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Research on ultrawideband photodetector module based on parasitic parameter regulation

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Abstract

A four-channel ultrawideband photodetector (PD) module with a size of 26.1 mm ×33.2 mm × 8.5 mm has been demonstrated in our laboratory. We propose a method to improve the bandwidth of the PD module based on compensating parasitic parameters by dual resistance regulation on the P and N terminals of the PD chip. A small signal equivalent circuit model with package matching network is established for the PD module, and the effectiveness of the proposed method and the accuracy of the model are verified by experiments. A four-channel photodetector module with a −3 dB bandwidth of up to 67 GHz is fabricated by using photodetector chips with −3 dB bandwidths of 46 GHz, and the responsivity is up to 0.50A/W.

© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

With the booming development of emerging technologies such as 5 G networks and internet data centers, information capacity has shown explosive growth, which puts forward higher technical requirements and huge challenges to the current communication system [1,2]. As one of the core devices in the optical communication system, the photodetector (PD) has developed greatly in terms of bandwidth, response, noise, and sensitivity. Generally, three effective solutions are employed to improve the communication capacity by increasing the single-channel transmission rate [3], increasing the number of channels and adopting the high-order modulation format [46], in which the transmission rate is positively correlated with the bandwidth of the device, so the utilization of various methods to improve bandwidth is one of the important ways to meet the requirements for improving communication capacity. In addition, the multi-lane method is also commonly utilized because the bandwidth requirement of microwave photonics devices can be reduced, such as in wavelength division multiplexing (WDM), the parallel four/eight/sixteen-lane method.

From the perspective of structure, a detector module is composed of package parasitic network, chip parasitic network and intrinsic detector. Therefore, the bandwidth of the detector module is not only related to the chip structure, but also the parasitic network. The photodetector has a high output impedance because it operates in a zero-bias or negative-bias state, so the circuit in parallel with the device will have a shunt effect on the photocurrent, especially at a higher operating frequency, resulting in a decrease in the high-frequency response of the photodetector [7]. A series of studies have been conducted to improve the frequency response characteristics of the detector module. The parasitic inductance of the gold wire can be used to compensate the parasitic capacitance effect of the laser chip and the carrier, so as to improve the frequency response of the device at certain frequencies, which has been confirmed in experimental studies [8]. This idea has also been successfully used to improve the frequency response characteristics of PIN photodetectors [9]. The response bandwidth of the detector module is increased from the original 15 GHz to 17 GHz by increasing the number of connected wires to reduce the parasitic inductance. In 2018, the Institute of Semiconductors of the Chinese Academy of Sciences designed a three-dimensional microwave circuit structure and obtained a receiver optical sub-assembly (ROSA) with a single channel bandwidth of 20 GHz by rationally arranging RF and DC transmission lines [10]. Reference [11] applies some useful methods to optimize the design of the flexible printed circuit (FPC) with high-frequency coplanar waveguide to improve the bandwidth, such as periodic via-hole, and the 3 dB bandwidth of obtained ROSA is 20 GHz. Also in 2018, the Japanese Sumitomo Electrician Transmission Equipment Laboratory optimized the RF circuit through adding capacitors and inductors to the parallel resonant circuit of the PD cathode, and the 3 dB OE response bandwidth of integrated ROSA is up to 36 GHz [12]. Then in 2020, the Korea Electronics and Communications Research Institute proposed a bandwidth-improved multilayer board architecture that could alleviate bandwidth limitations caused by typical edge connectors installed on multilayer boards when the required bandwidth exceeds 20 GHz. Applying this structure, a ROSA with 3 dB bandwidth >35.7 GHz was obtained [13]. In order to achieve the higher bandwidth requirements of photodetectors, researchers have turned their attention to single-carrier photodiodes (UTC-PD). However, most of the attention is focused on the chip, and there is little research on the modularization of UTC-PD chip. In 2020, Beijing National Research Center for Information Science and Technology designed an optimized top-ground microstrip line (TGMSL) structure to eliminate mode resonance, and the 3 dB bandwidth of the UTC-PD module obtained through the flip chip bonding process can reach 40 GHz [14]. In the field of commercial optical modules, the representative companies are Coherent and Fraunhofer Heinrich Hertz Institute. The 50 GHz PD modules [15] presented by Coherent uses a PD chip integrated with a matching network to minimize parasitic effects, and has since introduced 70 GHz [16] and 100 GHz [17] photodetector modules. Fraunhofer Heinrich Hertz Institute provides 65 GHz [18] and 100 GHz [19] photodetector modules, and in 2020 demonstrated a PD module with a 0.8mm-RF connector, which estimated 3 dB bandwidth is 145 GHz [20]. The relevant studies mentioned above are summarized in Table 1.

Tables Icon

Table 1. Research status of wideband photodetector module

In the present study, the response bandwidth of photodetector module is still limited by the chip structure due to the existence of packaging parasitic network. And the bandwidth decrease caused by the package structure of PD module will have an impact on the bit error rate (BER) in optical transmission system. In order to make the device achieve 50 ohm impedance matching, whether in previous studies or in commercial photodetectors, a 50 ohm matching resistor is often used in parallel, which seems to have become a common practice in the industry. However, this ignores the parasitic parameters introduced by the packaging process. The chip-parasite network causes the detector's RC bandwidth to be limited. In addition, some steps in the device packaging process, such as the length of gold wire and the amount of conductive adhesive, that are difficult to quantify and accurately control, resulting in different parasitic parameters introduced. In this paper, the routine is broken taking full account of the parasitic parameters of the package, and a method based on compensating parasitic parameters is proposed to improve the bandwidth of PD module by dual resistance control on the P and N terminals of PD chip and gold wire regulation. This method can compensate the bandwidth attenuation caused by the packaging process, but also has the advantage of available for regulation so that each device can achieve the best performance. Low cost is also an important factor for the program to be practical. In addition, a small signal equivalent circuit model with package matching network is established for the photodetector module, and the effectiveness of the proposed method and the accuracy of the model are verified by experiments. A four-channel parallel photodetector module is fabricated using photodetector chips with −3 dB bandwidths of 46 GHz. Its −3 dB bandwidth exceeds the bandwidth of the chip itself up to 67 GHz, which is an important breakthrough, and the maximum response is 0.5A/W.

In this paper, we present a method to improve the bandwidth of PD module by dual resistance control on the P and N terminals of PD chip, which breaks the convention and considers the parasitic parameters of the package. Further, the method is validated again by experiments, and the 67 GHz module is developed, whose bandwidth exceeds the chip bandwidth, which is an important breakthrough

2. Circuit model and simulation results

It is well known that the -3 dB bandwidth of the PD chip is jointly determined by the RC bandwidth and the carrier transport bandwidth. Among them, the carrier transport bandwidth is limited by the carrier transit time in the epitaxial layer of the detector chip, which is greatly related to the thickness of the epitaxial layer. On the other hand, the effect of distributed capacitance and resistance in the device structure of the PD chip generates charge and discharge time, also known as the RC time constant, which similarly limits the photodetector's -3 dB bandwidth. The parasitic parameters introduced in the packaging process will further change the RC time constant of the whole module, thus affecting the bandwidth. Therefore, the parasitic parameters of the chip can be compensated by adjusting the parameters in the package structure, and the parasitic parameters introduced by some uncontrollable factors in the package process can be improved.

In addition, in order to ensure that the RF signal can be output with little loss, it is necessary to design a suitable transmission line structure. Considering the positions of the PD chip and the RF connection port of the shell, the RF circuit board model with high frequency bending transmission line, as shown in Fig. 1(a), is designed. The structure adopts the structure of microstrip line. The substrate material for the RF circuit board is Rogers RT5880 with a dielectric constant of 2.2 and a dielectric loss of only 0.0009, making it ideal for high frequency and wide band applications where dispersion and loss are minimized. The design size of the substrate is 4.83mm × 5.07mm × 0.13 mm. In order to prevent the circuit board from warping and resulting in poor grounding during the mounting process, it is designed into a trapezoidal shape. The characteristic impedance of the transmission line is determined by the width and thickness of the signal line, the thickness of the dielectric substrate and the dielectric constant. In order to reduce electrical reflection and loss, the characteristic impedance of the microstrip line should be designed to be 50 ohms [21]. We studied the influence of signal line width on transmission performance, as shown in Fig. 1(b). The results show that the transmission performance of the transmission line is the best when the width of the signal line is 0.4 mm. In the range of 0∼80 GHz, the insertion loss (S21) is only about 0.5 dB, and the reflection loss (S11) is less than -20 dB, which can meet the design requirements of the module at 67 GHz.

 figure: Fig. 1.

Fig. 1. RF circuit board with high frequency curved transmission line. (a) Model. (b) Transmission performance under different signal line widths.

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By modeling a small signal equivalent circuit of a photodetector in Advanced Design System (ADS), we evaluate the influence of component parameters in the package structure. First, based on the chip structure, the small signal equivalent circuit model of PD chip as shown in Fig. 2 is established [22]. When the photodetector is in normal operation, the junction capacitance and resistance of the active region are modeled as Cj and Rj. The semiconductor bulk resistance of the non-depletion region is represented by Rb. The contact capacitance introduced at the top of the PD chip is represented by Ca. The PD chip used in this paper consists of a photodiode and a ceramic base, and the photodiode is fixed to a ceramic submount with GSG electrodes by flip-chip bonding. Rs and Ls represent the parasitic parameters introduced by the electrode pad of the photodiode. The parasitic capacitance introduced through the bonding interconnection between the electrode of the photodiode and that of the ceramic submount is characterized as CSM1, CSM2, and LSM is the parasitic inductance introduced by the solder used in the bonding. Taking into account the factors mentioned above that affect the frequency response of the device, the carrier transit time effect of the photodetector is characterized by an approximate Rt·Ct time constant, and the frequency dependence of the photocurrent can be controlled by the relationship I = GVRF using the voltage-controlled current source (VCCS) model, where the parameter G is the constant adjusted according to the quantum efficiency of the photodetector. The VCCS model consists of an ideal current source and two control resistors r1 and r2. ZL1 and ZL2 are used for simulating the port impedance of the device. In order to determine the values of each parameter in the model, the transmission curve of the PD chip was measured using a vector network analyzer and the model was fitted, as shown in Fig. 3. It can be seen that the -3 dB bandwidth reaches 46 GHz, and the measurement results of S21 and S22 are highly consistent with the simulation results, which initially ensures the accuracy of the PD chip model. The specific component parameters are listed in Table 2.

 figure: Fig. 2.

Fig. 2. Small signal equivalent circuit model for PD chip.

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 figure: Fig. 3.

Fig. 3. Measurement and simulation results of the PD chip’s (a) S21; (b) S22.

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Table 2. Equivalent circuit model parameters of PD chip

The small signal equivalent circuit model of the whole photodetector module is shown in Fig. 4, and the specific parameters are listed in Table 3. In order to evaluate the impact of the electronic component parameters used and the parasitic parameters introduced in the packaging process, the package matching network is taken into account on the basis of the equivalent circuit model of PD chip. Among them, a small capacitor C1 of 100nF is used to stabilize the bias voltage and prevent the PD chip from breaking down during sudden switching. The bypass capacitor C2 is used to achieve the effect of filtering. In addition, adjustable resistors, R1 and R2, are respectively connected with the P and N poles of the PD chip. The impact of parasitic parameters is compensated by adjusting the resistance values of the resistors, so as to achieve the effect of adjusting the bandwidth. Among them, parameters Rs1, Ls1, Rs2, Ls2, Rs3, Ls3 are parasitic parameters introduced by gold wire bonding. The RF circuit board is characterized as a transmission line (MLIN) model, whose parameters are consistent with those of the designed RF circuit board, which will be discussed next. Rs4, Ls4, Cp, Ls5 represent parasitic parameters introduced by solder and the RF through-wall structure.

 figure: Fig. 4.

Fig. 4. The small signal equivalent circuit model for PD module.

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Tables Icon

Table 3. Equivalent circuit model parameters of package network in PD module

From the equivalent circuit, the Z parameter can be expressed as follows:

$${Z_{11}} = {Z_{L1}} + {Z_t}$$
$${Z_{12}} = 0$$
$${Z_{21}} = \frac{{G{Z_t}{Z_j}{Z_a}{Z_{SM1}}{Z_{SM2}}{Z_p}{Z_{L2}}{{({A + B} )}^2}}}{{({B + {Z_{trans}}} )({{Z_p} + {Z_{s5}} + {Z_{L2}}} )+ {Z_p}({{Z_{s5}} + {Z_{L2}}} )}} \cdot \frac{1}{{AB + ({A + B} )({{Z_{s1}} + {R_1} + {Z_{SM2}}} )}}$$
$$\cdot \frac{1}{{AB({{Z_a} + {Z_{SM1}} + {Z_s}} )+ ({A + B} )[{{Z_s} + {Z_{SM1}}({{Z_{s1}} + {R_1} + {Z_{SM}}} )+ {Z_a}C} ]}}$$
$${ \cdot \frac{{AB({{Z_a} + {Z_{SM1}} + {Z_s}} )+ ({A + B} )C({{Z_a} + {Z_s}} )}}{{AB[{{Z_a}({{Z_{SM}} + {Z_s}} )+ ({{R_b} + {Z_j}} )({{Z_a} + {Z_{SM1 + }}{Z_s}} )} ]+ ({A + B} )C[{{Z_a}{Z_s} + ({{R_b} + {Z_j}} )({{Z_a} + {Z_s}} )} ]}}}$$
$${{Z_{22}} = \frac{{AB[{{Z_j}{Z_a}({{Z_{SM1}} + {Z_s}} )+ {R_b}{Z_j}({{Z_a} + {Z_{SM1}} + {Z_s}} )} ]+ ({A + B} )C[{{Z_j}{Z_a}{Z_s} + {R_b}{Z_j}({{Z_a} + {Z_s}} )} ]}}{{AB[{{Z_a}({{Z_{SM}} + {Z_s}} )+ ({{R_b} + {Z_j}} )({{Z_a} + {Z_{SM1 + }}{Z_s}} )} ]+ ({A + B} )C[{{Z_a}{Z_s} + ({{R_b} + {Z_j}} )({{Z_a} + {Z_s}} )} ]}}}$$
where, $A = {Z_{trans}}{Z_p} + ({{Z_{trans}} + {Z_p}} )({{Z_{s5}} + {Z_{L2}}} ),\,B = {Z_{s2}} + {R_2} + {Z_c}$, $C = {Z_{s1}} + {R_1} + {Z_{SM}} + {Z_{SM1}},\,{Z_t} = {R_t} + \frac{1}{{j\omega {C_t}}},\,{Z_j} = \frac{{{R_j}}}{{1 + j\omega {C_j}{R_j}}},\,{Z_a} = \frac{1}{{j\omega {C_a}}}$, ${Z_t} = {R_t} + \frac{1}{{j\omega {C_t}}}$, ${Z_j} = \frac{{{R_j}}}{{1 + j\omega {C_j}{R_j}}}$, ${Z_a} = \frac{1}{{j\omega {C_a}}}$, ${Z_s} = j\omega {L_s}$, ${Z_{SM1}} = \frac{1}{{j\omega {C_{SM1}}}}$, ${Z_{SM}} = j\omega {L_{SM}}$, ${Z_{SM2}} = \frac{1}{{j\omega {C_{SM2}}}}$, ${Z_{s1}} = j\omega {L_{s1}} + {R_{s1}}$, ${Z_{s2}} = j\omega {L_{s2}} + {R_{s2}}$, ${Z_c} = j\omega ({{C_1} + {C_2}} )$, ${Z_{trans}} = {Z_{s3}} + {Z_{MLIN}} + {Z_{s4}}$, ${Z_{s3}} = ({j\omega {L_{s3}} + {R_{s3}}} )$, ${Z_{s4}} = ({j\omega {L_{s4}} + {R_{s4}}} )$, ${Z_p} = \frac{1}{{j\omega {C_p}}}$, ${Z_{s5}} = j\omega {L_{s5}} + {R_{s5}}$.

Then, the S parameter of this equivalent circuit can be expressed by:

$${S = \frac{1}{{1 + {\Delta _Z} + {Z_{11}} + {Z_{22}}}}\left[ {\begin{array}{cc} { - 1 + {\Delta _Z} + {Z_{11}} - {Z_{22}}}&{2{Z_{12}}}\\ {2{Z_{21}}}&{ - 1 + {\Delta _Z} - {Z_{11}} + {Z_{22}}} \end{array}} \right]}$$

Here, ΔZ denotes the determinant corresponding to the Z parameter matrix, ${\Delta _Z} = {Z_{11}}{Z_{22}} - {Z_{12}}{Z_{21}}$.

This paper mainly studies the effect of the parasitic inductance introduced by gold wire bonding and two matching resistors in parallel with PD chip in package matching network. Figure 5 shows the calculated results of S21 with different values of Ls3, R1, and R2. RF signal obtained by photoelectric conversion of the photodetector is transmitted to the transmission line through the gold wire, and then transmitted to the outside of the module through the through-wall structure. Therefore, the gold wire connecting the PD chip and the transmission line plays an indispensable role on the overall transmission performance of the module, which corresponds to Ls3 in Fig. 4. The longer the gold wire, the greater the parasitic inductance introduced, and Fig. 5(a) shows the calculated frequency response for different Ls3 values. The results show that the increase of inductance intensifies the resonant peaks around 35 GHz, 45 GHz, and 65 GHz in the frequency response curve, thus affecting the module's −3 dB bandwidth. When the inductance range is 0 to 0.1nH, the resonance peak around 65 GHz is the main factor limiting the bandwidth of the module. When the inductance is 0nH, the bandwidth is 68 GHz, and the bandwidth is reduced by 2 GHz for every 0.05nH increase in inductance. However, when the inductance exceeds 0.1nH, the resonant peak around 45 GHz is the main factor limiting the bandwidth of the module. It can be seen that when the inductance is 0.15nH, the bandwidth is only 45 GHz, and 0.2nH corresponds to 43 GHz. Therefore, the distance between the P electrode of the photodetector chip and the signal line of the RF circuit board should be as close as possible during the module fabrication process. In fact, it was found in the study that the inductance Ls4 introduced by the solder and the wall structure has an approximate influence with Ls3. But compared with the control of the solder, the control of the gold wire is easier, and it should be considered comprehensively in the experiment process. Figure 5(b) shows the calculated frequency response of different R1 values. When the resistance value increases from 25Ω to 145Ω by step of 30Ω, the resonance at the low frequency decreases, which is conducive to improving the flatness of the frequency response curve. The resonance at high frequencies will be intensified, which can improve the bandwidth to a certain extent. However, when R1 increases to 115Ω and then continues to increase, the changing trend slows down. Figure 5(c) shows the frequency response of the calculated R2 values. When the resistance value increases from 15Ω to 55Ω by step of 10Ω, the gain of the module in the range of 0∼40 GHz will increase, and the increase effect will be more obvious at the lower frequency. This trend will improve the flatness, but when the resistance value increases to 35Ω, the attenuation becomes faster and the bandwidth decreases. Considering flatness and bandwidth comprehensively, the simulation results show that when R1 resistance is above 85Ω and R2 resistance is 25Ω, the frequency response characteristics of the module are optimal, and the bandwidth can reach nearly 70 GHz.

 figure: Fig. 5.

Fig. 5. Calculated transmission responses S21 for different values of (a) Ls3, (b) R1 and (c) R2.

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3. Experimental results

Figure 6(a) shows the overall structure of the proposed photodetector module with dimensions of 26.1mm × 33.2mm × 8.5 mm. It consists of a four-channel package shell, top- illuminated PIN PD chips, 41.5° bevel fibers, a DC circuit board, RF circuit boards, and bias matching network consisting of capacitors and resistors. The optical fiber transmits the light to the surface of the PD chip, and the optical signal is converted into an RF signal, which is transmitted through the RF circuit board and then output. The photograph of the detector module is shown in Fig. 6(b). The components are mounted in the tube shell by conductive silver adhesive connected by gold wire bonding.

 figure: Fig. 6.

Fig. 6. (a) The photodetector module configuration. (b) Photograph of the photodetector module. Inset is the photograph of the module with the detailed inner distribution.

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We selected two channels, channel 1 and channel 2, and changed the resistance values of R1 and R2 respectively. The experimental results obtained were shown in Fig. 7 and Fig. 8. It can be observed from Fig. 7 that when the resistance value of R2 is 25Ω, the resonance peak at the low frequency significantly decreases and the flatness increases with the increase of R1. The resonance peak around 35 GHz is weakened, which can improve flatness on the one hand, and improve bandwidth on the other hand. When the R1 value is 85Ω and above, the frequency response characteristics are very excellent, and the bandwidth can reach 67 GHz. Compared with the simulation results obtained through the small-signal equivalent circuit model analysis, the trend of the experimental results is consistent, but the position of the resonant peak moves to the low frequency slightly, which may be caused by some aspects in the packaging process that are difficult to quantify and control, such as the amount of conductive adhesive. Figure 8(a) shows the experimental results obtained by changing R2 on channel 2. The strong resonance peak around 20 GHz seriously affects the frequency response characteristics of the module, resulting in the bandwidth being limited to 20 GHz. Under the microscope, it is observed that the gold wire grounded in R2 in channel 2 is longer than that in channel 1. Combined with the simulation analysis of the frequency response characteristics of the parasitic inductance introduced by the gold wire bonding mentioned above in Fig. 5(a), we shorten the gold wire length. The experimental results are shown in Fig. 8(b), and the resonance peaks of 20 GHz and 40 GHz are significantly suppressed, due to the weakening of the resonant effect of a series resonant circuit formed by parasitic capacitance introduced by PD chip and parasitic inductance introduced by wire-bonding. The experimental results of different R2 values are observed. With the increase of R2, the initial gain of the PD module is increased, the attenuation speed is accelerated, and the flatness is improved. The frequency response characteristic of the PD module is the best when the R2 is 25Ω, which is also very consistent with the simulation results. Therefore, on the one hand, it can be proved that the resistance regulation and gold wire regulation technology really improve the bandwidth of the PD module, and on the other hand, it can be proved that the small signal equivalent circuit model of the PD module established by us has a certain accuracy.

 figure: Fig. 7.

Fig. 7. Experimental results of transmission responses S21 with different values of R1.

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 figure: Fig. 8.

Fig. 8. Experimental results of transmission response S21 with different values of R2. (a) The length of R2 grounding wire is 1.5 mm and (b) the length of grounding wire is 0.6 mm. Inset is the diagram of the gold wire connection.

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4. 67-GHz four-channel PD module

Using the proposed packaging scheme, we packed a four-channel hybrid integrated PD module, as shown in Fig. 9, and the photograph of the module with the detailed inner distribution is inserted. The -3 dB bandwidths of chips used in the module are 46 GHz, as shown as Fig. 3. Figure 9 shows its transmission response (S21) when the value of R1 is 110Ω and the value of R2 is 25Ω, measured at a 3 V bias voltage. It indicates that there are three lanes with -3 dB bandwidth exceeding 67 GHz, and another lane’s -3 dB bandwidth also up to 65.3 GHz. At around 45 GHz, channels 1 and 2 show an upward resonant peak, while channels 3 and 4 show a downward resonant peak. According to the analysis results of the previous simulation, the parasitic inductance introduced by gold wire bonding, solder and RF through-wall structure in the package network is the main reason for the resonance peak at this position. Figure 10 shows the measured response curve of the packaged photodetector module, which shows the responsivity of four lanes are 0.50, 0.47, 0.44 and 0.46A/W, respectively. The difference in responsiveness between each channel comes from the coupling efficiency of optical fiber and PD chip.

 figure: Fig. 9.

Fig. 9. Measured transmission response S21 and reflection response S22 of the four-channel PD module.

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 figure: Fig. 10.

Fig. 10. Measured responsiveness of the PD module.

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5. Conclusion

In conclusion, we propose a method to control the bandwidth of the photodetector module based on parasitic parameter compensation, and fabricate a four-channel ultrawideband detector module by means of resistance control and gold wire control. The −3 dB bandwidth of the photodetector chip used is only 46 GHz, and the −3 dB bandwidth of the photodetector module made by this method is up to 67 GHz, and the responsiveness is up to 0.50A/W. The effect of resistance regulation and gold wire regulation on the bandwidth of photodetector module is studied by establishing a small signal equivalent circuit model with package matching network. The effectiveness of the method and the accuracy of the model are also verified by experiments.

Funding

National Natural Science Foundation of China (62204014).

Acknowledgments

We thank the Intelligent photon research group of the Institute of Semiconductors of the Chinese Academy of Sciences for the support for this work.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (10)

Fig. 1.
Fig. 1. RF circuit board with high frequency curved transmission line. (a) Model. (b) Transmission performance under different signal line widths.
Fig. 2.
Fig. 2. Small signal equivalent circuit model for PD chip.
Fig. 3.
Fig. 3. Measurement and simulation results of the PD chip’s (a) S21; (b) S22.
Fig. 4.
Fig. 4. The small signal equivalent circuit model for PD module.
Fig. 5.
Fig. 5. Calculated transmission responses S21 for different values of (a) Ls3, (b) R1 and (c) R2.
Fig. 6.
Fig. 6. (a) The photodetector module configuration. (b) Photograph of the photodetector module. Inset is the photograph of the module with the detailed inner distribution.
Fig. 7.
Fig. 7. Experimental results of transmission responses S21 with different values of R1.
Fig. 8.
Fig. 8. Experimental results of transmission response S21 with different values of R2. (a) The length of R2 grounding wire is 1.5 mm and (b) the length of grounding wire is 0.6 mm. Inset is the diagram of the gold wire connection.
Fig. 9.
Fig. 9. Measured transmission response S21 and reflection response S22 of the four-channel PD module.
Fig. 10.
Fig. 10. Measured responsiveness of the PD module.

Tables (3)

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Table 1. Research status of wideband photodetector module

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Table 2. Equivalent circuit model parameters of PD chip

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Table 3. Equivalent circuit model parameters of package network in PD module

Equations (7)

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Z 11 = Z L 1 + Z t
Z 12 = 0
Z 21 = G Z t Z j Z a Z S M 1 Z S M 2 Z p Z L 2 ( A + B ) 2 ( B + Z t r a n s ) ( Z p + Z s 5 + Z L 2 ) + Z p ( Z s 5 + Z L 2 ) 1 A B + ( A + B ) ( Z s 1 + R 1 + Z S M 2 )
1 A B ( Z a + Z S M 1 + Z s ) + ( A + B ) [ Z s + Z S M 1 ( Z s 1 + R 1 + Z S M ) + Z a C ]
A B ( Z a + Z S M 1 + Z s ) + ( A + B ) C ( Z a + Z s ) A B [ Z a ( Z S M + Z s ) + ( R b + Z j ) ( Z a + Z S M 1 + Z s ) ] + ( A + B ) C [ Z a Z s + ( R b + Z j ) ( Z a + Z s ) ]
Z 22 = A B [ Z j Z a ( Z S M 1 + Z s ) + R b Z j ( Z a + Z S M 1 + Z s ) ] + ( A + B ) C [ Z j Z a Z s + R b Z j ( Z a + Z s ) ] A B [ Z a ( Z S M + Z s ) + ( R b + Z j ) ( Z a + Z S M 1 + Z s ) ] + ( A + B ) C [ Z a Z s + ( R b + Z j ) ( Z a + Z s ) ]
S = 1 1 + Δ Z + Z 11 + Z 22 [ 1 + Δ Z + Z 11 Z 22 2 Z 12 2 Z 21 1 + Δ Z Z 11 + Z 22 ]
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