## 2 Materials and Methods  
Si pieces with a 200 nm-thick thermally-grown SiO\({}_{2}\) layer on top were used as substrates. A supporting Ti structure of contact pads, each 100 nm in thickness, was deposited in the pieces by optical lithography before the growth of the nanowires.  
Both the fabrication and electrical characterization of the samples were performed with a Thermo Fisher _Helios 650 NanoLab_ FIB/SEM microscope, fitted with a Ga\({}^{+}\) ion column and a gas injection system (GIS) for the W(CO)\({}_{6}\) precursor. The acceleration voltage, ion beam current, and dwell time were kept at 30 kV, 7.7 pA, and 200 ns, respectively, in all the growth processes.  
Apart from the temperature, two operating parameters are fundamentally different in a Cryo-FIBID procedure when compared to conventional FIBID: the distance between the sample and the GIS nozzle from which the gaseous precursor is delivered, and the ion dose. The two are intertwined: on the one hand, the GIS-sample distance coarsely determines the amount of precursor that reaches the sample. In room-temperature FIBID, sub-mm distances are typically used to ensure that a continuously replenished precursor monolayer is maintained. Since in Cryo-FIBID precursor molecules reaching the substrate condensate on arrival, larger distances are used, typically in the 5-10 mm range. On the other hand, the ion dose required to decompose the condensed layer will in turn depend on the amount of precursor available, but this will in any case be much lower than its room-temperature counterpart. The GIS-sample distance was set at 10 and 7.5 mm, and the ion dose was modified in the 10-500 uC/cm\({}^{2}\) range.  
To properly achieve the condensation of the precursor layer on top of the substrate, its delivery is performed in a different manner than that used in conventional FIBID: instead of continuously delivering the gaseous precursor to maintain the dynamical equilibrium in the adsorbed monolayer, the GIS nozzle is opened for a fixed amount of time of 10 s, during which the 20 nm-thick precursor condensed layer (estimated from FIB/SEM cross-sectioning of deposited material) forms as the gaseous molecules arrive to the cooled substrate, and is then closed during ion irradiation. The vacuum chamber of the FIB/SEM instrument was kept at a base pressure of \(3\times 10^{-6}\) mbar, which reached pressure values around \(8\times 10^{-6}\) mbar during the 10 s-long injection of the gaseous precursor into the chamber.  
The sample temperature was controlled and regulated using a Kleindiek Nanotechnik _Micro Heating Cooling Stage_ (MHCS) (Figure 1). For precursor delivery and deposition, the temperature of the stage was set at \(-60\)\({}^{\circ}\)C, which was reached after a 7 min-long cooling period. The sample was reheated to 20 \({}^{\circ}\)C following a slower ramp of 5 \({}^{\circ}\)C/min for 16 min, amounting to a total of 23 min for a complete cycle (the actual growth times are negligible, only consisting of the 10 s of GIS delivery and the s/ms-long exposures).  
The composition of the samples was assessed by Energy Dispersive X-ray Spectroscopy (EDX), carried out in a commercial Thermo Fisher _Inspect 50_ Scanning Electron Microscope using an acceleration voltage of 5 kV. The electrical measurements were taken with a Kleindiek Nanotechnik commercial microprobe station mounted on the FIB/SEM microscope,  
Figure 1: Open chamber of the _Helios 650 NanoLab_ FIB/SEM microscope with the MHCS mounted.  
equipped with four microprobes and connected by a chamber feedthrough to a Keithley Instruments 6221 DC current source and 2182 A nanovoltmeter.