Lithuanian Journal of Physics article / Lietuvos fizikos žurnalo straipsnis

STOCHASTIC THEORY OF CHARGE DYNAMICS AND RECOMBINATION IN DEFECT CLUSTERS IN BULK SILICON
Darius Abramavicius
Institute of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio 9, 10222 Vilnius, Lithuania
Email: darius.abramavicius@ff.vu.lt

Received 21 December 2022; accepted 18 January 2023

Various types of defect clusters are generated in bulk Si-based high-energy particle detectors. They become either recombination centres or charge trapping centres. Populated trapping centres create internal fields which may affect the dynamics and recombination of remaining free charges. In the semiclassical regime, the charge dynamics can be described by the Boltzmann equation. In this paper, the stochastic description is presented as an alternative to a direct solution of the Boltzmann equation approach. It is demonstrated that the hole dynamics can be described in the overdamped regime in both light-hole and heavy-hole cases. Electrons have to be described by including ballistic components. The theory allows an efficient simulation of the electron and hole dynamics in the vicinity of a defect cluster and demonstrates that local trapping centres are the major components enabling fast charge recombinations. The dipolar type internal fields of permanently trapped charges only weakly influence the charge recombination kinetics.
Keywords: stochastic Boltzmann equation, silicon, recombination kinetics

STOCHASTINĖ KRŪVININKŲ DINAMIKOS IR REKOMBINACIJOS SILICYJE TEORIJA
Darius Abramavičius

Vilniaus universiteto Fizikos fakulteto Cheminės fizikos institutas, Vilnius, Lietuva

Silicio pagrindu sukurtuose elektringų dalelių detektoriuose didelės energijos spinduliuotė sukuria daugybę taškinių defektų, kurie yra laisvųjų krūvininkų pagavimo ir rekombinacijos centrai. Užpildyti pagavimo centrai sukuria vidinius elektrinius laukus, kurie gali daryti įtaką laisvųjų krūvininkų dinamikai bei jų rekombinacijos charakteristikoms. Norint įvertinti skirtingų reiškinių įtaką rekombinacijos spartai, buvo atliktas kompiuterinis elektronų ir skylių dinamikos modeliavimas. Pusiau klasikiniame modelyje krūvininkų dinamika aprašoma Bolcmano lygtimi. Šiame straipsnyje naudojamas alternatyvus stochastinis modelis, kuris yra Bolcmano lygties atitikmuo, tačiau paprasčiau realizuojamas kompiuteriniais modeliavimo metodais. Be to, stochastiniame modelyje paprasta įtraukti pagavimo ir rekombinacijos centrus. Skaičiavimais parodoma, kad skylių dinamika gerai aprašoma, naudojant nuslopintos dinamikos artinį, kai inerciniai reiškiniai neįskaitomi. Elektronų dinamika turi būti aprašoma įskaitant inercinius narius. Parodoma, kad vidiniai elektriniai laukai daro silpną įtaką rekombinacijos kinetikoms, o esminis dalykas yra tiesiog rekombinacijos centrų tankis.

References / Nuorodos

[1] F. Hartmann, Evolution of Silicon Sensor Technology in Particle Physics, 2nd ed. (Springer, 2017),
https://doi.org/10.1007/978-3-319-64436-3
[2] C. Gallrapp, M. Fernández García, S. Hidalgo, I. Mateu, M. Moll, S. Otero Ugobono, and G. Pellegrini, Study of gain homogeneity and radiation effects of Low Gain Avalanche Pad Detectors, Nucl. Instrum. Methods Phys. Res. A 875, 27–34 (2017),
https://doi.org/10.1016/j.nima.2017.07.038
[3] G. Lindström, Radiation damage in silicon detectors, Nucl. Instrum. Methods Phys. Res. A 512, 30–43 (2003),
https://doi.org/10.1016/S0168-9002(03)01874-6
[4] R. Radu, I. Pintilie, L.C. Nistor, E. Fretwurst, G. Lindstroem, and L.F. Makarenko, Investigation of point and extended defects in electron irradiated silicon—Dependence on the particle energy, J. Appl. Phys. 117, 164503 (2015),
https://doi.org/10.1063/1.4918924
[5] S.A. Centoni, B. Sadigh, G.H. Gilmer, T.J. Lenosky, T. Díaz de la Rubia, and C.B. Musgrave, First-principles calculation of intrinsic defect formation volumes in silicon, Phys. Rev. B 72, 195206 (2005),
https://doi.org/10.1103/PhysRevB.72.195206
[6] W.-K. Leung, R.J. Needs, G. Rajagopal, S. Itoh, and S. Ihara, Calculations of silicon self-interstitial defects, Phys. Rev. Lett. 83, 2351–2354 (1999),
https://doi.org/10.1103/PhysRevLett.83.2351
[7] R.C. Newman, Defects in silicon, Rep. Prog. Phys. 45, 1163 (1982),
https://doi.org/10.1088/0034-4885/45/10/003
[8] E. Žąsinas and J.V. Vaitkus, Disordered small defect clusters in silicon, Lith. J. Phys. 55, 330–334 (2016),
https://doi.org/10.3952/physics.v55i4.3231
[9] M.M. Aye, E. Rivasto, M.Z. Khan, H. Rijckaert, E. Salojärvi, C. Haalisto, E. Mäkilä, H. Palonen, H. Huhtinen, I. Van Driessche, and P. Paturi, Control of the nanosized defect network in superconducting thin films by target grain size, Sci. Rep. 11, 6010 (2021),
https://doi.org/10.1038/s41598-021-85304-4
[10] M. Huhtinen, Simulation of non-ionising energy loss and defect formation in silicon, Nucl. Instrum. Methods Phys. Res. A 491, 194–215 (2002),
https://doi.org/10.1016/S0168-9002(02)01227-5
[11] H.P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, 2007),
https://doi.org/10.1093/acprof:oso/9780199213900.001.0001
[12] R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II, Vol. 31 of Springer Series in Solid-State Sciences (Springer, Berlin, Heidelberg, 1991),
https://doi.org/10.1007/978-3-642-58244-8
[13] D. Abramavičius and J.V. Vaitkus, Charge trapping and recombination in dipolar field of charged defect cluster in silicon, J. Vac. Sci. Technol. A (submitted, 2022),
https://doi.org/10.48550/arXiv.2212.10927
[14] E. Gaubas, T. Ceponis, L. Deveikis, D. Meskauskaite, J. Pavlov, V. Rumbauskas, J. Vaitkus, M. Moll, and F. Ravotti, Anneal induced transformations of defects in hadron irradiated Si wafers and Schottky diodes, Mater. Sci. Semicond. Process. 75, 157–165 (2018),
https://doi.org/10.1016/j.mssp.2017.11.035