# The Frequency Response Characteristics of Ge-on-Si Photodetectors Under High Incident Power
## 3 Experiments and Discussion  
We experimentally tested the bandwidth characteristic curves of the photodetector under various incident light powers at a \(-1\) V bias voltage, as shown in Figure 2. The noise generated by the device and the circuit's jitter can lead to testing inaccuracies. To mitigate this, we performed a full calibration of the entire system prior to conducting the tests. The vector network analyzer emits electrical signals, which are amplified and loaded onto a 40 GHz bandwidth lithium niobate modulator. The modulated optical signal enters the detector and is converted into an electrical signal, which is transmitted back to the vector network analyzer. Before testing, it is necessary to calibrate the entire link system to deduct errors generated by the instrument. A 1550 nm laser was utilized; all the lasers mentioned in this paper operate within this wavelength range. To facilitate a clear understanding of the relationship between the bandwidth and the incident light power, power is expressed in milliwatt (mW) units. The minimum incident light power was set to 0.5 mW, with increments of 0.5 mW, resulting in the following power levels: 0.5 mW, 1 mW, 1.5 mW, 2 mW, 2.5 mW, 3 mW, 3.5 mW, and 4 mW. The corresponding optoelectronic bandwidths for each incident light power were determined to be 38.56 GHz, 37.33 GHz, 35.62 GHz, 32.34 GHz, 28.75 GHz, 23.41 GHz, 16.26 GHz, and 6.52 GHz, respectively, as shown in Figure 2. The experimental results demonstrate that the bandwidth decreases with increasing incident light power and that the rate of the decrease becomes more pronounced at higher power levels. The relationship between the bandwidth and the incident light power is further illustrated in Figure 2b. As optical power increases, the responsivity follows a two-stage behavior. In the first stage, the responsivity remains linear, with a value of 1.13 A/W when the incident optical power is \(\leq\)4.37 mW. However, when the incident optical power exceeds 4.37 mW, the responsivity gradually decreases with increasing optical power. Also, the rate of decrease becomes progressively slower. The absorption conversion efficiency of this photodetector is 90.4%. The main causes of light loss include the reflection and scattering of light at the silicon/germanium heterojunction, the absorption of signal light by the metal electrodes, and defects and impurities in the germanium material, which promote the recombination of photogenerated carriers. At a bias voltage of \(-1\) V, the dark current of the detector is 10.32 nA. We used a commercially available modulator to modulate the transmitted pseudo-random sequence code elements and measured a bit error rate of 1.23 \(\times\) 10\({}^{-6}\) for the photodetector. Figure 2: (**a**) Normalized S\({}_{21}\) traces of the photodetector under different incident light power levels. (**b**) The 3 dB bandwidths of the photodetector under different incident light power levels. A major factor contributing to the reduction in bandwidth at high incident light power is the carrier-shielding effect [12; 13; 14]. This carrier-shielding effect occurs due to the rearrangement of photogenerated carriers under the influence of an external electric field. Photogenerated holes move in the direction of the applied electric field, whereas photogenerated electrons move in a direction opposite to the applied electric field. Then, the electrons and holes generate an internal electric field in the opposite direction to that of the external electric field. When the built-in electric field is superimposed with the external electric field, the electric field strength in the absorption region is weakened by the built-in electric field. When the concentration of photogenerated carriers is high, this effect is more pronounced. The carrier-shielding effect leads to a decrease in the electric field strength in the absorption region, thereby reducing the migration rate of the carriers.