## Resonant normal-incidence separate-absorption-charge-multiplication Ge/Si avalanche photodiodes

Optics Express, Vol. 17, Issue 19, pp. 16549-16557 (2009)

http://dx.doi.org/10.1364/OE.17.016549

Acrobat PDF (821 KB)

### Abstract

In this work the impedance of separate-absorption-charge-multiplication Ge/Si avalanche photodiodes (APD) is characterized over a large range of bias voltage. An equivalent circuit with an inductive element is presented for modeling the Ge/Si APD. All the parameters for the elements included in the equivalent circuit are extracted by fitting the measured S_{22} with the genetic algorithm optimization. Due to a resonance in the avalanche region, the frequency response of the APD has a peak enhancement when the bias voltage is relatively high, which is observed in the measurement and agrees with the theoretical calculation shown in this paper.

© 2009 OSA

## 1. Introduction

1. J. C. Campbell, W. T. Tsang, G. J. Qua, and B. C. Johnson, “High-speed InP /InGaAsP /InGaAs avalanche photodiodes grown by chemical beam epitaxy,” IEEE J. Quantum Electron. **24**(3), 496–500 (1988). [CrossRef]

2. A. R. Hawkins, W. Wu, P. Abraham, K. Streubel, and J. E. Bowers, “High gain-bandwidth-product silicon heterointerface photodetector,” Appl. Phys. Lett. **70**(3), 303–305 (1997). [CrossRef]

3. Y. Kang, H.-D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y.-H. Kuo, H.-W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic Ge/Si Avalanche Photodiodes with 340GHz Gain-Bandwidth Product,” Nat. Photonics **3**(1), 59–63 (2008). [CrossRef]

5. S. J. Koester, C. L. Schow, L. Schares, G. Dehlinger, J. D. Schaub, F. E. Doany, and R. A. John, “Ge-on-SOI-detector/Si-CMOS-amplifier receivers for high-performance optical-communication applications,” J. Lightwave Technol. **25**(1), 46–57 (2007). [CrossRef]

3. Y. Kang, H.-D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y.-H. Kuo, H.-W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic Ge/Si Avalanche Photodiodes with 340GHz Gain-Bandwidth Product,” Nat. Photonics **3**(1), 59–63 (2008). [CrossRef]

3. Y. Kang, H.-D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y.-H. Kuo, H.-W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic Ge/Si Avalanche Photodiodes with 340GHz Gain-Bandwidth Product,” Nat. Photonics **3**(1), 59–63 (2008). [CrossRef]

7. W. S. Zaoui, H.-W. Chen, J. E. Bowers, Y. Kang, M. Morse, M. J. Paniccia, A. Pauchard, and J. C. Campbell, “Frequency response and bandwidth enhancement in Ge/Si avalanche photodiodes with over 840 GHz gain-bandwidth-product,” Opt. Express **17**(15), 12641–12649 (2009). [CrossRef] [PubMed]

8. G. Wang, T. Tokumitsu, I. Hanawa, K. Sato, and M. Kobayashi, “Analysis of high speed p-i-n photodiodes s-parameters by a novel small-signal equivalent circuit model,” IEEE Microw. Wirel. Compon. Lett. **12**(10), 378–380 (2002). [CrossRef]

_{22}, one can extract the circuit component values for the various elements (R, C, L) in the equivalent circuit. In this paper, we use the measured S

_{22}parameters to extract all the component values at different bias voltages simultaneously. Based on the extracted circuit model, we calculate the device frequency response, which is in good agreement with measurements.

## 2. The device structures

**3**(1), 59–63 (2008). [CrossRef]

## 3. Results and discussion

_{b}. The input optical power is –14dBm and the wavelength is 1310nm. Devices with larger diameters have larger junction capacitances, which will limit the bandwidth. This can be seen clearly in Figs. 2(a)-2(c). Here the APD with D = 50μm has the largest bandwidth. We note that the bandwidth is also strongly dependent on the bias voltage. When the bias voltage is relatively low (e.g., –23V), very little impact ionization occurs and consequently the frequency response is similar to that of a PIN photodetector. When the bias voltage increases, more impact ionization occurs and the DC gain increases (as can be seen in the responses in the low-frequency range shown in Fig. 2). When the bias voltage increases further (e.g., |V|>24.6V for D = 80μm), the response at low frequency decreases while there is an enhancement in the high frequency range. The enhancement becomes greater as the bias voltage increases. This behavior is observed in all three APDs with different diameters. For example, for the APD with D = 80μm, the maximal peak enhancement is as large as 4dB when it operates at V

_{bias}= –26.6V. Such behavior can be used to enhance the bandwidth of the APD.

9. J.-W. Shi, Y.-S. Wu, Z.-R. Li, and P.-S. Chen, “Impact-ionization-induced bandwidth enhance-ment of a Si–SiGe-based avalanche photodiode operating at a wavelength of 830 nm with a gain-bandwidth product of 428 GHz,” IEEE Photon. Technol. Lett. **19**(7), 474–476 (2007). [CrossRef]

10. M.-J. Lee, H.-S. Kang, and W.-Y. Choi, “Equivalent Circuit model for Si avalanche photodetectors fabricated in standard CMOS process,” IEEE Electron Device Lett. **29**(10), 1115–1117 (2008). [CrossRef]

11. G. Kim, I. G. Kim, J. H. Baek, and O. K. Kwon, “Enhanced frequency response associated with negative photoconductance in an InGaAs/InAlAs avalanche photodetector,” Appl. Phys. Lett. **83**(6), 1249–1251 (2003). [CrossRef]

_{22}as the bias voltage is varied by using an Agilent E8364A network analyzer. The frequency range is from 45MHz to 30GHz. The results for D = 150μm, 80μm, and 50μm are shown in Figs. 5(a) -5(c), respectively. From this figure, one sees that S

_{22}changes with bias voltage in the same way for all three devices. Since the shapes of the curves for different diameters are similar, here we focus our discussions on the case of D = 80μm. For the APD with D = 80μm, when the bias voltage is low (e.g., V = –24.6V), the entire curve is below the line

*Г*

_{i}= 0. This corresponds to the expected frequency response similar to that of a PIN photodetector (which corresponds to a resistor and capacitor in parallel, representing the diode capacitance and diode resistance). For a higher bias voltage, one has

*Г*

_{i}>0 in a certain frequency range. The phenomenon becomes stronger when the bias voltage increases further. Figure 6 (a) and 6(b) show the real part Z

_{r}and the imaginary part Z

_{i}of the impedance for the APD with D = 80μm, respectively. Both parts are strongly voltage-dependent. At relatively high voltage (e.g., V>25.4V), one sees that the real part Z

_{r}of the APD impedance has a peak at a certain frequency

*f*

_{r}. The imaginary part Z

_{i}of the APD impedance has a transition from a positive to a negative value at almost the same position

*f*

_{r}. This is what usually occurs when there is a resonance. Since the field distribution in the presented Si/Ge APD is similar to that in an impact ionization avalanche transit-time (IMPATT) diode structure, we make an analysis similar to that shown in Ref [12]. In the avalanche region, the impact ionization avalanche will introduce a delay between the AC current and the electric field (i.e., the AC voltage). With a small signal model, this delay due to the impact ionization avalanche in the Si multiplication layer is equivalent to an inductance. Therefore, an equivalent circuit model with an LC-circuit for the avalanche region will be presented below.

*L*

_{A}and

*C*

_{A}) [12, 13

13. Y.-C. Wang, “Small-signal characteristics of a Read diode under conditions of field-dependent velocity and finite reverse saturation current,” Solid-State Electron. **21**(4), 609–615 (1978). [CrossRef]

*R*

_{A}and

*R*

_{l}) which are lossy elements in the avalanche region due to the finite reverse saturation current and field-dependent velocity [13

13. Y.-C. Wang, “Small-signal characteristics of a Read diode under conditions of field-dependent velocity and finite reverse saturation current,” Solid-State Electron. **21**(4), 609–615 (1978). [CrossRef]

*R*

_{l}represents the leakage of the diode and R

*is the series resistance of the inductor. The small signal model analysis shows that the inductance should be inversely proportional to the current density*

_{A}*J*

_{0}[12], which will be verified below. The resistance

*R*

_{d}connected to the LC circuit is for the resistance in the drift region.

_{22}with a genetic-algorithm (GA) optimization. In order to obtain more reasonable fitting parameters, here we take the measured S

_{22}parameters at a series of reverse bias voltages (e.g., V

_{bias}= –26.6, –26.4, –26.2 and –26.0V) and extract all the parameters at each bias voltage. At different bias voltages, all the parasitic impedances (

*R*

_{s},

*C*

_{p},

*L*

_{p},

*R*

_{p}) should be the same while the other parameters will change as the gain changes.

_{22}parameters for the APD with D = 80μm at different bias voltages V

_{bias}= – 26.6, – 26.4, – 26.2, and – 26V, respectively, when the input optical power is P = –14dBm. The fitted results for the

*R*

_{s},

*C*

_{p},

*L*

_{p}, and

*R*

_{p}are:

*R*

_{s}= 16.76Ω,

*C*

_{p}= 0.193pF,

*L*

_{p}= 0.082nH, and

*R*

_{p}= 6.65Ω, independent of the bias voltage. The fitted parameters for all other bias-dependent elements are shown in Table 1 . For the avalanche region, the capacitance

*C*

_{A}changes very slightly while the inductance decreases as the bias voltage increases (which is due to the variation of current density as theoretically predicted). The measured currents are

*I*= 9.66, 8.06, 6.65, and 5.36 mA for the case of the bias voltage V

_{bias}= –26.6, –26.4, –26.2, and –26V, respectively. Correspondingly, the products

*L*

_{A}×

*I*are 29.74, 29.78, 29.33, and 29.18 (nH·mA), respectively. One sees that this product is almost constant as the bias voltage varies. This indicates that the inductance

*L*

_{A}is almost inversely proportional to the current density, which is similar to the theoretically predicted relationship for an IMPATT diode in Ref [12].

_{22}for the case of P = –20dBm. The parameters

*R*

_{s},

*C*

_{p},

*L*

_{p}, and

*R*

_{p}are the same as in the case of P = –14dBm since they are independent of the optical power. The other fitting parameters are shown in Table 2 . The values are slightly different from the case of P = –14dBm. The products

*L*

_{A}×

*I*are 29.12, 29.3, 29.2, and 29.1 for the case of V

_{bias}= –26.6, –26.4, –26.2, and –26V, respectively. This verifies that the products (

*L*

_{A}×

*I*) are almost constant as the bias voltage varies.

_{bias}= –26.6, –26.4, –26.2 and –26.0V. Here we only show the results for the case of P = –14dBm in Figs. 9(a) -9(d) since the results for P = –20dBm are similar. The responsivity for a gain of one is about 0.55A/W in the calculation here. The fitting parameters are shown in Table 3 . The transit-time changes slightly as the bias voltage varies. The fitted gain is about 14.8, which is close to the measured DC gain (about 15). From Fig. 9(a)-9(d), one sees that the simulated curve (dashed) and measured data (circled) agree well with each other, especially the peak-enhancement at the high frequency. Such a peak enhancement increases the bandwidth, which is similar to results for other types of APDs reported in Ref.s [11

11. G. Kim, I. G. Kim, J. H. Baek, and O. K. Kwon, “Enhanced frequency response associated with negative photoconductance in an InGaAs/InAlAs avalanche photodetector,” Appl. Phys. Lett. **83**(6), 1249–1251 (2003). [CrossRef]

13. Y.-C. Wang, “Small-signal characteristics of a Read diode under conditions of field-dependent velocity and finite reverse saturation current,” Solid-State Electron. **21**(4), 609–615 (1978). [CrossRef]

## 4. Conclusion

_{22}parameters. In this equivalent circuit, one of the key elements is the inductance, which is from a delay between the AC current and the electric field. This delay is introduced by the impact ionization avalanche in the avalanche region. It has been shown that this inductance is inversely proportional to the injected current, which is in agreement with the theoretical prediction. With these fitted parameters, we have also calculated the frequency responses, which agree well with the measured one. Due to the LC resonance, the present Ge/Si APD shows a peak enhancement at high frequency range when the bias voltage is high. Consequently a large bandwidth is achieved at high bias voltage.

## Acknowledgments

## References and links

1. | J. C. Campbell, W. T. Tsang, G. J. Qua, and B. C. Johnson, “High-speed InP /InGaAsP /InGaAs avalanche photodiodes grown by chemical beam epitaxy,” IEEE J. Quantum Electron. |

2. | A. R. Hawkins, W. Wu, P. Abraham, K. Streubel, and J. E. Bowers, “High gain-bandwidth-product silicon heterointerface photodetector,” Appl. Phys. Lett. |

3. | Y. Kang, H.-D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y.-H. Kuo, H.-W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic Ge/Si Avalanche Photodiodes with 340GHz Gain-Bandwidth Product,” Nat. Photonics |

4. | S. J. Koester, J. D. Schaub, G. Dehlinger, and J. O. Chu, “Germanium-on-SOI infrared detectors for integrated photonic applications,” IEEE J. Sel. Top. Quantum Electron. |

5. | S. J. Koester, C. L. Schow, L. Schares, G. Dehlinger, J. D. Schaub, F. E. Doany, and R. A. John, “Ge-on-SOI-detector/Si-CMOS-amplifier receivers for high-performance optical-communication applications,” J. Lightwave Technol. |

6. | W. S. Zaoui, H.-W. Chen, J. E. Bowers, Y. Kang, M. Morse, M. J. Paniccia, A. Pauchard, and J. C. Campbell, “Origin of the gain-bandwidth-product enhancement in separate-absorption-charge-multiplication Ge/Si avalan-che photodiodes,” Optical fiber communication (OFC) (San Diego, CA, 2009). |

7. | W. S. Zaoui, H.-W. Chen, J. E. Bowers, Y. Kang, M. Morse, M. J. Paniccia, A. Pauchard, and J. C. Campbell, “Frequency response and bandwidth enhancement in Ge/Si avalanche photodiodes with over 840 GHz gain-bandwidth-product,” Opt. Express |

8. | G. Wang, T. Tokumitsu, I. Hanawa, K. Sato, and M. Kobayashi, “Analysis of high speed p-i-n photodiodes s-parameters by a novel small-signal equivalent circuit model,” IEEE Microw. Wirel. Compon. Lett. |

9. | J.-W. Shi, Y.-S. Wu, Z.-R. Li, and P.-S. Chen, “Impact-ionization-induced bandwidth enhance-ment of a Si–SiGe-based avalanche photodiode operating at a wavelength of 830 nm with a gain-bandwidth product of 428 GHz,” IEEE Photon. Technol. Lett. |

10. | M.-J. Lee, H.-S. Kang, and W.-Y. Choi, “Equivalent Circuit model for Si avalanche photodetectors fabricated in standard CMOS process,” IEEE Electron Device Lett. |

11. | G. Kim, I. G. Kim, J. H. Baek, and O. K. Kwon, “Enhanced frequency response associated with negative photoconductance in an InGaAs/InAlAs avalanche photodetector,” Appl. Phys. Lett. |

12. | S. M. Sze, |

13. | Y.-C. Wang, “Small-signal characteristics of a Read diode under conditions of field-dependent velocity and finite reverse saturation current,” Solid-State Electron. |

14. | A. Banoushi, M. R. Kardan, and M. A. Naeini, “A circuit model simulation for separate absorption, grading, charge, and multiplication avalanche photodiodes,” Solid-State Electron. |

**OCIS Codes**

(040.0040) Detectors : Detectors

(040.1345) Detectors : Avalanche photodiodes (APDs)

**ToC Category:**

Detectors

**History**

Original Manuscript: August 5, 2009

Revised Manuscript: August 27, 2009

Manuscript Accepted: August 27, 2009

Published: September 1, 2009

**Citation**

Daoxin Dai, Hui-Wen Chen, John E. Bowers, Yimin Kang, Mike Morse, and Mario J. Paniccia, "Resonant normal-incidence separate-absorption-charge-multiplication Ge/Si avalanche photodiodes," Opt. Express **17**, 16549-16557 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-19-16549

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### References

- J. C. Campbell, W. T. Tsang, G. J. Qua, and B. C. Johnson, “High-speed InP /InGaAsP /InGaAs avalanche photodiodes grown by chemical beam epitaxy,” IEEE J. Quantum Electron. 24(3), 496–500 (1988). [CrossRef]
- A. R. Hawkins, W. Wu, P. Abraham, K. Streubel, and J. E. Bowers, “High gain-bandwidth-product silicon heterointerface photodetector,” Appl. Phys. Lett. 70(3), 303–305 (1997). [CrossRef]
- Y. Kang, H.-D. Liu, M. Morse, M. J. Paniccia, M. Zadka, S. Litski, G. Sarid, A. Pauchard, Y.-H. Kuo, H.-W. Chen, W. S. Zaoui, J. E. Bowers, A. Beling, D. C. McIntosh, X. Zheng, and J. C. Campbell, “Monolithic Ge/Si Avalanche Photodiodes with 340GHz Gain-Bandwidth Product,” Nat. Photonics 3(1), 59–63 (2008). [CrossRef]
- S. J. Koester, J. D. Schaub, G. Dehlinger, and J. O. Chu, “Germanium-on-SOI infrared detectors for integrated photonic applications,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1489–1502 (2006). [CrossRef]
- S. J. Koester, C. L. Schow, L. Schares, G. Dehlinger, J. D. Schaub, F. E. Doany, and R. A. John, “Ge-on-SOI-detector/Si-CMOS-amplifier receivers for high-performance optical-communication applications,” J. Lightwave Technol. 25(1), 46–57 (2007). [CrossRef]
- W. S. Zaoui, H.-W. Chen, J. E. Bowers, Y. Kang, M. Morse, M. J. Paniccia, A. Pauchard, and J. C. Campbell, “Origin of the gain-bandwidth-product enhancement in separate-absorption-charge-multiplication Ge/Si avalan-che photodiodes,” Optical fiber communication (OFC) (San Diego, CA, 2009).
- W. S. Zaoui, H.-W. Chen, J. E. Bowers, Y. Kang, M. Morse, M. J. Paniccia, A. Pauchard, and J. C. Campbell, “Frequency response and bandwidth enhancement in Ge/Si avalanche photodiodes with over 840 GHz gain-bandwidth-product,” Opt. Express 17(15), 12641–12649 (2009). [CrossRef] [PubMed]
- G. Wang, T. Tokumitsu, I. Hanawa, K. Sato, and M. Kobayashi, “Analysis of high speed p-i-n photodiodes s-parameters by a novel small-signal equivalent circuit model,” IEEE Microw. Wirel. Compon. Lett. 12(10), 378–380 (2002). [CrossRef]
- J.-W. Shi, Y.-S. Wu, Z.-R. Li, and P.-S. Chen, “Impact-ionization-induced bandwidth enhance-ment of a Si–SiGe-based avalanche photodiode operating at a wavelength of 830 nm with a gain-bandwidth product of 428 GHz,” IEEE Photon. Technol. Lett. 19(7), 474–476 (2007). [CrossRef]
- M.-J. Lee, H.-S. Kang, and W.-Y. Choi, “Equivalent Circuit model for Si avalanche photodetectors fabricated in standard CMOS process,” IEEE Electron Device Lett. 29(10), 1115–1117 (2008). [CrossRef]
- G. Kim, I. G. Kim, J. H. Baek, and O. K. Kwon, “Enhanced frequency response associated with negative photoconductance in an InGaAs/InAlAs avalanche photodetector,” Appl. Phys. Lett. 83(6), 1249–1251 (2003). [CrossRef]
- S. M. Sze, Physics of Semiconductor Devices, (New York: Wiley, 1981) Chap. 5.
- Y.-C. Wang, “Small-signal characteristics of a Read diode under conditions of field-dependent velocity and finite reverse saturation current,” Solid-State Electron. 21(4), 609–615 (1978). [CrossRef]
- A. Banoushi, M. R. Kardan, and M. A. Naeini, “A circuit model simulation for separate absorption, grading, charge, and multiplication avalanche photodiodes,” Solid-State Electron. 49(6), 871–877 (2005). [CrossRef]

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