pimiПриборы и методы измеренийDevices and Methods of Measurements2220-95062414-0473BNTU10.21122/2220-9506-2021-12-3-202-210pimi-723Research ArticleМетоды измерений, контроля, диагностикиMethods of measurements, monitoring, diagnosticsНизкочастотный адмиттанс конденсатора с рабочим веществом «изолятор – частично разупорядоченный полупроводник – изолятор»Low-Frequency Admittance of Capacitor with Working Substance “Insulator–Partially Disordered Semiconductor– Insulator”ПоклонскийН. А.PoklonskiN. A.

Адрес для переписки: Поклонский Н.А. – Белорусский государственный университет, пр-т Независимости, 4, г. Минск 220030, Беларусь e-mail: poklonski@bsu.by; poklonski@tut.by

Address for correspondence: Poklonski N.A. – Belarusian State University, Nezavisimosti Ave., 4, Minsk 220030, Belarus e-mail: poklonski@bsu.by; poklonski@tut.by

poklonski@bsu.byАникеевИ. И.AnikeevI. I.

пр-т Независимости, 4, г. Минск 220030

Nezavisimosti Ave., 4, Minsk 220030

ВыркоС. А.VyrkoS. A.

пр-т Независимости, 4, г. Минск 220030

Nezavisimosti Ave., 4, Minsk 220030

Белорусский государственный университетБеларусьBelarusian State UniversityBelarus202115102021123202210Copyright © Поклонский Н.А., Аникеев И.И., Вырко С.А., 20212021Поклонский Н.А., Аникеев И.И., Вырко С.А.Poklonski N.A., Anikeev I.I., Vyrko S.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://pimi.bntu.by/jour/article/view/723

Исследование электрофизических характеристик кристаллических полупроводников с дефектами структуры представляет практический интерес при создании радиационно-стойких варакторов. По вольт-фарадным характеристикам разупорядоченного полупроводника можно определять концентрацию точечных дефектов в его кристаллической матрице. Цель работы – рассчитать низкочастотный адмиттанс конденсатора с рабочим веществом «изолятор – кристаллический полупроводник с точечными t-дефектами в зарядовых состояниях (−1), (0) и (+1) – изолятор».

Слой частично разупорядоченного полупроводника толщиной 150 мкм отделен от металлических обкладок конденсатора диэлектрическими прослойками из полиимида толщиной 3 мкм. Частично разупорядоченный полупроводник рабочего вещества конденсатора представляет собой, например, сильнодефектный кристаллический кремний, содержащий точечные t-дефекты, случайно (пуассоновски) распределенные по кристаллу, в зарядовых состояниях (−1), (0) и (+1) между которыми прыжковым образом мигрируют одиночные электроны. Считается, что прыжки электронов происходят только с t-дефектов в зарядовом состоянии (−1) на t-дефекты в зарядовом состоянии (0) и с t-дефектов в зарядовом состоянии (0) на t-дефекты в зарядовом состоянии (+1).

В работе впервые проведено усреднение коэффициентов прыжковой диффузии по всем вероятным длинам прыжка электрона между t-дефектами в зарядовых состояниях (−1), (0) и (0), (+1) в ковалентной кристаллической матрице. Для такого элемента рассчитаны низкочастотный адмиттанс и угол сдвига фаз между током и напряжением в зависимости от приложенного на электроды конденсатора напряжения при концентрации t-дефектов 3∙1019 см−3 для температур 250, 300 и 350 К и при температуре 300 К для концентраций t-дефектов 1∙1019, 3∙1019 и 1∙1020 см−3.

The study of the electrophysical characteristics of crystalline semiconductors with structural defects is of practical interest in the development of radiation-resistant varactors. The capacitance-voltage characteristics of a disordered semiconductor can be used to determine the concentration of point defects in its crystal matrix. The purpose of this work is to calculate the low-frequency admittance of a capacitor with the working substance “insulator–crystalline semiconductor with point t-defects in charge states (−1), (0) and (+1)–insulator”. A layer of a partially disordered semiconductor with a thickness of 150 μm is separated from the metal plates of the capacitor by insulating layers of polyimide with a thickness of 3 μm. The partially disordered semiconductor of the working substance of the capacitor can be, for example, a highly defective crystalline silicon containing point t-defects randomly (Poissonian) distributed over the crystal in charge states (−1), (0), and (+1), between which single electrons migrate in a hopping manner. It is assumed that the electron hops occur only from t-defects in the charge state (−1) to t-defects in the charge state (0) and from t-defects in the charge state (0) to t-defects in the charge state (+1).

In this work, for the first time, the averaging of the hopping diffusion coefficients over all probable electron hopping lengths via t-defects in the charge states (−1), (0) and (0), (+1) in the covalent crystal matrix was carried out. For such an element, the low-frequency admittance and phase shift angle between current and voltage as the functions on the voltage applied to the capacitor electrodes were calculated at the t-defect concentration of 3∙1019 cm−3 for temperatures of 250, 300, and 350 K and at temperature of 300 K for the t-defect concentrations of 1∙1019, 3∙1019, and 1∙1020 cm−3.

 

частично разупорядоченный полупроводникнизкочастотный адмиттанс конденсаторатрехзарядные собственные точечные дефектыpartially disordered semiconductorlow-frequency admittance of capacitortriple-charged intrinsic point defectsThe work was supported by the Belarusian National Research Program “Materials Science, New Materials and Technologies” and by the European Union Framework Programme for Research and Innovation Horizon 2020 (grant No. H2020-MSCARISE- 2019-871284 SSHARE).ReferencesZvyagin I.P. Controlling the jump-over conductivity of compensated semiconductors with the aid of an electrical field. Sov. Phys. Dokl., 1977, vol. 22, no. 11, pp. 647–648.Zvyagin I.P. Controlling the jump-over conductivity of compensated semiconductors with the aid of an electrical field. Sov. Phys. Dokl., 1977, vol. 22, no. 11, pp. 647–648.Poklonskii N.A., Vyrko S.A. Screening of an electric field and the quasi-static capacitance of an induced charge in semiconductors with hopping conductivity. Russ. Phys. J., 2002, vol. 45, no. 10, pp. 1001–1007. DOI: 10.1023/A:1022867001332Poklonskii N.A., Vyrko S.A. Screening of an electric field and the quasi-static capacitance of an induced charge in semiconductors with hopping conductivity. Russ. Phys. J., 2002, vol. 45, no. 10, pp. 1001–1007. DOI: 10.1023/A:1022867001332Poklonski N.A., Vyrko S.A., Zabrodskii A.G. Calculation of capacitance of self-compensated semiconductors with intercenter hops of one and two electrons (by the example of silicon with radiation defects). Semiconductors, 2008, vol. 42, no. 12, pp. 1388–1394. DOI: 10.1134/S1063782608120038Poklonski N.A., Vyrko S.A., Zabrodskii A.G. Calculation of capacitance of self-compensated semiconductors with intercenter hops of one and two electrons (by the example of silicon with radiation defects). Semiconductors, 2008, vol. 42, no. 12, pp. 1388–1394. DOI: 10.1134/S1063782608120038Poklonski N.A., Vyrko S.A., Zabrodskii A.G. Field effect and capacitance of silicon crystals with hopping conductivity over point radiation defects pinning the Fermi level. Semiconductors, 2007, vol. 41, no. 11, pp. 1300–1306. DOI: 10.1134/S1063782607110048Poklonski N.A., Vyrko S.A., Zabrodskii A.G. Field effect and capacitance of silicon crystals with hopping conductivity over point radiation defects pinning the Fermi level. Semiconductors, 2007, vol. 41, no. 11, pp. 1300–1306. DOI: 10.1134/S1063782607110048Poklonski N.A., Kovalev A.I., Vyrko S.A. [Lowfrequency electrical capacitance of semiconductor diode with hopping conductivity via triple-charged defects]. Doklady Natsional’noi akademii nauk Belarusi [Doklady of the National Academy of Sciences of Belarus], 2017, vol. 61, no. 4, pp. 52–59 (in Russian).Poklonski N.A., Kovalev A.I., Vyrko S.A. [Lowfrequency electrical capacitance of semiconductor diode with hopping conductivity via triple-charged defects]. Doklady Natsional’noi akademii nauk Belarusi [Doklady of the National Academy of Sciences of Belarus], 2017, vol. 61, no. 4, pp. 52–59 (in Russian).Żukowski P.W., Kantorow S.B., Kiszczak K., Mączka D., Rodzik A., Stelmakh V.F., CzarneckaSuch E. Study of the dielectric function of silicon irradiated with a large dose of neutrons. Phys. Status Solidi A, 1991, vol. 128, № 2, pp. K117–K121. DOI: 10.1002/pssa.2211280243Żukowski P.W., Kantorow S.B., Kiszczak K., Mączka D., Rodzik A., Stelmakh V.F., CzarneckaSuch E. Study of the dielectric function of silicon irradiated with a large dose of neutrons. Phys. Status Solidi A, 1991, vol. 128, № 2, pp. K117–K121. DOI: 10.1002/pssa.2211280243Djurić Z., Smiljanić M. Static characteristics of metal–insulator–semiconductor–insulator–metal (MISIM) structures—I. Electric field and potential distributions. Solid-State Electron., 1975, vol. 18, no. 10, pp. 817–825. DOI: 10.1016/0038-1101(75)90001-5Djurić Z., Smiljanić M. Static characteristics of metal–insulator–semiconductor–insulator–metal (MISIM) structures—I. Electric field and potential distributions. Solid-State Electron., 1975, vol. 18, no. 10, pp. 817–825. DOI: 10.1016/0038-1101(75)90001-5Djurić Z., Smiljanić M., Tjapkin D. Static characteristics of the metal–insulator–semiconductor–insulator– metal (MISIM) structure—II. Low frequency capacitance. Solid-State Electron., 1975, vol. 18, no. 10, pp. 827–831. DOI: 10.1016/0038-1101(75)90002-7Djurić Z., Smiljanić M., Tjapkin D. Static characteristics of the metal–insulator–semiconductor–insulator– metal (MISIM) structure—II. Low frequency capacitance. Solid-State Electron., 1975, vol. 18, no. 10, pp. 827–831. DOI: 10.1016/0038-1101(75)90002-7Ng K.K. Complete Guide to Semiconductor Devices. New-York, Wiley–IEEE Press, 2002, xxiv+740 p. DOI: 10.1002/9781118014769Ng K.K. Complete Guide to Semiconductor Devices. New-York, Wiley–IEEE Press, 2002, xxiv+740 p. DOI: 10.1002/9781118014769Krupski J. Interfacial capacitance. Phys. Status Solidi B, 1990, vol. 157, no. 1, pp. 199–207. DOI: 10.1002/pssb.2221570119Krupski J. Interfacial capacitance. Phys. Status Solidi B, 1990, vol. 157, no. 1, pp. 199–207. DOI: 10.1002/pssb.2221570119Berman L.S., Klinger P.M., Fistul’ V.I. Determination of the parameters of deep centers in an overcompensated semiconductor from the temperature dependence of the capacitance and active conductance. Sov. Phys. Semicond., 1989, vol. 23, no. 11, p. 1206–1208.Berman L.S., Klinger P.M., Fistul’ V.I. Determination of the parameters of deep centers in an overcompensated semiconductor from the temperature dependence of the capacitance and active conductance. Sov. Phys. Semicond., 1989, vol. 23, no. 11, p. 1206–1208.Elfimov L.B., Ivanov P.A. Surface capacitance of a semiconductor with a deep dopant (in the example of p-6H-SiC<B>). Semiconductors, 1994, vol. 28, no. 1, pp. 97–100.Elfimov L.B., Ivanov P.A. Surface capacitance of a semiconductor with a deep dopant (in the example of p-6H-SiC<B>). Semiconductors, 1994, vol. 28, no. 1, pp. 97–100.Poklonski N.A., Gorbachuk N.I. [Fundamentals of impedance spectroscopy of composites]. Minsk, BSU, 2005, 130 p. (in Russian).Poklonski N.A., Gorbachuk N.I. [Fundamentals of impedance spectroscopy of composites]. Minsk, BSU, 2005, 130 p. (in Russian).Poklonskii N.A., Stelmakh V.F., Tkachev V.D., Voitikov S.V. Screening of electrostatic fields in semiconductors by multichargeddefects. Phys. Status Solidi B, 1978, vol. 88, no. 2, pp. K165–K168. DOI: 10.1002/pssb.2220880266Poklonskii N.A., Stelmakh V.F., Tkachev V.D., Voitikov S.V. Screening of electrostatic fields in semiconductors by multichargeddefects. Phys. Status Solidi B, 1978, vol. 88, no. 2, pp. K165–K168. DOI: 10.1002/pssb.2220880266Mott N. Impurity bands in silicon and germanium. Disordered Semiconductors, ed. by M.A. Kastner, G.A. Thomas, S.R. Ovshinsky. New York, Plenum Press, 1987, pp. 3–10. DOI: 10.1007/978-1-4613-1841-5_2Mott N. Impurity bands in silicon and germanium. Disordered Semiconductors, ed. by M.A. Kastner, G.A. Thomas, S.R. Ovshinsky. New York, Plenum Press, 1987, pp. 3–10. DOI: 10.1007/978-1-4613-1841-5_2Mott N. The mobility edge since 1967. J. Phys. C: Solid St. Phys., 1987, vol. 20, no. 21, pp. 3075–3102. DOI: 10.1088/0022-3719/20/21/008Mott N. The mobility edge since 1967. J. Phys. C: Solid St. Phys., 1987, vol. 20, no. 21, pp. 3075–3102. DOI: 10.1088/0022-3719/20/21/008Lugakov P.F., Lukashevich T.A., Shusha V.V. Nature of the defect determining the Fermi level stabilization in irradiated silicon. Phys. Status Solidi A, 1982, vol. 74, no. 2, pp. 445–452. DOI: 10.1002/pssa.2210740209Lugakov P.F., Lukashevich T.A., Shusha V.V. Nature of the defect determining the Fermi level stabilization in irradiated silicon. Phys. Status Solidi A, 1982, vol. 74, no. 2, pp. 445–452. DOI: 10.1002/pssa.2210740209Kuznetsov N.V., Soloviev G.G. [Radiation resistance of silicon]. Moscow, Energoatomizdat Publ., 1989, 96 p. (in Russian).Kuznetsov N.V., Soloviev G.G. [Radiation resistance of silicon]. Moscow, Energoatomizdat Publ., 1989, 96 p. (in Russian).Brudnyi V.N. Charge neutrality in semiconductors: defects, interfaces, surface. Russ. Phys. J., 2013, vol. 56, no. 7, pp. 754–756. DOI: 10.1007/s11182-013-0095-4.Brudnyi V.N. Charge neutrality in semiconductors: defects, interfaces, surface. Russ. Phys. J., 2013, vol. 56, no. 7, pp. 754–756. DOI: 10.1007/s11182-013-0095-4.Poklonski N.A., Vyrko S.A., Poklonskaya O.N., Zabrodskii A.G. Transition temperature from band to hopping direct current conduction in crystalline semiconductors with hydrogen-like impurities: Heat versus Coulomb attraction. J. Appl. Phys., 2011, vol. 110, no. 12, pp. 123702 (1–7). DOI: 10.1063/1.3667287Poklonski N.A., Vyrko S.A., Poklonskaya O.N., Zabrodskii A.G. Transition temperature from band to hopping direct current conduction in crystalline semiconductors with hydrogen-like impurities: Heat versus Coulomb attraction. J. Appl. Phys., 2011, vol. 110, no. 12, pp. 123702 (1–7). DOI: 10.1063/1.3667287Poklonski N.A., Vyrko S.A., Poklonskaya O.N., Zabrodskii A.G. Role of electrostatic fluctuations in doped semiconductors upon the transition from band to hopping conduction (by the example of p-Ge:Ga). Semiconductors, 2016, vol. 50, no. 6, pp. 722–734. DOI: 10.1134/S1063782616060191Poklonski N.A., Vyrko S.A., Poklonskaya O.N., Zabrodskii A.G. Role of electrostatic fluctuations in doped semiconductors upon the transition from band to hopping conduction (by the example of p-Ge:Ga). Semiconductors, 2016, vol. 50, no. 6, pp. 722–734. DOI: 10.1134/S1063782616060191Poklonskii N.A., Lopatin S.Yu. Stationary hopping photoconduction among multiply charged impurity atoms in crystals. Phys. Solid State, 1998, vol. 40, no. 10, pp. 1636–1640. DOI: 10.1134/1.1130623Poklonskii N.A., Lopatin S.Yu. Stationary hopping photoconduction among multiply charged impurity atoms in crystals. Phys. Solid State, 1998, vol. 40, no. 10, pp. 1636–1640. DOI: 10.1134/1.1130623Grundmann M. The Physics of Semiconductors. An Introduction Including Nanophysics and Applications. Berlin, Springer, 2021, xxxvii+889 p. DOI: 10.1007/978-3-030-51569-0Grundmann M. The Physics of Semiconductors. An Introduction Including Nanophysics and Applications. Berlin, Springer, 2021, xxxvii+889 p. DOI: 10.1007/978-3-030-51569-0Poklonski N.A., Vyrko S.A., Podenok S.L. [Statistical physics of semiconductors]. Moscow, KomKniga Publ., 2005, 264 p. (in Russian).Poklonski N.A., Vyrko S.A., Podenok S.L. [Statistical physics of semiconductors]. Moscow, KomKniga Publ., 2005, 264 p. (in Russian).Poklonski N.A., Vyrko S.A., Kovalev A.I., Dzeraviaha A.N. Drift-diffusion model of hole migration in diamond crystals via states of valence and acceptor bands. J. Phys. Commun., 2018, vol. 2, no. 1, pp. 015013 (1–14). DOI: 10.1088/2399-6528/aa8e26Poklonski N.A., Vyrko S.A., Kovalev A.I., Dzeraviaha A.N. Drift-diffusion model of hole migration in diamond crystals via states of valence and acceptor bands. J. Phys. Commun., 2018, vol. 2, no. 1, pp. 015013 (1–14). DOI: 10.1088/2399-6528/aa8e26Baranovskii S., Rubel O. Chapter 9. Charge transport in disordered materials. Springer Handbook of Electronic and Photonic Materials, eds. S. Kasap, P. Capper. Berlin, Springer, 2017, pp. 193–218. DOI: 10.1007/978-3-319-48933-9_9Baranovskii S., Rubel O. Chapter 9. Charge transport in disordered materials. Springer Handbook of Electronic and Photonic Materials, eds. S. Kasap, P. Capper. Berlin, Springer, 2017, pp. 193–218. DOI: 10.1007/978-3-319-48933-9_9Shklovskii B.I., Efros A.L. Electronic Properties of Doped Semiconductors. Berlin, Springer, 1984, xii+388 p.Shklovskii B.I., Efros A.L. Electronic Properties of Doped Semiconductors. Berlin, Springer, 1984, xii+388 p.Klimkovich B.V., Poklonskii N.A., Stelmakh V.F. Alternating-current hopping electrical-conductivity of covalent semiconductors with deep-level defects. Sov. Phys. Semicond., 1985, vol. 19, no. 5, pp. 522–524Klimkovich B.V., Poklonskii N.A., Stelmakh V.F. Alternating-current hopping electrical-conductivity of covalent semiconductors with deep-level defects. Sov. Phys. Semicond., 1985, vol. 19, no. 5, pp. 522–524Dyre J.C., Schrøder T.B. Universality of ac conduction in disordered solids. Rev. Mod. Phys, 2000, vol. 72, no. 3, pp. 873–892. DOI: 10.1103/RevModPhys.72.873Dyre J.C., Schrøder T.B. Universality of ac conduction in disordered solids. Rev. Mod. Phys, 2000, vol. 72, no. 3, pp. 873–892. DOI: 10.1103/RevModPhys.72.873Long A.R. Frequency-dependent loss in amorphous semiconductors. Adv. Phys., 1982, vol. 31, no. 5, pp. 553–637. DOI: 10.1080/00018738200101418Long A.R. Frequency-dependent loss in amorphous semiconductors. Adv. Phys., 1982, vol. 31, no. 5, pp. 553–637. DOI: 10.1080/00018738200101418

The authors declare that there are no conflicts of interest present.