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Multistep staircase avalanche photodiodes with extremely low noise and deterministic amplification

An Author Correction to this article was published on 15 June 2023

This article has been updated


In 1982, Capasso and co-workers proposed the solid-state analogue of the photomultiplier tube, termed the staircase avalanche photodiode. Through a combination of compositional grading and small applied bias, the conduction band profile is arranged into a series of steps that function similar to the dynodes of a photomultiplier tube, with twofold gain arising at each step via impact ionization. A single-step staircase was previously reported but did not demonstrate gain scaling through cascading multiple steps or report noise properties. Here we demonstrate gain scaling of up to three steps; measurements show the expected 2N scaling with the number of staircase steps, N. Furthermore, measured noise increased more slowly with gain than for photomultiplier tubes, probably due to the lower stochasticity of impact ionization across well-designed heterojunctions as compared with the secondary electron emission from metals. Excellent agreement was found between the experiments and Monte Carlo simulations for both gain and noise.

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Fig. 1: A structural comparison of a low-noise PMT and multistep staircase APD.
Fig. 2: Staircase APD design used to produce localized, single-carrier 2N gain.
Fig. 3: Demonstration of deterministic 2N gain scaling.
Fig. 4: Calculated staircase APD impact ionization probability and excess noise factors.
Fig. 5: Measured and modelled staircase APD noise benefit at 300 K.
Fig. 6: Estimated SNR comparison between staircase and conventional APDs in the shot-noise limit.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request. Source data are provided with this paper.

Code availability

Simulation software used to produce electrostatic models are available at the following GitHub repository:

Change history


  1. Engstrom, R. W. et al. Photomultiplier Manual (RCA Corporation, 1970).

  2. Iams, H. & Salzberg, B. The secondary emission phototube. Proc. IRE 23, 55–64 (1935).

    Article  Google Scholar 

  3. Morton, G. A. Photomultipliers for scintillation counting. RCA Rev. 10, 525–553 (1949).

    Google Scholar 

  4. Hadfield, R. H. Single-photon detectors for optical quantum information applications. Nat. Photon. 3, 696–705 (2009).

    Article  ADS  Google Scholar 

  5. Yalow, R. S. & Berson, S. A. Assay of plasma insulin in human subjects by immunological methods. Nature 184, 1648–1649 (1959).

    Article  Google Scholar 

  6. Phelps, M. E., Hoffman, E. J., Mullani, N. A. & Ter-Pogossian, M. M. Application of annihilation coincidence detection to transaxial reconstruction tomography. J. Nucl. Med. 16, 210–224 (1975).

    Google Scholar 

  7. The ATLAS Collaboration. The ATLAS experiment at the CERN Large Hadron Collider. J. Instrum. 3, S08003 (2008).

  8. Suzuki, Y. & Satellite, K. The super-Kamiokande experiment. Eur. Phys. J. C 79, 298 (2019).

    Article  ADS  Google Scholar 

  9. Giacconi, R., Gursky, H., Paolini, F. R. & Rossi, B. B. Evidence for X-rays from sources outside the solar system. Phys. Rev. Lett. 9, 439–443 (1962).

    Article  ADS  Google Scholar 

  10. Zworykin, V. A., Hillier, J. & Snyder, R. L. A scanning electron microscope. Bull. Am. Soc. Test. Mater. 117, 15–23 (1942).

    Google Scholar 

  11. Hell, S. W. & Wichmann, J. Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy. Opt. Lett. 19, 780 (1994).

    Article  ADS  Google Scholar 

  12. König, K. Clinical multiphoton tomography. J. Biophoton. 1, 13–23 (2008).

    Article  Google Scholar 

  13. Photomultiplier Tubes: Photomultiplier Tubes and Related Products (Hamamatsu Photonics, 2016).

  14. Bay, Z. & Papp, G. Determination of the probability distribution of the number of secondary electrons. IEEE Trans. Nucl. Sci. 11, 160–168 (1964).

    Article  ADS  Google Scholar 

  15. Prescott, J. R. A statistical model for photomultiplier single-electron statistics. Nucl. Instrum. Methods 39, 173–179 (1966).

    Article  ADS  Google Scholar 

  16. Lachs, G. The statistics for the detection of light by nonideal photomultipliers. IEEE J. Quantum Electron. 10, 590–596 (1974).

    Article  ADS  Google Scholar 

  17. Campbell, J. C. et al. Recent advances in avalanche photodiodes. IEEE J. Sel. Top. Quantum Electron. 10, 777–787 (2004).

    Article  ADS  Google Scholar 

  18. McIntrye, R. J. Multiplication noise in uniform avalanche diodes. IEEE Trans. Electron Devices 13, 164–168 (1966).

    Article  ADS  Google Scholar 

  19. Matsuo, K., Teich, M. C. & Saleh, B. E. A. Noise properties and time response of the staircase avalanche photodiode. IEEE Trans. Electron Devices 32, 2615–2623 (1985).

    Article  ADS  Google Scholar 

  20. Teich, M. C., Matsuo, K. & Saleh, B. E. A. Excess noise factors for conventional and superlattice avalanche photodiodes and photomultiplier tubes. IEEE J. Quantum Electron. 22, 1184–1193 (1986).

    Article  ADS  Google Scholar 

  21. Chin, R., Holonyak, N., Stillman, G. E., Tang, J. Y. & Hess, K. Impact ionisation in multilayered hetero junction structures. Electron. Lett. 16, 467–469 (1980).

    Article  ADS  Google Scholar 

  22. Williams, G. F., Capasso, F. & Tsang, W. T. The graded bandgap multilayer avalanche photodiode: a new low-noise detector. IEEE Electron Device Lett. 3, 71–73 (1982).

    Article  ADS  Google Scholar 

  23. Capasso, F., Tsang, W. T. & Williams, G. F. Staircase solid-state photomultipliers and avalanche photodiodes with enhanced ionization rates ratio. IEEE Trans. Electron Devices 30, 381–390 (1983).

    Article  ADS  Google Scholar 

  24. Ripamonti, G. et al. Realization of a staircase photodiode: towards a solid-state photomultiplier. Nucl. Instrum. Methods Phys. Res. A 288, 99–103 (1990).

    Article  ADS  Google Scholar 

  25. Toivonen, M., Salokatve, A., Hovinen, M. & Pessa, M. GaAs/AIGaAs delta-doped staircase avalanche photodiode with separated absorption layer. Electron. Lett. 28, 32–34 (1992).

    Article  ADS  Google Scholar 

  26. Czajkowski, I. K., Allam, J. & Adams, A. R. Role of satellite valleys in ionisation rate enhancement in multiple quantum well avalanche photodiodes. Electron. Lett. 26, 1311–1313 (1990).

    Article  ADS  Google Scholar 

  27. Tsuji, M., Watanabe, I., Makita, K. & Taguchi, K. InAlGaAs staircase avalanche photodiodes. Jpn. J. Appl. Phys. 33, L32–L34 (1994).

    Article  ADS  Google Scholar 

  28. Lambert, B. et al. Feasibility of 1.5 µm staircase solid state photomultipliers in the AlGaSb/GaInAsSb system. Semicond. Sci. Technol. 11, 226 (1996).

    Article  ADS  Google Scholar 

  29. Vaughn, L. G., Dawson, L. R., Xu, H., Jiang, Y. & Lester, L. F. Characterization of AlInAsSb and AlGaInAsSb MBE-grown Digital Alloys Vol. 744, 397–408 (MRS Online Proceedings Archive, 2002).

  30. Maddox, S. J., March, S. D. & Bank, S. R. Broadly tunable AlInAsSb digital alloys grown on GaSb. Cryst. Growth Des. 16, 3582–3586 (2016).

    Article  Google Scholar 

  31. Woodson, M. E. et al. Low-noise AlInAsSb avalanche photodiode. Appl. Phys. Lett. 108, 081102 (2016).

    Article  ADS  Google Scholar 

  32. Yi, X. et al. Extremely low excess noise and high sensitivity AlAs0.56Sb0.44 avalanche photodiodes. Nat. Photon. 13, 683–686 (2019).

    Article  ADS  Google Scholar 

  33. Ren, M. et al. AlInAsSb separate absorption, charge, and multiplication avalanche photodiodes. Appl. Phys. Lett. 108, 191108 (2016).

    Article  ADS  Google Scholar 

  34. Jones, A. H., March, S. D., Bank, S. R. & Campbell, J. C. Low-noise high-temperature AlInAsSb/GaSb avalanche photodiodes for 2-μm applications. Nat. Photon. 14, 559–563 (2020).

    Article  ADS  Google Scholar 

  35. Zheng, J. et al. Characterization of band offsets in AlxIn1–xAsySb1–y alloys with varying Al composition. Appl. Phys. Lett. 115, 122105 (2019).

    Article  ADS  Google Scholar 

  36. Bank, S. R. et al. Avalanche photodiodes based on the AlInAsSb materials system. IEEE J. Sel. Top. Quantum Electron. (2018).

  37. Ren, M. et al. AlInAsSb/GaSb staircase avalanche photodiode. Appl. Phys. Lett. 108, 081101 (2016).

    Article  ADS  Google Scholar 

  38. David, J. P. R. Photodetectors: the staircase photodiode. Nat. Photon. 10, 364–366 (2016).

    Article  ADS  Google Scholar 

  39. Maddox, S. J. et al. Low-noise high-gain tunneling staircase photodetector. In 2016 74th Annual Device Research Conference (IEEE, 2016).

  40. Bude, J. & Hess, K. Thresholds of impact ionization in semiconductors. J. Appl. Phys. 72, 3554–3561 (1992).

    Article  ADS  Google Scholar 

  41. van der Ziel, A., Yu, Y. J., Bosman, G. & van Vliet, C. M. Two simple proofs of Capasso’s excess noise factor FN of an ideal N-stage staircase multiplier. IEEE Trans. Electron Devices 33, 1816–1817 (1986).

    Article  ADS  Google Scholar 

  42. Maddox, S. J. et al. Enhanced low-noise gain from InAs avalanche photodiodes with reduced dark current and background doping. Appl. Phys. Lett. 101, 151124 (2012).

    Article  ADS  Google Scholar 

  43. Sun, W. et al. High-gain InAs avalanche photodiodes. IEEE J. Quantum Electron. 49, 154–161 (2013).

    Article  ADS  Google Scholar 

  44. Pilotto, A. et al. Optimization of GaAs/AlGaAs staircase avalanche photodiodes accounting for both electron and hole impact ionization. Solid State Electron. 168, 107728 (2020).

    Article  Google Scholar 

  45. Shockley, W. & Pierce, J. R. A theory of noise for electron multipliers. Proc. IRE 26, 321–332 (1938).

    Article  Google Scholar 

  46. Friis, H. T. Noise figures of radio receivers. Proc. IRE 32, 419–422 (1944).

    Article  Google Scholar 

  47. Ferraro, M. S. et al. Position sensing and high bandwidth data communication using impact ionization engineered APD arrays. IEEE Photon. Technol. Lett. 31, 58–61 (2019).

    Article  ADS  Google Scholar 

  48. Forrest, S. R. Performance of InxGa1–xAsyP1–y photodiodes with dark current limited by diffusion, generation recombination, and tunneling. IEEE J. Quantum Electron. 17, 217–226 (1981).

    Article  ADS  Google Scholar 

  49. Hess, K. Advanced Theory of Semiconductor Devices (Wiley, 2000).

  50. Ma, F. et al. Monte Carlo simulations of Hg0.7Cd0.3Te avalanche photodiodes and resonance phenomenon in the multiplication noise. Appl. Phys. Lett. 83, 785–787 (2003).

    Article  ADS  Google Scholar 

  51. Yuan, Y. et al. AlInAsSb impact ionization coefficients. IEEE Photon. Technol. Lett. 31, 315–318 (2019).

    Article  ADS  Google Scholar 

  52. van der Ziel, A. Noise in Solid State Devices and Circuits (John Wiley & Sons, 1986).

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This work was supported by the Army Research Office and DARPA (contract no. W911NF-17-1-0065) and DARPA (contract no. W909MY-12-D-0008). We acknowledge use of Texas Nanofabrication Facilities supported by the NSF NNCI Award 1542159.

Author information

Authors and Affiliations



S.D.M. and S.R.B. carried out simulations, crystal growth and materials characterization. A.H.J. and J.C.C. were responsible for device fabrication and experimental characterization. Analysis was performed by S.D.M. and A.H.J. S.D.M. and A.H.J. wrote the paper with assistance from J.C.C. and S.R.B. S.D.M., A.H.J., J.C.C. and SRB all contributed to the structure design.

Corresponding authors

Correspondence to Stephen D. March or Seth R. Bank.

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The authors declare no competing interests.

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Peer review information Nature Photonics thanks M. Saif Islam and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–8 and Discussion.

Source data

Source Data Fig. 2

Impact ionization, band diagrams, gain distributions, source data.

Source Data Fig. 3

Measured and simulated staircase gain.

Source Data Fig. 4

Fit-to-measured staircase gain and excess noise.

Source Data Fig. 5

Staircase excess noise compared to conventional APDs and PMTs.

Source Data Fig. 6

Estimated SNR performance comparing staircase APD to conventional APDs.

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March, S.D., Jones, A.H., Campbell, J.C. et al. Multistep staircase avalanche photodiodes with extremely low noise and deterministic amplification. Nat. Photonics 15, 468–474 (2021).

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