B.I. Yakubovich – Ph.D.(Phys.-Math.), Senior Research Scientist, 
Petersburg Nuclear Physics Institute named by B.P. Konstantinov of NRC «Kurchatov Institute» E-mail: yakubovich_bi@pnpi.nrcki.ru

Fluctuations in electrical conduction in semiconductors and semiconductor devices are studied for both fundamental and applied purposes. This is due to the following circumstances. Fluctuations in the conduction of semiconductors are caused mainly by fluctuations in the number of free charge carriers in the sample. Fluctuations in the number of free carriers in semiconductors are the basis of several types of fundamental electrical noises. Such noises are widely studied, and their study is important for the development of ideas about fluctuation phenomena in solids. In addition, fluctuations in the conduction of semiconductors largely determine electrical noise of semiconductor devices. Electric noise affects the characteristics and stability of electronic devices, which stimulates research aimed at reducing noise. A useful application of noise is possible: for non-destructive testing and diagnostics of devices. In connection with the above reasons, the study fluctuations of electrical conduction of semiconductors is in principle important for both fundamental and applied purposes. The purpose of this work is to study fluctuations in the electrical conduction of semiconductors and to calculate fluctuation spectrum in a more general form than previously done.
Fluctuations in the electrical conduction of semiconductor caused by a change in the number of free charge carriers are analyzed. Fluctuations of number of electrons in conduction band are considered in detail. Fluctuation process is considered in the following enough general form. Probability of a change in the number of electrons in conduction band is statistically connected to the number of electrons in band at a given moment when the statistical connections are given in a general form. Fluctuations of number of free electrons considered are a random sequence of pulses in which pulse duration is statistically connected to its amplitude, and pulse amplitude is statistically connected to amplitude of previous pulse. Spectrum of such a random sequence of pulses is calculated. Further, probability of finding a certain number of electrons in conduction band of semiconductor is strictly calculated. For this, the Kolmogorov system of differential equations is used. The probabilities of increasing and decreasing number of electrons in conduction band are determined. Next, the expression for fluctuation spectrum of number of electrons in conduction band of semiconductor is calculated. As a result, the expression for spectrum of fluctuations in the conduction of semiconductor is calculated. This expression has a very general form. It is applicable for various types of semiconductors. The resulting expression allows us to determine the spectrum of fluctuation processes having various statistical properties.
Thus, fluctuations of electrical conduction of semiconductors are considered in a very general form, and the expression for fluctuation spectrum is calculated. It can be widely used to describe and analyze fluctuations in semiconductors: in various types of semiconductors and for fluctuation processes having different statistical properties. The results can be applied in the development of semiconductor devices: to reduce noise and improve characteristics of devices, and in some cases to increase stability and reliability of electronic devices based on semiconductors. That is, the results of the article can be used in solving both fundamental and applied problems.

Yakubovich B.I. Fluctuations electrical conduction of semiconductors. Electromagnetic waves and electronic systems. 2020. V. 25. № 1–2. P. 48−53. DOI: 10.18127/j15604128-202001-2-06 (in Russian).

1. Bonani F., Chione G. Noise in semiconductor devices, modeling and simulation. Berlin: Springer-Verlag. 2001. 212 p.
2. Kogan Sh. Electronic noise and fluctuations in solids. Cambridge: Cambr. Univ. Press. 1996. 354p.
3. Yakubovich B.I. Elektricheskie fluktuatsii v tverdykh telakh. Germany: AV Akademikerverlag. 2013. 212 s. (in Russian).
4. Yakubovich B.I. Elektricheskie fluktuatsionnye yavleniya v tverdykh telakh. Riga: SIA OmniScriptum Publishing. 2018. 264 s. (in Russian).
5. Jones B.K. Electrical noise as a measure of quality and reliability in electronic devices. Adv. Electron. Electron. Phys. 1993. V. 87. P. 201−257.
6. Yakubovich B.I. Elektricheskie fluktuatsii v nemetallakh. SPb.: Energoatomizdat. 1999. 208 s. (in Russian).
7. Kirton M.J., Uren M.J. Noise in solid-state microstructures: A new perspective on individual defects, interface states and low-frequency (1/f) noise. J. Adv. Phys. 1989. V. 38. № 4. P. 367−468.
8. Fleetwood D.M. 1/f noise and defects in microelectronic materials and devices. IEEE Trans. Nucl. Sci. 2015. V. 62. № 4. P. 1462−1486.
9. Yakubovich B.I. Osobennosti elektricheskogo nizkochastotnogo shuma v poluprovodnikakh. Elektromagnitnye volny i elektronnye sistemy. 2018. T. 23. № 4. S. 46−50 (in Russian).
10. Kleinpenning T.G.M. On 1/f noise and random telegraph noise in very small electronic devices. Physica B. 1990. V. 164. № 3. P. 331−334.
11. Vandamme L.K.J. Noise as a diagnostic tool for quality and reliability of electron devices. IEEE Trans. Electron Devices. 1994. V. 41. № 11. P. 2176−2187.
12. Yakubovich B.I. Elektricheskii shum i defekty struktury tverdykh tel. Germany: LAP Lambert Academic Publishing. 2012. 116 s. (in Russian).
13. Venttsel E.S. Ovcharov L.A. Teoriya sluchainykh protsessov i ee inzhenernye prilozheniya. M.: Vysshaya shkola. 2000. 383 s. (in Russian).
14. Burgess R.E. Fluctuations in the number of charge carriers in a semiconductor. Physica. 1954. V. 20. № 7−12. P. 1007−1010.
15. Feller V. Teoriya veroyatnostei i ee prilozheniya. T. 1. M.: Mir. 1984. 528 s. (in Russian).