Field effect and capacitance of silicon crystals with hopping conductivity over point radiation defects pinning the Ferm
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TRONIC AND OPTICAL PROPERTIES OF SEMICONDUCTORS
Field Effect and Capacitance of Silicon Crystals with Hopping Conductivity over Point Radiation Defects Pinning the Fermi Level N. A. Poklonskia^, S. A. Vyrkoa, and A. G. Zabrodskiib aBelarussian
State University, pr. Nezavisimosti 4, Minsk, 22030 Belarus ^e-mail: [email protected] bIoffe Physicotechnical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia Submitted March 12, 2007; accepted for publication April 3, 2007
Abstract—The static field effect and capacitance of Si crystals with hopping conductivity over defects in the charge states (+1), (0), and (–1), which pin the Fermi level, are calculated. In the Si band gap, the defects in the (0) and (+1) charge states form a v' band, and in the charge states (–1) and (0), they form a c' band. The width of the c' and v' energy bands is calculated under the assumption of Coulomb interaction of each charged defect with only the nearest ion. The energy gap between the c' and v' bands is assumed to be constant. Nonmonotonicity of the dependence of capacitance and surface hopping conductivity on the electric potential on the surface of the highly damaged Si crystals is predicted. PACS numbers: 72.10.Fk, 72.20.Ee, 72.80.Cw DOI: 10.1134/S1063782607110048
1. INTRODUCTION Using the ionizing radiation, one can control the properties of semiconductor materials without varying their atomic composition, which is important for the development of functional elements of electronics [1]. The method of “doping” of semiconductors by stable radiation defects is advantageous compared to metallurgical doping [2] since it allows one to introduce defects with deep energy levels in the band gap (energy gap) in high concentrations. It was experimentally found that radiation defects, which are rather stable in the temperature region of functioning semiconductor devices, are formed in many elemental semiconductors and semiconductor compounds under the effect of ionizing radiation such as γ-ray photons, electrons, and fast reactor neutrons, and partially under the effect of thermal annealing [3]. In this case, the Fermi level is shifted with an increase in the radiation fluence to the limiting position in the band gap; more rarely, EF is shifted to a conduction band (c) or to a valence band (v). This limiting position of the Fermi level is a characteristic of crystalline semiconductors [4–6]. Pinning of the Fermi level is induced by accumulation of intrinsic radiation defects such as vacancies, interstitials, and their associations. Defects of one type that can be present in three charged states (+1, 0, –1) are sufficient to provide the electrical neutrality of the crystal. The specific features of temperature dependences of capacitance and electrical conductivity of highly damaged crystals have been dis-
cussed previously [7]. However, quantitative description of these crystals has not been carried out. The purpose of this study is to calculate the quasistatic capacitance and surface conductivity (f
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