Low-Frequency Admittance of Capacitor with Working Substance “Insulator–Partially Disordered Semiconductor– Insulator”

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.

1. 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.

2. 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:1022867001332

3. Poklonski 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/S1063782608120038

4. Poklonski 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/S1063782607110048

5. 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).

6. 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.2211280243

7. Djurić 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)90001-5

8. Djurić 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)90002-7

9. Ng K.K. Complete Guide to Semiconductor Devices. New-York, Wiley–IEEE Press, 2002, xxiv+740 p. DOI: 10.1002/9781118014769

10. Krupski J. Interfacial capacitance. Phys. Status Solidi B, 1990, vol. 157, no. 1, pp. 199–207. DOI: 10.1002/pssb.2221570119

11. 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.

12. 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.

13. Poklonski N.A., Gorbachuk N.I. [Fundamentals of impedance spectroscopy of composites]. Minsk, BSU, 2005, 130 p. (in Russian).

14. 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.2220880266

15. Mott 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_2

16. Mott N. The mobility edge since 1967. J. Phys. C: Solid St. Phys., 1987, vol. 20, no. 21, pp. 3075–3102. DOI: 10.1088/0022-3719/20/21/008

17. Lugakov 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.2210740209

18. Kuznetsov N.V., Soloviev G.G. [Radiation resistance of silicon]. Moscow, Energoatomizdat Publ., 1989, 96 p. (in Russian).

19. 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.

20. 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: 10.1063/1.3667287

21. Poklonski 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/S1063782616060191

22. Poklonskii 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: 10.1134/1.1130623

23. Grundmann M. The Physics of Semiconductors. An Introduction Including Nanophysics and Applications. Berlin, Springer, 2021, xxxvii+889 p. DOI: 10.1007/978-3-030-51569-0

24. Poklonski N.A., Vyrko S.A., Podenok S.L. [Statistical physics of semiconductors]. Moscow, KomKniga Publ., 2005, 264 p. (in Russian).

25. 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/aa8e26

26. Baranovskii 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_9

27. Shklovskii B.I., Efros A.L. Electronic Properties of Doped Semiconductors. Berlin, Springer, 1984, xii+388 p.

28. 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. 522–524

29. Dyre 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.72.873

30. Long A.R. Frequency-dependent loss in amorphous semiconductors. Adv. Phys., 1982, vol. 31, no. 5, pp. 553–637. DOI: 10.1080/00018738200101418