# Research on Fast Detection Technology of Dark Currents in a Ge-Si Detector Array
## 2 Principle and System  
### New Ge-Si Detector Array  
A photodetector is a device that converts light signals into electrical signals. In order to effectively capture the reflected light signals of the target object on the LiDAR in space, we designed and prepared a 32 \(\times\) 32-pixel Ge-Si photodetector array with a Ge active area of up to 707 \(\upmu\)m\({}^{2}\), as shown in Figure 1. The array consisted of pixels, leads, and electrodes. The pixel-doping structure was achieved by injecting boron elements into the top Si layer on the SOI wafer, forming a P-type doping region and a heavily doped P++ region, respectively. The P++ region formed a cathode through ohmic contact with the Al metal electrode. Afterward, selective epitaxy was carried out on the Si substrate to prepare Ge thin films as the active absorption region of the detector. Finally, phosphorus was injected above the Ge absorption region to form a heavily doped N++ region, which formed an anode through ohmic contact with the Al electrode. In order to characterize the photodetectors, we mainly studied their responsivity and quantum efficiency, dark current, noise characteristics, response bandwidth, gain, gain-bandwidth product, and other parameters [35]. When the photodetector is in a reverse-bias state, even without incident light, a weak current is generated, which is known as a dark current. Dark current generation is related to the electron-hole pairs generated by the thermal motion inside the detector. On the other hand, it is related to the defect of the detector surface, bias voltage, and surface area. Figure 2a shows the equivalent circuit model of the PIN photodetector under no light conditions. In the circuit, \(C_{j}\) is the junction capacitance, \(C_{s}\) is the equivalent parallel capacitance, \(R_{s}\) is the equivalent series resistance, and the dark current \(I_{dark}\) includes the reverse-bias current \(I_{gen}\), the tunneling current \(I_{tun}\), and the parasitic leakage current \(I_{olm}\)[36]. In addition, the dark current is related to the thermal ion emission and temperature [18], and its impact on Ge-Si detectors is relatively small and can be ignored. Figure 2b shows the corresponding bias voltage-dark current curve, where the dark current increases with an increase in the reverse-bias voltage. Figure 1: New Ge-Si detector array structure. As shown in Equation (1), the dark current can be expressed as:  
\[I_{dark}=I_{gen}+I_{tun}+I_{bohm} \tag{1}\]  
Under reverse-bias voltage, electron-hole pairs are generated in the space charge region. Once an electron hole is generated, it is swept out of the space charge region by an electric field, forming a reverse bias to generate current. Equation (2) is the calculation method for the current \(I_{gen}\) generated by reverse bias:  
\[I_{gen}=\frac{Aen_{i}w}{2\tau_{0}} \tag{2}\]  
where \(\tau_{0}\) is the average lifetime of the carrier, \(n_{i}\) is the intrinsic carrier concentration, \(e\) is the electron charge, \(w\) is the volume of the space charge region, and \(A\) is the device area. According to the tunneling effect, when the reverse-bias voltage is too high, the probability of carriers passing through the barrier width of the space charge region greatly increases, resulting in a large current that cannot be ignored. This current is called the tunneling current, and the calculation method for the tunneling current is:  
\[I_{tun}=\left(\frac{2m^{*}}{E_{g}}\right)^{\frac{1}{2}}\cdot\exp\left(-\frac{ 4}{3 eE\hbar}\sqrt{2m^{*}E_{g}^{3}}\right)\cdot A\cdot\frac{e^{3}EV}{4\pi^{2} \hbar^{2}} \tag{3}\]  
where \(E\) is the maximum field strength in the depletion region of the PN junction, \(V\) is the applied reverse-bias voltage, \(A\) is the device area, \(m^{*}\) is the effective mass of the electron, \(E_{g}\) is the energy band gap, \(\hbar\) is the reduced Planck constant, and \(e\) is the electronic quantity.