# Advances in High-Speed, High-Power Photodiodes: From Fundamentals to Applications
## 2 Overall Design Considerations for Photodiodes
### Equivalent Circuit Models
In addition, the elements in an external circuit, such as in the air bridge, CPW pad (and P-contact shapes [66]), and load, also have an effect on the overall frequency response of PDs. The similar and/or improved equivalent circuit models and RF small-signal equivalent circuit models, which are given from some specific examples for both PIN-PD and UTC-PD, with and without air bridge, can be found in previous works [85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119]. Some typical improved RC-delay time models are the modified UTC-PD (MUTC-PD) (Figure 12a) [89] and the dipole-doped UTC-PD (Figure 12b) [50], which are exploited as  
Figure 8: (a) Waveguide PIN–PD [84,86]; (b) equivalent circuit model [85,86]. Figure 10: PD equivalent circuit model with coplanar waveguide (CPW) pad and load resistance. Figure 9: PD equivalent circuit model with coplanar waveguide (CPW) pad, and load resistance. follows. For the MUTC-PD [89] (Figure 12a) and dual-drifting layer UTC-PD (DDL-UTC-PD) [100], [PERSON] et al. focus on the analysis of the absorbing depleted region (resistance, R\({}_{\text{u}}\), and capacitance, C\({}_{\text{u}}\)) and the non-absorbing depleted region (resistance, R\({}_{\text{j}}\), and capacitance, C\({}_{\text{j}}\)). Based on the RF small-signal equivalent circuit model without considering the air-bridge circuit, as shown in Figure 13a, the improved equivalent circuit model of the RC-delay time is shown in Figure 13b, while the further simplified one without considering R\({}_{\text{u}}\) and C\({}_{\text{u}}\) is reported by [PERSON] et al. [90], as shown in Figure 13c. In the above-mentioned RC-delay time models, the bulk material resistance is R\({}_{\text{11}}\), while R\({}_{\text{22}}\) represents P- and N-contact resistance, C\({}_{\text{p-elect}}\) is the P-electrode parasitic capacitance. Based on this model, the experimental and circuit analysis exhibit the bandwidth of an MUTC-PD up to 40 GHz, while the affected factors of the device performance, such as space charge screening, self-induced electrical field and over-shoot effects, are also discussed in detail [89]. In particular, the dipole-doped structure [50], as shown in Figure 12b, has been proposed by [PERSON] et al. to tackle the bandgap discontinuity between the InGaAs absorber and the InP collector interface, and also to simplify the difficulty of epitaxy growth. The corresponding equivalent circuit for the RC-delay time [96] proposed by [PERSON] et al. is shown in Figure 13d, where the resistance and capacitance for the dipole-doped part are denoted as R\({}_{\text{dd}}\) and C\({}_{\text{dd}}\). R\({}_{\text{aborb}}\) and R\({}_{\text{collect}}\) represent the resistance of the absorber and collector, while the junction capacitance is C\({}_{\text{j}}\). Through carefully choosing the values for circuit components, the simulated bandwidth matches the measured value very well from 10 MHz to 20 GHz and can be estimated to be \(\sim\)62.5 GHz at a \(-\)5 V bias voltage. Figure 11: RF small–signal equivalent circuit model of PD, including internal circuit and external circuits which consist of air bridge, coplanar waveguide (CPW) pad, and load resistance. Figure 12: Epitaxial structures of (**a**) modified UTC–PD [89]; and (**b**) dipole–doped UTC–PD [50]. To carefully analyze and depict UTC-PD impedance and photoresponse behavior, an accurate circuit model is proposed [99]. This model not only provides detailed explanations for inconsistent values at low frequencies (here, from DC to 30 GHz, the CPW parasitic effects are negligible) between the classical circuit models of PDs and measurements but even presents a comprehensive study for both the measured device impedance and S11 up to 110 GHz, while showing the values of frequency photoresponse up to 67 GHz.