# Vertical-Type Ni/GaN UV Photodetectors Fabricated on Free-Standing GaN Substrates
## 3 Results and Discussion  
In our previous study, a low growth rate of the GaN epitaxial layer is preferred to reduce the incorporation of unintentional impurities such as C or O. The mobility of the GaN drift layer at a growth rate of 2.61 \(\upmu\)m/h was estimated to be 1370 cm\({}^{2}\)/Vs, and the nearly ideal Schottky contact with an ideality factor \(n=1.04\) and SBH of 0.97 eV were obtained using the Schottky contact of Ni  
Figure 1: (a) I-V characteristics for device-A (5-nm-thick Ni) and device-B (Ni (20 nm)/Au (80 nm)). The reverse I-V curves can be well seen by the TFE model. The inset depicts the schematic structure of device-A. (b) The reverse dark current and photo-current under 350 nm illumination for device-A. The fitting curves governed by TFE are shown. (20 nm)/Au (80 nm) (named device-B) [12]. However, as a photodetector, to obtain the sufficient UV light absorption, the thickness of the Schottky contact should be less than 10 nm, while this may degrade the \(I-V\) properties. The thickness of the Schottky contact of device-B is too thick (Ni (20 nm)/Au (80 nm)), and this device cannot be regarded as the detectors since the electrode is not transparent to the UV light. Therefore, we only compare the \(I-V\) characteristics between device-A and device-B. The optical performances are compared among device A, C, and D. Figure 1a is the \(I-V\) characteristic of the photodetector with a 5-nm-thick Ni Schottky contact (device-A), in comparison to device-B. As can be seen, the thinner Schottky contact degrades the \(I-V\) property both in the forward and reverse regions. The leakage current density is increased by \(\sim\)2 orders of magnitude, but it still shows a low value of \(10^{-7}\) A/cm\({}^{2}\) at the applied voltage of \(-\)5 V. In the forward region, the rectifying characteristics of the device-B is also better than that of device-A. The forward \(I-V\) characteristic of the Schottky contact can be described by the modified thermionic emission (TE) theory, which is given by [12]:  
\[J=J_{s}\left[exp\left(\frac{q(V-IR)}{nkT}\right)-1\right] \tag{1}\]  
where \(q\) is the electronic charge, \(k\) the Boltzmann constant, \(T\) the absolute temperature, and \(n\) the ideality factor. The saturation current density \(J_{s}\) is expressed by:  
\[J_{s}=AA^{*}T^{2}exp\left(\frac{-q\phi_{B}}{kT}\right) \tag{2}\]  
where \(A\) is the effective area of the Schottky contact, \(A^{*}\) the Richardson constant (26 A/(cm\({}^{2}\)-K\({}^{2}\)) for GaN), and \(\phi_{B}\) the Schottky barrier height. For device-A, the ideality factor \(n\) is \(\sim\)1.8, which is much higher than that of device-B (\(n\) = 1.04). This is because of the barrier inhomogeneities at the metal-semiconductor interface with the super-thin Schottky contact [13]. The reverse leakage current of the photodetectors can be well fitted by the thermionic field emission (TFE) model [14]:  
\[J_{TFE}=J_{s}exp\left[\frac{q(V_{R}+V_{n})}{\varepsilon^{\prime}}\right] \tag{3}\]  
\[J_{s}=\frac{A^{*}T\sqrt{\pi q}E_{00}}{k}exp\left[-\frac{q(\phi_{B}-V_{n})}{E_ {0}}\right]\left[q(V_{R}-V_{n})+\frac{q\phi_{B}}{cosh^{2}\left(qE_{00}/kT \right)}\right]^{1/2} \tag{4}\]  
\[\varepsilon^{\prime}=\frac{E_{00}}{E_{00}/kT-tanh(E_{00}/kT)} \tag{5}\]  
\[E_{0}=E_{00}\cot h(E_{00}/kT) \tag{6}\]  
\[E_{00}=\frac{qh}{4\pi}\sqrt{\frac{N_{e}}{m^{*}\varepsilon_{s}}} \tag{7}\]  
\[V_{n}=\frac{kT}{q}\ln(\frac{N_{c}}{N_{e}}) \tag{8}\]  
where \(m^{*}\) is the effective electron mass, \(V_{R}\) the applied reverse bias voltage and \(\varepsilon_{s}\) the dielectric constant of GaN. \(N_{c}\) and \(N_{e}\) represent the effective density of states in the conduction band and the electron density on the \(n\)-GaN surface. \(E_{00}\) reflects the tunneling probability. From fitting, tunneling factor \(E_{00}\) is estimated to be 2.72 meV and 5.61 meV at room temperature, corresponding to the \(N_{e}\) of \(4.52\times 10^{16}\)/cm\({}^{3}\) and \(1.90\times 10^{17}\)/cm\({}^{3}\), for device-B and device-A, respectively.