# Advances in High-Speed, High-Power Photodiodes: From Fundamentals to Applications
## 2 Overall Design Considerations for Photodiodes
### 3-dB Bandwidth Analysis and Discussion
However, the electron drift time, \(\tau_{\rm c}\), usually can be ignored for a designed UTC-PD which has a similar thickness for the absorber and collector due to the relatively greater carrier traveling time (\(\tau_{\rm a}\)) in the absorber. The \(\tau_{\rm a}\) can be separately calculated to be 3.74 ps and 11.2 ps for the 200 nm and 600 nm absorber by [44; 54]  
\[\tau=\sqrt{\tau_{\rm a}^{2}+\tau_{\rm c}^{2}+\tau_{\rm RC}^{2}}, \tag{1}\]1  
It is quite clear that we can ignore the electron drift time when the thickness of the absorber approximately equals the collector. Therefore, the total bandwidth, \(f_{\rm 3 dB,UTC}\), as a general case, can be written as  
\[\tau=\sqrt{\tau_{\rm a}^{2}+\tau_{\rm c}^{2}+\tau_{\rm RC}^{2}}, \tag{1}\]2  
while the similar values for the absorber and collector, i.e., \(W_{\rm a}\cong W_{\rm c}\), so Equation (10) can be changed to  
\[\tau=\sqrt{\tau_{\rm a}^{2}+\tau_{\rm c}^{2}+\tau_{\rm RC}^{2}}, \tag{1}\]3  
and the \(f_{\rm 3 dB,UTC}\) also has another form, as shown in Equation (12), for treating PD with a small junction area less than 10 \(\mu\)m\({}^{2}\). \[\tau=\sqrt{\tau_{\rm a}^{2}+\tau_{\rm c}^{2}+\tau_{\rm RC}^{2}}, \tag{1}\]4 \begin{table}
\begin{tabular}{c l l} \hline
**Symbol** & **Value and Units** & **Explanations** \\ \hline \(k_{\rm B}\) & \(1.38\times 10^{-23}\) J/K & Boltzmann constant \\ q & \(1.6\times 10^{-19}\) C & Electron charge \\ T & 300 K & Temperature \\ m\({}_{0}\) & \(9.11\times 10^{-31}\) kg & Electron mass in vacuum \\ \(\mu_{\rm e}\) & 5000 cm\({}^{2}\)/Vs & Electron mobility in p–InGaAs \\ \(\mu_{\rm h}\) & 150 cm\({}^{2}\)/Vs & Hole mobility in p–InGaAs \\ \(v_{\rm e,os}\), Vns & \(4\times 10^{7}\) cm/s & Electron overshoot velocity in InGaAs and InP \\ \(v_{\rm hs}\) & \(4.5\times 10^{6}\) cm/s & Hole saturation velocity \\ D\({}_{\rm e}\) & \(2k_{\rm B}T\mu_{\rm e}/q\) & Electron diffusion constant \\ m\({}^{*}\) & \(0.043m_{0}\) & Electron effective mass at the band edge \\ \(v_{\rm th}\) & \(\sqrt{2k_{\rm B}T/\pi m^{*}}\) & Thermionic–emission velocity \\ \(v_{\rm e,dri}\) & \(\sim\mu_{\rm e}(\phi/W_{\rm a})\) & Electron drift velocity in absorber \\ \(v_{\rm e,diff}\) & \(\sim 3D_{\rm e}/W_{\rm a}\) & Electron diffusion velocity in absorber \\ \(\tau_{\rm a}\) & \(W_{\rm a}^{2}/3D_{\rm e}+W_{\rm a}/v_{\rm th}\) & Carrier traveling time by electron diffusion \\ \(\tau_{\rm c}\) & \(W_{\rm c}/v_{\rm e,os}\) & Electron drift time in collector \\ k\({}_{\rm B}\) & \(1.38\times 10^{-23}\) J/K & Boltzmann constant \\ \hline \end{tabular}
\end{table} 
Table 1: The explanations for parameters [44] used for the 3–dB bandwidth calculation. For PIN-PD, both of the holes and electrons are in the single intrinsic/depletion layer, \(\rm W_{a}\), while the hole and electron saturation velocity are \(\rm v_{hs}\) and \(\rm v_{ns}\), so the 3-dB bandwidth for a PIN-PD with a thin absorber can be given as [43; 54]  
\[\rm f_{3 dB,PIN}\approx\frac{3.5}{2\pi\tau_{a}}, \tag{13}\]  
where the \(\tau_{a}\) equals \(\rm W_{a}/\bar{\
u}\), and the average velocity formula is \(1/\bar{\
u}^{4}=0.5\big{(}1/\bar{\
u}_{ns}^{4}+1/\bar{\
u}_{hs}^{4}\big{)}\). Meanwhile, a thinner absorber can make PIN-PD obtain a larger transit-time-limited bandwidth, but it also causes a decrease in the RC-limited bandwidth by Equation (2), while the drawback can be overcome in UTC-PD, just by independently designing the absorber and collector. Therefore, a thinner absorber can be used in UTC-PD for a larger transit-time-limited bandwidth without sacrificing the RC-limited bandwidth by well-designing a relatively thick collector. Additionally, some references show the detailed theoretical and experimental analysis of the characteristics for PIN-PD and UTC-PD, including energy band, electrical field, doping mechanism, optimization of absorber and collector, bandwidth, responsivity, saturation, and output power [56; 57; 58; 59; 60; 61; 62] as well as transient response [63], dark current [64; 65], and P-contact shapes [66].