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Analytical description of hopping electrical conductivity of compensated semiconductors and calculations on the example of p-Ge : Ga
Russian version
Poklonski N. A. 1, Anikeev I. I. 1, Vyrko S. A. 1, Zabrodskii A. G. 2
1Belarusian State University, Minsk, Republic of Belarus
2Ioffe Institute, St. Petersburg, Russia
Email: poklonski@bsu.by, ilyaanikeev35@mail.ru, vyrko@bsu.by, Andrei.Zabrodskii@mail.ioffe.ru
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Analytical expressions are proposed for the prefactor σ03 and the thermal activation energy of direct current electrical ε3-conductivity σ h=σ03exp(-ε_3/k BT) of compensated n- and p-type semiconductors for hydrogen-like impurities. The obtained formulas are applicable to describe the hopping migration of both holes via acceptors and electrons via donors. For certainty, we considered p-type crystalline semiconductors in the range of doping levels corresponding to the insulator side of the insulator-metal (Mott) concentration phase transition. For simplicity, it was assumed that the majority and compensating impurities form a single simple nonstoichiometric cubic lattice in the crystal matrix. The calculation of σ03 and ε3 values is based on the preliminary determination of the characteristic temperature T3, in the region of which phonon-assisted tunnel hopping of holes via nearest neighbor acceptors is observed. The shift of the top of the v-band deep into the band gap due to the formation of a quasi-continuous band of allowed energy values for v-band holes from the excited states of neutral acceptors is taken into account. The distribution of the density of hole states in the acceptor band was assumed to be Gaussian. The influence of the configurational entropy and thermal entropy of holes in the acceptor band on the values of σ03 and ε3 was also taken into account. The values of σ03 and ε3 calculated from the obtained formulas for moderately compensated p-Ge : Ga are in quantitative agreement with the known experimental data on the entire insulator side of the Mott transition. Keywords: doped and moderately compensated semiconductor, hydrogen-like impurities, hopping migration of charge carriers via impurities, stationary hopping electrical conductivity, thermal activation energy and prefactor of electrical ε3-conductivity, mobility edge, p-Ge : Ga crystals.
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