were found to exhibit either
ambipolar or unipolar behavior with a subthreshold swing as low as 228
mV/decade measured at 85 K. Moreover, varying the top gate voltage from -1 V to
5 V yields nearly one order of magnitude increase in the photocurrent generated
by the nanowire phototransistor under a 2330 nm illumination. This study shows
that the core/shell nanowire architecture with a super thin core not only
mitigates the challenges associated with strain buildup observed in thin films
but also provides a promising platform for all-group IV mid-infrared photonics
and nanoelectronics paving the way toward sensing and imaging applications.
