## 3 Device Measurement Results
Figure 4: The measured bias dependent O-E frequency responses for (**a**) Device A and (**b**) Device B under a 50 (1) uW optical pumping power at the 1.31(1.55) uW wavelength. Figure 3: The measured Dark current, photocurrent, and operation gain versus bias voltages under different optical pumping powers at 1.31 and 1.55 uW wavelengths for (**a**) devices A and (**b**) device B. The delay time induced by the avalanched gain, which is the major bandwidth limiting factor of an APD under high-gain (high-bias) operation is thus minimized, resulting in the observed invariance of the 3-dB O-E bandwidth [11]. Figure 6a,b shows the 3-dB O-E bandwidth versus operation gain of Devices A and B, respectively, measured under low 20 (1) uW and high 1 (0.1) mW optical pumping power. As can be seen, for the low pumping power case, our demonstrated Device A can achieve a GBP as high as 459 GHz with a 38% unit-gain external efficiency and Device B has a GBP of around 460 GHz with a 1 A/W unit-gain external responsivity. The maximum GBP values given here just follow the definitions reported for high-speed APDs [6; 17] and these numbers suggest the maximum intrinsic speed of the APD [6; 17]. However, for practical applications, APDs usually cannot be operated in such high-gain regions due to the increase of associated excess noise. Under 0.9 V\({}_{\text{br}}\) operation, the corresponding GBP values for Devices A and B are around 122 (M\({}_{\text{g}}\) = 8.7, 14 GHz) and 42 (M\({}_{\text{g}}\) = 33.5, 1.25 GHz) GHz, respectively. On the other hand, there is a gradual decrease in the maximum values of the GBP to 118 and 40 GHz when the optical pumping power reaches 1 mW and 100 uW, respectively, which can be attributed to the reduction in the multiplication gain versus the increase of optical power, as discussed above. The high GBP of around 460 GHz achieved in our fabricated APDs can be attributed to effect of the multiplication layer, which is thinner than the conventional APD with its uniformly thick M-layer. Thus, localization impact ionization in the M-layer (in the lower M-layer) reduces the probability of the avalanche process occurring in the whole M-layer. In addition, the  
Figure 5: The measured Bias dependent O-E frequency responses for (**a**) Device A (**b**) Device B under a 1 (0.1) mW optical pumping power at the 1.31(1.55) μm wavelength. Figure 6: The measured 3-dB O-E bandwidth versus multiplication gain for (**a**) Devices A and (**b**) Device B at low 20(1) μW and high 1(0.1) mW optical pumping powers. overall gain in our dual multiplication layer is higher, with each layer contributing to the gain, M1 and M2. Thus, the overall gain in our structure is M1*M2 to sustain a constant bandwidth. Furthermore, compared to the gain-bandwidth curves of typical APDs, which usually exhibit monotonic decreases of bandwidth with an increase in the multiplication gain [3; 17], our device curves exhibit different trends. As can be seen for Device A, under a very-high operation gain (>30), the decrease in the bandwidth versus the gain is gradually minimized; for more details, please refer to our previous work [11]. Our APD (Device B) demonstrates a constant O-E bandwidth (~1.25 GHz) over a wide range of operation gains (from 10 to ~300), which means a larger operation window. Figure 7a,b shows the corresponding O-E responses measured under high-gain and low power operation. We can clearly see, the measured bandwidths for devices A and B are pinned at around 3 and 0.9 GHz, regardless of the gain. thereby resulting in the high gain-bandwidth product, as discussed above. In order to further increase the responsivity of Device A for 100 GbE-ER4-Lite (40 km) applications, we increased the absorber layer thickness from 400 to 800 nm [1] to fabricate device C. Figure 8a shows conceptual cross-sectional views of the top-illuminated structure. This absorption layer thickness and the ratio of p-type/intrinsic layer thickness were chosen to balance the resistance-capacitance (RC) and transit time limited bandwidth [1].