# The Frequency Response Characteristics of Ge-on-Si Photodetectors Under High Incident Power
## 3 Experiments and Discussion
To quantitatively study the effect of carrier shielding on the bandwidth, we simulated the distribution of the internal electric field at different incident light power levels with the finite-difference time-domain (FDTD) method. The results are shown in Figure 3. The simulation boundary conditions are set to the perfectly matched layer (PML), with a mesh size of 1 nm. The convergence of the FDTD method relies on the careful selection of step size, appropriate boundary condition settings, and effective error control. The carrier-shielding effect occurs in the light field distribution region within the germanium absorption area, and its intensity is directly proportional to the concentration of photogenerated carriers. Its maximum value is located about 1 \(\upmu\)m from the front end of the germanium absorption region [18]. Therefore, the simulation is focused on the 1D electric field intensity in the germanium absorption region between the metal electrode and the silicon waveguide at this position. When a bias voltage of \(-\)1 V is applied, the minimum internal electric field intensity is approximately 2.34 \(\times\) 10\({}^{4}\) V/cm at an incident light power of 0.5 mW. As the incident light power increases to 4 mW, the minimum internal electric field intensity decreases significantly to 0.26 \(\times\) 10\({}^{4}\) V/cm. This indicates that the electric field in the photogenerated carrier region decreases substantially, whereas the field outside the carrier region increases. These results suggest a pronounced carrier-shielding effect in the region where the electric field weakens. Figure 3: The magnitude of the electric field in the germanium layer is measured along the metal contact and the silicon waveguide at a point 1.1 \(\upmu\)m from the front edge of the absorber and at the center along the width. The electric field intensity required to reach the saturation drift velocity of charge carriers in germanium is 0.97 \(\times\) 10\({}^{4}\) V/cm [19]. When the incident light power is less than 2.5 mW, although the carrier-shielding effect reduces the local electric field intensity, it still allows the carriers to reach their saturation drift velocity. In other words, when the incident light power is below 2.5 mW, the decrease in electric field intensity due to the carrier-shielding effect does not impact the device bandwidth. However, when the incident light power exceeds 3.0 mW, the carrier-shielding effect begins to reduce the bandwidth. The carrier-shielding effect can reduce the electric field intensity in the photodetector at high incident light power levels. To counter this, we can increase the device's internal electric field intensity by increasing the bias voltage, thereby reducing or even eliminating the impact of carrier-shielding on the device bandwidth. The experimental results are presented in Figure 4.  
We applied voltages of \(-2\) V, \(-3\) V, \(-4\) V, and \(-5\) V for incident light powers of 0.5 mW and 4 mW, and we compared the resulting bandwidth characteristics to those observed at a \(-1\) V bias. Given that the photodetector's reverse breakdown voltage is \(-6\) V, those test voltages were set within an appropriate range. At an incident light power of 0.5 mW, increasing the applied bias voltage from \(-1\) V to \(-5\) V resulted in almost no change in bandwidth. However, at an incident light power of 4 mW, increasing the bias voltage to \(-2\) V, \(-3\) V, \(-4\) V, or \(-5\) V increased the bandwidth to 10.84 GHz, 15.03 GHz, 18.62 GHz, or 18.62 GHz, respectively. When the bias voltage is increased to \(-5\) V, the bandwidth characteristics remain almost consistent with those at \(-4\) V and do not continue to increase. The test was conducted by only changing the voltage while keeping the link unchanged so that the bandwidth curves at \(-5\) V and \(-4\) V overlap.