# Effects of 450 MeV Kr Swift Heavy Ion Irradiation on GaN-Based Terahertz Schottky Barrier Diodes
## 3 Results and Discussion  
### Effects of Irradiation on Electrical Properties  
The room temperature _I-V_ and _C-V_ characteristics of the GaN-based THz SBDs were measured as shown in Figure 2a,b. GaN-based THz SBDs with and without SHI irradiation exhibit excellent Schottky diode properties, and their _C-V_ characteristics are consistent with traditional Schottky junction depletion. Compared to pristine GaN-based THz SBDs, the SBDs with SHI irradiation exhibit similar forward _I-V_ and _C-V_ characteristics, but a slight increase in \(I_{R}\). The extracted \(I_{R}\) values under varying irradiation fluences at \(-20\) V are presented in Figure 2c. In SHI irradiation experiments, the standard irradiation fluence is typically \(10^{7}\) ions/cm\({}^{2}\). By linearly fitting the \(I_{R}\) data of GaN-based THz SBDs at \(-20\) V, the \(I_{R}\) increases by \(1.48\times 10^{-7}\) A for every \(10^{7}\) ions/cm\({}^{2}\) increase in Kr SHI irradiation fluence. The \(f_{c}\) at zero bias determines the operating frequency of GaN-based THz SBDs, which can be calculated based on the series resistance (\(R_{s}\)) and total capacitance (\(C_{0}\)), as follows [31; 32]:  
\[f_{c}=\frac{1}{2\pi R_{s}C_{0}} \tag{1}\]  
The \(R_{s}\) and \(C_{0}\) were extracted from forward _I-V_ and _C-V_ data, respectively, and the \(f_{c}\) of GaN-based THz SBDs for varying irradiation fluences were calculated in Figure 2d. As the irradiation fluence increases, the \(f_{c}\) of GaN-based THz SBDs decreases, with a 4% reduction in \(f_{c}\) observed at Kr SHI irradiation fluence of \(10^{7}\) ions/cm\({}^{2}\). The continuous degradation of device performance was accompanied by a sustained increase in the irradiation fluence. The primary transmission mechanism of forward current in Schottky diodes is the thermionic emission (TE) theory, and the forward _I-V_ relationship is given by Equation (2) [33]. \[I=AA^{*}T^{2}exp\Big{(}-\frac{q\varphi_{B}}{kT}\Big{)}\left[exp\left(\frac{q(V -IR_{s})}{nkT}\right)-1\right] \tag{2}\]  
Here, \(A\), _A_*, \(T\), \(\varphi_{B}\), \(k\), and \(n\) are the anode contact area, Richardson constant (26.5 A\(\cdot\)cm\({}^{-2}\)K\({}^{-2}\)) [34], temperature, Schottky barrier height, Boltzmann constant, and ideality factor, respectively. We measured the _I-V_ and _C-V_ data of 50 devices both before  
Figure 1: (**a**) Cross-sectional view, (**b**) image, and (**c**) distribution of GaN-based THz SBD. and after Kr SHI irradiation, the \(n\), and \(\varphi_{B}\) were extracted based on Equation (2), and the average parameter values of GaN-based THz SBDs are displayed in Table 1. Based on the impact of Kr SHIs of 2.5 \(\times\) 10\({}^{7}\) ions/cm\({}^{2}\) fluence, the \(f_{c}\) deteriorated by 9%, the \(I_{R}\) has increased more than twice, the \(n\) has slightly increased, and \(\varphi_{B}\) has slightly decreased; this was determined by comparing the device performance before and after irradiation. At higher doses of Kr SHI irradiation, radiation damage accumulates further, leading to continued degradation of the performance of GaN-based THz SBDs. To analyze the performance of GaN-based THz SBDs by Kr SHI irradiation at 2.5 \(\times\) 10\({}^{7}\) ions/cm\({}^{2}\) fluence, the degradation distribution of key parameters for 50 GaN-based THz SBDs before and after irradiation is statistically summarized in Figure 3. \(\Delta f_{c}\), \(\Delta I_{R}\), \(\Delta n\), and \(\Delta\varphi_{B}\) follow Gaussian distributions centered at 27 GHz, 3.7 \(\times\) 10\({}^{-7}\) A@ \(-\)20 V, 0.022, and 0.016 eV, respectively. The \(n\) and \(\varphi_{B}\) of GaN-based THz SBDs exhibit minor changes under Kr SHI irradiation, which do not significantly impact the Schottky junction properties. However, the \(f_{c}\) and \(I_{R}\) of GaN-based THz SBDs show significant degradation, with \(\Delta f_{c}\) deteriorating by up to 50 GHz and \(\Delta I_{R}\) increasing by up to 3.5 times at \(-\)20V, which highlight the sensitivity of high-frequency parameters to Kr SHI irradiation.