# Advances in High-Speed, High-Power Photodiodes: From Fundamentals to Applications
## 2 Overall Design Considerations for Photodiodes
### 3-dB Bandwidth Analysis and Discussion
According to the above-mentioned bandwidth equations and the values from Table 1, the 3-dB bandwidths for PIN-PD and UTC-PD can be calculated as shown in Figure 5a, including the assumed values during the calculation. It can be seen that the bandwidth of UTC-PD is proportional to \(1/\rm A^{2}\)[44; 54] when the absorber thickness is larger than 100 nm, while it is proportional to \(1/\rm A\) for PIN-PD [44; 54]. Figure 5c is from [44] as a reference. The well-designed UTC-PD has improved 3-dB bandwidths over 150 GHz, 220 GHz [70], while the maximum value is up to 310 GHz (Figure 5b), and the 10-dB and 15-dB bandwidths are separately 750 GHz and >1 THz,  
Figure 5: (**a**)The calculated 3-dB bandwidth versus the absorber thickness for UTC-PD and PIN–PD. (**b**) The 310 GHz bandwidth [67] is used to indicate the calculated accuracy in (**a**). (**c**) Measured and calculated 3-dB bandwidth for UTC–PD (at high and low input) and PIN–PD [44]. (**d**) Quantum efficiency, responsivity versus 3-dB bandwidth for back-illuminated UTC–PD [44], refracting–facet UTC–PD (RF–PD) [68], and total-reflection UTC–PD (TR–PD) [69]. but the responsivity is only 0.07 A/W [67]. To improve the low responsivity of UTC-PD, the refracting-facet UTC-PD (RF-PD) [68] and total-reflection UTC-PD (TR-PD) [69] are proposed to increase the light propagation length in the absorber, where RF-PD uses an angled edge to reflect the light while TR-PD employs a V-grooved mirror integrated with two PD to totally reflect the back-illuminated light. A high responsivity of 1 A/W with 50 GHz 3-dB bandwidth (0.32 A/W and 170 GHz) is achieved for RF-PD, while the TR-PD shows 0.83 A/W responsivity and a 58 GHz 3-dB bandwidth, as shown in Figure 5d. Up to now, many PIN-PD and UTC-PD structures are proposed to improve the device performance, including frequency response, output power, saturation current, and responsivity, while the common band diagrams, including simple p-i-n type (Figure 2a), partially depleted absorber (PDA) type, dual depletion type, general UTC type, hybrid absorber type, charge-compensated (CC) hybrid absorber type and near-ballistic (NB)/NB-CC type [31; 32; 38; 44; 7; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80], are summarized and shown in Figure 6.  
In practice for UTC-PD, we need to choose one of them for adequate design (such as device size, bandwidth, absorber and collector layers, doping, electrical field, electron mobility, diffusivity, and diffusion time, etc.) according to the requirements and applications. We take the UTC-PD design as an example and assume three types of p-doping in the absorber with the values of \(2.5\times 10^{17}\) cm\({}^{-3}\), \(1\times 10^{18}\) cm\({}^{-3}\), and \(2.5\times 10^{18}\) cm\({}^{-3}\), corresponding the electron mobility (\(\mu_{\rm e}\)) of 6000, 5000 and 4000 cm\({}^{2}\)/Vs [44]. Using equations shown in Part 2.2, the electron traveling time in the absorber (\(\tau_{\rm a}\)), the electron drift time in the collector (\(\tau_{\rm c}\)), and the electron diffusion constant (i.e., electron diffusivity, D\({}_{\rm e}\)) can be calculated as given in Figure 7a-c and summarized in Figure 7d. From Figure 7d, we find that the \(\tau_{\rm a}\) is much bigger than \(\tau_{\rm c}\) and indicates the electron diffusion time in the absorber which determines the total carrier transit time [82], so it only needs to consider \(\tau_{\rm a}\) and use Equation (7), i.e., f\({}_{\rm 3 dB,tr}\), to evaluate the device's 3-dB bandwidth at MMW and THz frequency bands when the absorber thickness is smaller than 100 \(\mu\)m.  
Figure 6: Band diagrams for designing different kinds of PDs to realize various performances, including high responsivity, high speed, and high power [71; 72].