## 3 Results
According to the thermal emission theory [24]  
\[I=AA^{*}T^{2}\exp\left(\frac{-q\Phi_{B}}{kT}\right)\exp\left(\frac{qV}{kT}\right) \left\{1-\exp\left(\frac{-qV}{kT}\right)\right\} \tag{1}\]  
where \(A\) is the area of the Schottky contact, \(A^{*}\) is the effective Richardson constant, \(V\) is the applied voltage, and \(T\) is the temperature. The SBHs of the planar-type device, annealed Au/GaN-nanopillar device, and as-etched Au/GaN-nanopillar device can be fitted to be 0.39 eV, 0.19 eV, and \(\sim\)0 eV, respectively. The ideality factor of the planar-type device and annealed Au/GaN-nanopillar device are 1.6 and 2.2, respectively. It is noteworthy that the SBH was recovered to 0.19 eV from about 0 V after post-etching annealing, but was still much lower than the original value of 0.39 eV. The photoresponse performance at zero bias of the annealed Au/GaN-nanopillar device and the Au/GaN-nanopillar device without annealing under alternative light illumination from a blackbody with a long-wavelength pass filter (cutoff wavelength  
Figure 6: **(a)** The I-V curve for the Au contact with the GaN nanopillar as a function of the annealing temperature. **(b)** The typical I-V characteristics of an Au/GaN planar-type device, Au/GaN-nanopillar device (unannealed), and Au/GaN-nanopillar device (annealed). The current–time curve of the Au/GaN-nanopillar device without annealing **(c)**, annealed Au/GaN-nanopillar device, and GaN-nanopillar device **(d)** at zero bias. of 1.1 \(\upmu\)m) are presented in Figure 6c,d, respectively. The photo-to-dark current ratio (PDCR) gives information about the signal-to-noise ratio and can be expressed as follows:  
\[\text{PDCR}=\frac{I_{p}-I_{d}}{I_{d}} \tag{2}\]  
where \(I_{p}\) and \(I_{d}\) are the currents measured at the light illumination and in the absence of incident light, respectively. The photocurrent (\(I_{p}-I_{d}\)) of the Au/GaN-nanopillar device without annealing is larger than that of the annealed Au/GaN-nanopillar device, but its dark current (\(I_{d}\)) is also larger. As a result, the PDCR of the annealed Au/GaN-nanopillar device (-3.1) is about four times larger than that of the Au/GaN-nanopillar device without annealing (-0.65). The results indicate that annealing is an effective way to improve the detection performance. In order to show whether the IR response is from the defect, the photoresponse of the GaN-nanopillar device was measured, as illustrated in Figure 6d. The GaN-nanopillar device had no response to IR, which suggests the IR response was from the hot-electrons generated in metal, instead of the defect or other factors in GaN. Figure 7a presents the wavelength-dependent responsivities of the Au/GaN planar-type device and the annealed Au/GaN-nanopillar device. The photoresponse of the annealed Au/GaN-nanopillar device clearly extended beyond 2000 nm, which indicates that the proposed device is capable of detecting light well below the bandgap of GaN. The responsivity ratio is the ratio of the responsivity of the Au/GaN-nanopillar device to the Au/GaN planar-type device, which increases at first and decreases later, as shown in Figure 7b. The responsivity of the Au/GaN-nanopillar device in the SWIR range can be enhanced by about two orders of magnitude, which is mainly attributed to the surface plasmons generated by the Au/GaN-nanopillar device.