Monte Carlo Simulation of Photoresponse in Silicon Photodiodes with p-n-Junction and p-i-n-Structure

Numerical modeling of semiconductor photodiodes’ electrical characteristics is an important task at the stage of their development and design. In this regard, it should be noted that one of the most promising methods that can be used for this purpose is the ensemble Monte Carlo method, which allows including, along with the dominant mechanisms of charge carriers’ scattering in the device structure, also the processes of impact ionization, which is very important for adequate modeling of a wide class of silicon photodiodes operating in the reverse bias mode. The aim of the work was to study the influence of the impact ionization process on the electrical characteristics of silicon photodiodes with a p-n-junction and a p-i-n-structure operating in the reverse bias mode under the influence of picosecond pulses of visible radiation. Using selfconsistent simulation by the ensemble Monte Carlo method, the electron ionization coefficient in bulk silicon at a crystal lattice temperature of 300 K was calculated and compared with known experimental data. Photoresponse in silicon submicron photodiodes with a p-n-junction and photodiodes with a p-i-n-structure was calculated for different thicknesses of the undoped i-region. It was shown that use of simple models similar to the Keldysh model with constant values of the threshold energy and other parameters for calculating the rate of the impact ionization process did not allow obtaining values of the ionization coefficient matched with experimental data in a wide range of electric field strengths. This result raises the question on the adequacy of the device structures’ electrical characteristics modeling with a non-uniform electric field when using such simple impact ionization models.

1. Filachev AM, Taubkin II, Trishenkov M. A. Solid-state photoelectronics. Photodiodes. Moscow: Fizmatkniga, 2011, 448 p.

2. Lozovoy KA, Douhan RMH, Dirko VV, Deeb H, Khomyakova KI, Kukenov OI, Sokolov AS, Akimenko NYu, and Kokhanenko AP. Silicon-based avalanche photodiodes: advancements and applications in medical imaging. Nanomaterials. 2023;(13):3078-1–3078-24. DOI: 10.3390/nano13233078

3. Bronzi D, Villa F, Tisa S, Tosi A, and Zappa F. SPAD figures of merit for photon-counting, photon-timing, and imaging applications: a review. IEEE Sensors Journal. 2016;16(1):3-12. DOI: 10.1109/JSEN.2015.2483565

4. Koziy AA, Losev AV, Zavodilenko VV, Kurochkin YuV, Gorbatsevich AA. Modern methods of detecting single photons and their application in quantum communications. Quantum Electronics. 2021;51(8):655-669. doi: 10.1070/QEL17566

5. Borzdov VM, Zhevnyak OG, Komarov FF, Galenchik VO. Monte Carlo simulation of device structures of integrated electronics. Minsk: BSU, 2007, 175 p.

6. Jacoboni C, Lugli P. The Monte Carlo method for semiconductor device simulation. Wien–New York: Springer, 2012, 359 p.

7. Aboud S, Saraniti M, Goodnick S, Brodschelm A, and Leitenstorfer A. Full-band Monte Carlo simulations of photo excitation in silicon diode structures. Semiconductor Science and Technology. 2004;(19):S301-S303. DOI: 10.1088/0268-1242/19/4/101

8. Yanikgonul S, Leong V, Ong JR, Png CE, and Krivitsky L. 2D Monte Carlo simulation of silicon waveguide-based single-photon avalanche diode for visible wavelengths. Optics Express. 2018;26(12):15232-15246. DOI: 10.1364/OE.26.015232

9. Borzdov AV, Borzdov VM, Vyurkov VV. Monte Carlo simulation of picosecond laser irradiation photoresponse of deep submicron SOI MOSFET. Proceedings of SPIE. 2022;(12157):121570Y-1–121570Y-6. doi: 10.1117/12.2624174

10. Zhou X, Ng JS, Tan CH. A simple Monte Carlo model for prediction of avalanche multiplication process in Silicon. Journal of Instrumentation. 2012;7(08):P080061–10. DOI: 10.1088/1748-0221/7/08/P08006

11. Chau Q. An efficient numerical approach to studying impact ionization in sub-micrometer devices. Journal of Computational Electronics. 2014;13:329-337. DOI: 10.1007/s10825-013-0536-x

12. Chau Q. New Models for Impact Ionization in Submicrometer Devices. IEEE Transactions on Electron Devices. 2014;61(4):1153-1160. doi: 10.1109/TED.2014.2306417

13. Ridley BK. Soft-threshold lucky drift theory of impact ionization in semiconductors. Semiconductor Science and Technology. 1987;2:116-122. doi: 10.1088/0268-1242/2/2/009

14. Kamakura Y, Mizuno H, Yamaji M, Morifuji M, Taniguchi K, Hamaguchi C, Kunikiyo T, Takenaka M. Impact ionization model for full band Monte Carlo simulation. Journal of Applied Physics. 1994;75(7):35003506. DOI: 10.1063/1.356112

15. Kunikiyo T, Takenaka M, Morifuji M, Taniguchi K, Hamaguchi C. A model of impact ionization due to the primary hole in silicon for a full band Monte Carlo simulation. Journal of Applied Physics. 1996;79(10):7717725. DOI: 10.1063/1.362375

16. Borzdov AV, Borzdov VM, Dorozhkin NN. Numerical simulation of electric characteristics of deep submicron silicon-on-insulator MOS transistor. Devices and Methods of Measurements. 2016;7(2):161-168. doi: 10.21122/2220-9506-2016-7-2-161-168

17. Martin MJ, Gonzalez T, Velazquez JE, Pardo D. Simulation of electron transport in silicon: impact-ionization processes. Semiconductor Science and Technology. 1993;(8):1291-1297. DOI: 10.1088/0268-1242/8/7/017

18. Robbins VM, Wang T, Brennan KF, Hess K and Stillman GE. Electron and hole impact ionization coefficients in (100) and in (111) Si. Journal of Applied Physics. 1985;58,(12):4614-4617. DOI: 10.1063/1.336229

19. Takayanagi I, Matsumoto K, and Nakamura J. Measurement of electron impact ionization coefficient in bulk silicon under a low electric field. Journal of Applied Physics. 1992;72(5):1989-1992. DOI: 10.1063/1.351625

20. Maes W, De Meyer K. and Van Overstraeten R. Impact ionization in silicon: a review and update. SolidState Electronics. 1990;33(6):705-718. doi: 10.1016/0038-1101(90)90183-F

21. Redmer R, Madureira JR, Fitzer N, Goodnick SM, Schattke W, and Schöll E. Field effect on the impact ionization rate in semiconductors. Journal of Applied Physics. 2000;87(2):781-788. DOI: 10.1063/1.371941