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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 22 — Oct. 26, 2009
  • pp: 20221–20226
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Measurement and Modeling of High-Linearity Modified Uni-Traveling Carrier Photodiode with Highly-Doped Absorber

Huapu Pan, Zhi Li, Andreas Beling, and Joe C. Campbell  »View Author Affiliations


Optics Express, Vol. 17, Issue 22, pp. 20221-20226 (2009)
http://dx.doi.org/10.1364/OE.17.020221


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Abstract

The third-order intermodulation distortions of InGaAs/InP modified uni-traveling carrier photodiodes with a highly-doped p-type absorber are characterized. The third-order local intercept point is 55 dBm at low frequency (< 3 GHz) and remains as high as 47.5 dBm up to 20 GHz. The frequency characteristics of the OIP3 are well explained by an equivalent circuit model.

© 2009 OSA

1. Introduction

2. Device design and three-tone measurement

The vertical layer structure of the HD-MUTC photodiode is shown in Fig. 1
Fig. 1 Schematic cross section of InGaAs–InP HD-MUTC photodiode.
. The epitaxial layers were grown on a semi-insulating InP substrate by molecular beam epitaxy. The InGaAs absorbing region with a thickness of 950 nm is comprised of a 650 nm p+ absorbing region and a 300 nm unintentionally-doped absorber layer. Previously p-type InGaAs absorbing layers doped with Zn exhibited strong diffusion of the Zn dopant, which results in a non-abrupt junction doping profile. This non-abrupt doping profile causes the junction capacitance of the photodiode to have a strong dependence on bias voltage, which has been shown to be responsible for the decrease of OIP3 with frequency [10

10. H. Pan, A. Beling, H. Chen, J. C. Campbell, and P. D. Yoder, “The Influence of Nonlinear Capacitance on the Linearity of a Modified Uni-Traveling Carrier Photodiode,” 2008 International Topical Meeting on Microwave Photonics, (Institute of Electrical and Electronics Engineers, Gold Coast, Australia, 2008), pp. 82–85.

]. In order to form an abrupt junction doping profile, in this work C was used instead of Zn as the dopant in the 650 nm p+ absorbing layer. The p-type doping level was graded in 10 steps from 8⋅1019 to 5⋅1018 cm−3 so as to assist electron transport in the doped absorber. A 24 nm-thick InGaAs/InAlAs chirped superlattice and a 5 nm moderately n-type doped InP cliff layer were incorporated between the InGaAs and InP to reduce carrier pile up at the heterojunction interface. The 24 nm-thick InGaAs/InAlAs chirped superlattice is used to smooth the bandgap discontinuity between the InGaAs layer and the InP layer [11

11. Z. Griffith, Y. M. Kim, M. Dahlstrom, A.C. Gossard, and M. J. W. Rodwell, “InGaAs-InP metamorphic DHBTs grown on GaAs with lattice-matched device performance and fτ, fmax>268 GHz,” IEEE Electron Device Lett. 25, 675–677 (2004). [CrossRef]

], while the 5 nm moderately n-type doped InP cliff layer is used to enhance the electric field in the intrinsic InGaAs layer to help electrons inject into the intrinsic InP layer and reduce the space charge effect in the intrinsic InGaAs layer [12

12. H. Pan, A. Beling, H. Chen, and J. C. Campbell, “Characterization and Optimization of High-Power InGaAs/InP Photodiodes,” Opt. Quantum Electron. 40(1), 41–46 (2008). [CrossRef]

]. The background doping level in the unintentionally-doped absorbing layer was below 5⋅1015 cm−3. Back-illuminated mesa structures were fabricated by inductive coupled plasma reactive ion etching. Microwave contact pads and an air-bridge connection to the top p-contact layer were fabricated for high-speed measurements. Finally a 220 nm SiO2 anti-reflection layer was deposited on the back of the wafer. The devices were mounted on an Al heat sink for testing. Photodiodes with an active diameter of 40 μm exhibited a 3 dB bandwidth of 13 GHz at −6 V and responsivity of 0.49 A/W at 1550 nm. Compared with the CC-MUTC photodiode reported in Ref. [8

8. A. Beling, H. Pan, C. Hao, and J. C. Campbell, “Measurement and modeling of a high-linearity modified uni-traveling carrier photodiode,” IEEE Photon. Technol. Lett. 20(14), 1219–1221 (2008). [CrossRef]

], which has similar InGaAs absorber, the responsivity of the HD-MUTC is not as high. This is due to the fact that the p-type InGaAs absorber is so highly doped that the electron lifetime in the p-type InGaAs absorber of the HD-MUTC is much shorter than that of the CC-MUTC and thus a larger fraction of the photo-generated electrons before they diffuse into the intrinsic InGaAs layer.

When considering nonlinearities in photodiodes, the two-tone third-order intermodulation distortions (IMD3) are particularly interesting, since their frequencies may be close to the fundamental modulation frequencies. For conventional two-tone measurements, the output RF power Pf at the fundamental frequencies f1, f2 and the power of IMD3, PIMD3, at (2*f2-f1) and (2*f1-f2) were measured; following the approach in Ref [1

1. K. J. Williams, L. T. Nichols, and R. D. Esman, “Photodetector Nonlinearity on a High-Dynamic Range 3 GHz Fiber Optic Link,” J. Lightwave Technol. 16(2), 192–199 (1998). [CrossRef]

]. the conventional two-tone OIP3 is defined as OIP3= Pf+ (Pf– PIMD3)/2 dBm. However, it has recently been suggested that the harmonics from the optical modulators may result in inaccuracies in the two-tone measurement results [13

13. M. N. Draa, J. Ren, D. C. Scott, W. S. Chang, and P. K. Yu, “Three laser two-tone setup for measurement of photodiode intercept points,” Opt. Express 16(16), 12108–12113 (2008). [CrossRef] [PubMed]

]. Hence, a three-tone setup, which is less sensitive to nonlinearities in the modulator response [14

14. A. Ramaswamy, J. Klamkin, N. Nunoya, L. A. Johansson, L. A. Coldren, and J. E. Bowers, “Three-tone characterization of high-linearity waveguide uni-traveling-carrier photodiodes,” 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society, (Institute of Electrical and Electronics Engineers, Newport Beach, California, 2008), pp. 286–7.

], was also utilized to provide more accurate measurements. For the three-tone measurement, the output RF power Pf at the fundamental frequencies f1, f2, f3 and PIMD3 at (f1+f2-f3), (f2+f3-f1), (f3+f1-f2) were measured. The three-tone IMD3 is 6dB larger than the ideally measured two-tone IMD3. This difference in IMD3 can be understood from the fact that the coefficient of cos(ωit+ωjt-ωkt) (i,j,k=1,2,3 i≠j≠k) is 2 times as large as that of cos(2ωit-ωjt) (i,j=1,2,3 i≠j) after expanding the expression [cos(ωit)+cos(ωjt)+cos(ωkt)]3 (i,j,k=1,2,3 i≠j≠k). If the three-tone OIP3 is defined analogously to the two-tone OIP3, then, following the approach in Ref. [7

7. T. Ohno, H. Fukano, Y. Muramoto, T. Ishibashi, T. Yoshimatsu, and Y. Doi, “Measurement of intermodulation distortion in a unitravelingcarrier refracting-facet photodiode and a p–i–n refracting-facet photodiode,” IEEE Photon. Technol. Lett. 14(3), 375–377 (2002). [CrossRef]

], a factor of 3dB should be added to the measured three-tone OIP3 in order to compare with the two-tone measurements. The measured data were calibrated taking the losses of the components in the RF path into account.

3. Non-linear phenomena and equivalent circuit analysis

Figure 2
Fig. 2 Measured photodiode capacitance density for CC-MUTC and HD-MUTC photodiodes. Inset: Relative responsivity for CC-MUTC and HD-MUTC photodiodes.
compares the voltage-dependent capacitance and responsivity of the HD-MUTC and the CC-MUTC photodiodes reported in Ref [10

10. H. Pan, A. Beling, H. Chen, J. C. Campbell, and P. D. Yoder, “The Influence of Nonlinear Capacitance on the Linearity of a Modified Uni-Traveling Carrier Photodiode,” 2008 International Topical Meeting on Microwave Photonics, (Institute of Electrical and Electronics Engineers, Gold Coast, Australia, 2008), pp. 82–85.

]. The measured C(V) is normalized to capacitance density, which is independent of the size of the photodiodes. In contrast to CC-MUTC photodiodes, which exhibit significant variation of the capacitance density up to 7V, that of the HD-MUTC is only weakly dependent on the reverse bias when it is > 4V. This is a result of the high doping level of the undepleted absorber. The dependence of the responsivity of the HD-MUTC, however, shows a stronger dependence on voltage (an increase of ~6% as the bias increases to 8V) than that of the CC-MUTC photodiodes (~0.5% increase). This is due to the fact that impact ionization and the Franz Keldysh effect are more significant in the depleted InGaAs layers and the depleted InGaAs layer in the HD-MUTC (300 nm) is thicker than that of the CC-MUTC (designed to be 150 nm but actually much less due to Zn diffusion) [10

10. H. Pan, A. Beling, H. Chen, J. C. Campbell, and P. D. Yoder, “The Influence of Nonlinear Capacitance on the Linearity of a Modified Uni-Traveling Carrier Photodiode,” 2008 International Topical Meeting on Microwave Photonics, (Institute of Electrical and Electronics Engineers, Gold Coast, Australia, 2008), pp. 82–85.

].

The voltage dependent responsivity of the photodiodes was measured at very low photocurrent levels (< 200 µA) to avoid slow ohmic heating [16

16. T. H. Stievater and K. J. Williams, “Thermally induced nonlinearities in high-speed p-i-n photodetectors,” IEEE Photonics Technol. Lett. 16(1), 239–241 (2004).

]. However, the shape of the R(V) curve may change at high photocurrent levels due to the concomitant increase in temperature, since both impact ionization and the Franz-Keldysh effect vary with temperature. The OIP3 of the HD-MUTC was measured versus photocurrent at 320 MHz and reverse biases of 5 V, 7 V and 10 V. The results are shown in Fig. 3
Fig. 3 OIP3 of the HD-MUTC photodiode versus photocurrent at 5 V, 7 V and 10 V reverse bias. Inset: at 33 mA and 10 V, the power of IMD3 versus fundamental power showing a good slope of 3 and an extracted OIP3 of 55 dBm
. There is a strong dependence of OIP3 on photocurrent for all reverse bias values; the OIP3 reaches peaks at approximately 21 mA, 30 mA and 33 mA at 5 V, 7 V and 10 V reverse bias, respectively. Using bias modulation techniques [17

17. H. Pan, A. Beling, H. Chen, and J. C. Campbell, “The Frequency Behavior of the Intermodulation Distortions of Modified Uni-Traveling Carrier Photodiodes Based on Modulated Voltage Measurements,” Quantum Electronics,” IEEE J. 45(3), 273–277 (2009). [CrossRef]

], it can be shown that the strong dependence of the OIP3 on photocurrent is caused by the change of the shape of R(V) with photocurrent. At certain photocurrents the responsivity becomes a linear function of reverse bias and thus except for the second-order intermodulations all the higher order intermodulations produced by R(V) are significantly reduced. This is an important subject for a future study. At 33 mA of photocurrent and 10 V reverse bias, the drive power of the optical modulator was varied to measure the dependence of PIMD3 on Pf. As shown in the inset of Fig. 3, the slopes of Pf and PIMD3 are 1 and 3, respectively, and the OIP3 intercept is 55 dBm.

Figure 4
Fig. 4 OIP3 of CC-MUTC photodiode at 50 mA of photocurrent and 7 V reverse bias, and HD-MUTC at 34 mA of photocurrent and 10 V reverse bias. Dashed line: calculated OIP3 of CC-MUTC photodiode based on C(V); Dotted line: calculated OIP3 of HD-MUTC based on C(V).
compares the frequency dependence of the measured OIP3 for the HD-MUTC with that of the CC-MUTC photodiodes. Since the OIP3 of both the CC-MUTC and the HD-MUTC exhibit dependence on photocurrent and bias, the measurements were done at the photocurrent and bias conditions that maximized the OIP3 of each photodiode in order to make the “fairest” comparison (50 mA and 7 V for the CC-MUTC and 34 mA and 10 V for the HD-MUTC). For the HD-MUTC the voltage dependence of capacitance on reverse bias, dC/dV, is much smaller than that of the CC-MUTC when the reverse bias is > 4 V. However, as shown in Fig. 2, dC/dV decreases as the reverse bias increases. Thus the HD-MUTC photodiode was biased at a high reverse bias of 10 V to further reduce dC/dV so as to achieve higher OIP3 at high frequencies. As shown in Fig. 4, although the OIP3 of the CC-MUTC is high at low frequency, it rolls off as much as 16 dB as the frequency increases from 300 MHz to 21 GHz. This is due to the voltage-dependent capacitance, C(V), as explained in Ref [8

8. A. Beling, H. Pan, C. Hao, and J. C. Campbell, “Measurement and modeling of a high-linearity modified uni-traveling carrier photodiode,” IEEE Photon. Technol. Lett. 20(14), 1219–1221 (2008). [CrossRef]

]. The calculated OIP3 of the CC-MUTC photodiode based only on its C(V) curve, using the same equivalent circuit model reported in Ref [8

8. A. Beling, H. Pan, C. Hao, and J. C. Campbell, “Measurement and modeling of a high-linearity modified uni-traveling carrier photodiode,” IEEE Photon. Technol. Lett. 20(14), 1219–1221 (2008). [CrossRef]

], is shown as the dashed line in Fig. 4, which agrees well with the measurements for frequencies > 6 GHz. However, the OIP3 of the HD-MUTC starts at 55 dBm at low frequencies and decreases only 7.5 dB up to 20 GHz as a result of the weakly voltage-dependent capacitance. At 20 GHz, the OIP3 of the HD-MUTC remained as high as 47.5 dBm. The calculated OIP3 of the HD-MUTC based on its C(V) curve at 10 V is shown as the solid line in Fig. 4. The calculated C(V)-limited OIP3 begins to approach the measured values only when the frequency is greater than 6 GHz, and the measured OIP3 is almost independent of frequency when the frequency is less than 6 GHz. This indicates that the OIP3 of the HD-MUTC is primarily limited by R(V) in the frequency range up to 6 GHz and C(V) becomes significant only at higher frequencies. The drop of OIP3 accelerates as the frequency increases while the calculated OIP3 limited by C(V) shows the opposite trend at high frequencies. This is an indication that in addition to C(V), other frequency-dependent nonlinear mechanisms such as carrier speed modulation caused by the voltage swing may also contribute to the decrease of OIP3 in these photodiodes at high frequencies [3

3. K. Williams, R. Esman, and M. Dagenais, “Nonlinearities in p-i-n microwave photodetectors,” J. Lightwave Technol. 14(1), 84–96 (1996). [CrossRef]

].

4. Conclusions

In conclusion, the third-order intermodulation distortions of HD-MUTC photodiodes have been characterized using three-tone setup and compared to those of CC-MUTC photodiodes. The OIP3 of the HD-MUTC photodiode reaches 55 dBm at low frequencies with only slight roll off with frequency; at 20 GHz the OIP3 reaches 47.5 dBm. The excellent frequency behavior is due to the high doping levels in the undepleted absorber and the abrupt doping profile due to C doping. The frequency dependence of OIP3 is well explained by an equivalent circuit model.

References and links

1.

K. J. Williams, L. T. Nichols, and R. D. Esman, “Photodetector Nonlinearity on a High-Dynamic Range 3 GHz Fiber Optic Link,” J. Lightwave Technol. 16(2), 192–199 (1998). [CrossRef]

2.

K. J. Williams, D. A. Tulchinsky, and A. Hastings, “High-power and high-linearity photodiodes”, 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society, (Institute of Electrical and Electronics Engineers, Newport Beach, California, 2008), pp.290–291.

3.

K. Williams, R. Esman, and M. Dagenais, “Nonlinearities in p-i-n microwave photodetectors,” J. Lightwave Technol. 14(1), 84–96 (1996). [CrossRef]

4.

A. Joshi, S. Datta, and D. Becker, “GRIN Lens Coupled Top-Illuminated Highly Linear InGaAs Photodiodes,” IEEE Photon. Technol. Lett. 20(17), 1500–1502 (2008). [CrossRef]

5.

H. Jiang, D. S. Shin, G. L. Li, T. A. Vang, D. C. Scott, and P. K. L. Yu, “The Frequency Behavior of the Third-Order Intercept Point in a Waveguide photodiode,” IEEE Photon. Technol. Lett. 12(5), 540–542 (2000). [CrossRef]

6.

M. Chtioui, A. Enard, D. Carpentier, S. Bernard, B. Rousseau, F. Lelarge, F. Pommereau, and M. Achouche, “High-Power High-Linearity Uni-Traveling-Carrier photodiodes for Analog Photonic Links,” IEEE Photon. Technol. Lett. 20(3), 202–204 (2008). [CrossRef]

7.

T. Ohno, H. Fukano, Y. Muramoto, T. Ishibashi, T. Yoshimatsu, and Y. Doi, “Measurement of intermodulation distortion in a unitravelingcarrier refracting-facet photodiode and a p–i–n refracting-facet photodiode,” IEEE Photon. Technol. Lett. 14(3), 375–377 (2002). [CrossRef]

8.

A. Beling, H. Pan, C. Hao, and J. C. Campbell, “Measurement and modeling of a high-linearity modified uni-traveling carrier photodiode,” IEEE Photon. Technol. Lett. 20(14), 1219–1221 (2008). [CrossRef]

9.

A. Beling, H. Pan, H. Chen, and J. C. Campbell, “Measurement and modelling of high-linearity partially depleted absorber photodiode,” Electron. Lett. 44(24), 1419–1420 (2008). [CrossRef]

10.

H. Pan, A. Beling, H. Chen, J. C. Campbell, and P. D. Yoder, “The Influence of Nonlinear Capacitance on the Linearity of a Modified Uni-Traveling Carrier Photodiode,” 2008 International Topical Meeting on Microwave Photonics, (Institute of Electrical and Electronics Engineers, Gold Coast, Australia, 2008), pp. 82–85.

11.

Z. Griffith, Y. M. Kim, M. Dahlstrom, A.C. Gossard, and M. J. W. Rodwell, “InGaAs-InP metamorphic DHBTs grown on GaAs with lattice-matched device performance and fτ, fmax>268 GHz,” IEEE Electron Device Lett. 25, 675–677 (2004). [CrossRef]

12.

H. Pan, A. Beling, H. Chen, and J. C. Campbell, “Characterization and Optimization of High-Power InGaAs/InP Photodiodes,” Opt. Quantum Electron. 40(1), 41–46 (2008). [CrossRef]

13.

M. N. Draa, J. Ren, D. C. Scott, W. S. Chang, and P. K. Yu, “Three laser two-tone setup for measurement of photodiode intercept points,” Opt. Express 16(16), 12108–12113 (2008). [CrossRef] [PubMed]

14.

A. Ramaswamy, J. Klamkin, N. Nunoya, L. A. Johansson, L. A. Coldren, and J. E. Bowers, “Three-tone characterization of high-linearity waveguide uni-traveling-carrier photodiodes,” 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society, (Institute of Electrical and Electronics Engineers, Newport Beach, California, 2008), pp. 286–7.

15.

M. Dentan and B. de Cremoux, “Numerical Simulation of the Nonlinear Response of a p-i-n photodiode Under High Illumination,” J. Lightwave Technol. 8(8), 1137–1144 (1990). [CrossRef]

16.

T. H. Stievater and K. J. Williams, “Thermally induced nonlinearities in high-speed p-i-n photodetectors,” IEEE Photonics Technol. Lett. 16(1), 239–241 (2004).

17.

H. Pan, A. Beling, H. Chen, and J. C. Campbell, “The Frequency Behavior of the Intermodulation Distortions of Modified Uni-Traveling Carrier Photodiodes Based on Modulated Voltage Measurements,” Quantum Electronics,” IEEE J. 45(3), 273–277 (2009). [CrossRef]

OCIS Codes
(040.5160) Detectors : Photodetectors

ToC Category:
Detectors

History
Original Manuscript: August 28, 2009
Revised Manuscript: October 18, 2009
Manuscript Accepted: October 19, 2009
Published: October 21, 2009

Citation
Huapu Pan, Zhi Li, Andreas Beling, and Joe C. Campbell, "Measurement and modeling of high-linearity modified uni-traveling carrier photodiode with highly-doped absorber," Opt. Express 17, 20221-20226 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-20221


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References

  1. K. J. Williams, L. T. Nichols, and R. D. Esman, “Photodetector Nonlinearity on a High-Dynamic Range 3 GHz Fiber Optic Link,” J. Lightwave Technol. 16(2), 192–199 (1998). [CrossRef]
  2. K. J. Williams, D. A. Tulchinsky, and A. Hastings, “High-power and high-linearity photodiodes”, 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society, (Institute of Electrical and Electronics Engineers, Newport Beach, California, 2008), pp.290–291.
  3. K. Williams, R. Esman, and M. Dagenais, “Nonlinearities in p-i-n microwave photodetectors,” J. Lightwave Technol. 14(1), 84–96 (1996). [CrossRef]
  4. A. Joshi, S. Datta, and D. Becker, “GRIN Lens Coupled Top-Illuminated Highly Linear InGaAs Photodiodes,” IEEE Photon. Technol. Lett. 20(17), 1500–1502 (2008). [CrossRef]
  5. H. Jiang, D. S. Shin, G. L. Li, T. A. Vang, D. C. Scott, and P. K. L. Yu, “The Frequency Behavior of the Third-Order Intercept Point in a Waveguide photodiode,” IEEE Photon. Technol. Lett. 12(5), 540–542 (2000). [CrossRef]
  6. M. Chtioui, A. Enard, D. Carpentier, S. Bernard, B. Rousseau, F. Lelarge, F. Pommereau, and M. Achouche, “High-Power High-Linearity Uni-Traveling-Carrier photodiodes for Analog Photonic Links,” IEEE Photon. Technol. Lett. 20(3), 202–204 (2008). [CrossRef]
  7. T. Ohno, H. Fukano, Y. Muramoto, T. Ishibashi, T. Yoshimatsu, and Y. Doi, “Measurement of intermodulation distortion in a unitravelingcarrier refracting-facet photodiode and a p–i–n refracting-facet photodiode,” IEEE Photon. Technol. Lett. 14(3), 375–377 (2002). [CrossRef]
  8. A. Beling, H. Pan, C. Hao, and J. C. Campbell, “Measurement and modeling of a high-linearity modified uni-traveling carrier photodiode,” IEEE Photon. Technol. Lett. 20(14), 1219–1221 (2008). [CrossRef]
  9. A. Beling, H. Pan, H. Chen, and J. C. Campbell, “Measurement and modelling of high-linearity partially depleted absorber photodiode,” Electron. Lett. 44(24), 1419–1420 (2008). [CrossRef]
  10. H. Pan, A. Beling, H. Chen, J. C. Campbell, and P. D. Yoder, “The Influence of Nonlinear Capacitance on the Linearity of a Modified Uni-Traveling Carrier Photodiode,” 2008 International Topical Meeting on Microwave Photonics, (Institute of Electrical and Electronics Engineers, Gold Coast, Australia, 2008), pp. 82–85.
  11. Z. Griffith, Y. M. Kim, M. Dahlstrom, A.C. Gossard, and M. J. W. Rodwell, “InGaAs-InP metamorphic DHBTs grown on GaAs with lattice-matched device performance and fτ, fmax>268 GHz,” IEEE Electron Device Lett. 25, 675–677 (2004). [CrossRef]
  12. H. Pan, A. Beling, H. Chen, and J. C. Campbell, “Characterization and Optimization of High-Power InGaAs/InP Photodiodes,” Opt. Quantum Electron. 40(1), 41–46 (2008). [CrossRef]
  13. M. N. Draa, J. Ren, D. C. Scott, W. S. Chang, and P. K. Yu, “Three laser two-tone setup for measurement of photodiode intercept points,” Opt. Express 16(16), 12108–12113 (2008). [CrossRef] [PubMed]
  14. A. Ramaswamy, J. Klamkin, N. Nunoya, L. A. Johansson, L. A. Coldren, and J. E. Bowers, “Three-tone characterization of high-linearity waveguide uni-traveling-carrier photodiodes,” 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society, (Institute of Electrical and Electronics Engineers, Newport Beach, California, 2008), pp. 286–7.
  15. M. Dentan and B. de Cremoux, “Numerical Simulation of the Nonlinear Response of a p-i-n photodiode Under High Illumination,” J. Lightwave Technol. 8(8), 1137–1144 (1990). [CrossRef]
  16. T. H. Stievater and K. J. Williams, “Thermally induced nonlinearities in high-speed p-i-n photodetectors,” IEEE Photonics Technol. Lett. 16(1), 239–241 (2004).
  17. H. Pan, A. Beling, H. Chen, and J. C. Campbell, “The Frequency Behavior of the Intermodulation Distortions of Modified Uni-Traveling Carrier Photodiodes Based on Modulated Voltage Measurements,” IEEE J. Quantum Electron. 45(3), 273–277 (2009). [CrossRef]

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