**Igor P. Zvyagin**

**Alexander G. Mironov****Michail A. Ormont**

Research activity of the group is related to the theory of transport and optical properties of disordered semiconductors, in particular, the disorder effects in systems of reduced dimensionality. Studies of phonon-assisted hopping transport include the theory of hopping in quasi-one- and quasi-two-dimensional systems and hopping thermoelectric effects.

- I.P. Zvyagin. Anisotropy in hopping conductivity of quasi-one-dimensional
systems.
**JETP**, 1995, v.107, p.175-186.

Conductivity of macroscopic quasi-one-dimensional systems cannot be always evaluated reducing the problem to that of bond percolation. In fact, the longitudinal conductivity of a non-percolating system of isolated wires with random hopping sites remains finite due to the vanishing probability of asymptotically large inter-site resistances. The shape of optimal hopping paths and the applicability of the percolation theory to evaluate transport coefficients is analyzed for a system of hopping sites randomly distributed over a regular array of wires with low inter-wire transition rates. It is demonstrated that for percolation problems, due to the fast increase of the bond density above the percolation threshold, the conductivity can be evaluated using the approach based on the bond percolation theory. It yields optimal hopping paths lying in the critical subnetwork both for longitudinal and for transverse conduction giving rise to the isotropic exponential factor of the conductivity.

Quite a different situation can be encountered for percolation problems because of the specific shape of the optimal hopping paths which determine the conductivity. In the case of weak inter-wire coupling for temperatures region outside the region of applicability of the percolation approach the optimal hopping paths for longitudinal and for transverse conduction can be different from each other, this being a consequence of the structure of the infinite cluster of bonds in the relevant percolation problem. In fact, the critical subnetwork can consist of long longitudinal bond chains connected by rare transverse bonds. Therefore the situation is possible when any transverse hopping path lying in the critical subnetwork is convoluted so that its resistivity is higher than that for paths with shortcuts lying outside the critical subnetwork. This results in the anisotropy of the exponential factor of the conductivity, i.e. of its exponential temperature and concentration dependence, in contrast to the isotropic exponential factors predicted by the conventional percolative approach. - A.G. Andreev, A.G. Zabrodskii, I.P. Zvyagin, and S.V. Egorov.
Thermopower of Neutron Transmutation-Doped Ge:Ga in the Region of Hopping
Conductivity.
**Semiconductors**, 1997, v. 31, N 10, p. 1174-1179. - A.G. Andreev, A.G. Zabrodskii, I.P. Zvyagin, and S.V. Egorov.
Thermopower of Neutron Transmutation-Doped Ge:Ga In the Hopping Region.
**Phys. Stat. sol.(b)**, 1998, v. 205, N 1, p. 381-384.

The temperature dependence of the thermopower of moderately compensated neutron transmutation-doped Ge:Ga was measured at low temperatures. For valence band conduction ($\epsilon_1$-conductivity) the value of the thermopower shows the important role of the phonon drag effect which is suppressed for hopping conduction; the results in the region of transition from band to hopping conduction indicate the existence of additional conduction channel with characteristics similar to those of $\epsilon_2$-conductivity. Vanishing values of the hopping thermopower at lowest temperatures (<2 K) require the compensation of different contributions to the thermopower including terms arising from correlation and from the asymmetry of the density of states in the Coulomb gap. A different explanation is suggested based on the assumption of the transition to the regime of ballistic phonons. - I.P. Zvyagin. Hopping Thermopower in the Regime of Ballistic Phonons.
**Phys. Stat. sol.(b)**, 1998, v.205, N 1, p.391-394.

It is argued that at low temperatures, under the conditions when the phonon mean free path exceeds the system size (regime of ballistic phonons), the thermopower cannot be calculated using the standard approach based on the local equilibrium approximation for the electron distribution function. Under these conditions, the hopping thermopower is shown to vanish. - G. Richter, W. Stolz, P. Thomas, S. Koch, K. Maschke, and I.P. Zvyagin.
Effects of Coulomb Interaction in Intentionally Disordered Semiconductor
Superlattices.
**Superlattices and Microstructures**, 1997, v. 22, N 74, 475-480.

The intricate interplay between disorder and electron-electron interaction is studied using measurements of the vertical dc conductivity of intentionally disordered GaAs/Al_{0.3}Ga_{0.7}As superlattices. Surprisingly, at low temperatures a quasi-metallic behaviour is observed even for large disorder. At higher temperatures and large disorder the conductivity increases with temperature, whereas in weakly disordered structures it decreases in the whole temperature range. The experimental results are interpreted in terms of a model taking into account the Coulomb potential of the inhomogeneous charge distribution which screens the disorder potential at low temperatures. At low doping levels the short-range exchange-correlation part of the electron-electron interaction is expected to play an important role leading to the formation of a charge distribution similar to that in a 1D Wigner lattice. This picture appears to be confirmed by preliminary measurements of the conductivity of ordered weakly doped superlattices. - I.P. Zvyagin. Electronic Superstructures in Doped Superlattices.
**JETP**, 1998, v.114, p.1089-1100. - I.P. Zvyagin. Electronic Superstructures in Doped Semiconductor
Superlattices. 6th Int. Symp."Nanostructures: Physics and Technology",
St.Petersburg, Russia, June 22-26, 1998. Ed. Zh. Alferov and L. Esaki.
Ioffe Institute, St.Petersburg, 1998, p.50-53.

We argue that in doped semiconductor superlattices with narrow quantum wells at low temperatures and at sufficiently low doping levels the ground state can correspond to inhomogeneous distribution of electrons over the wells. In fact, using the density functional approach, we show that under the above conditions the exchange-correlation contribution to the system energy can exceed the sum of the kinetic and Hartree energies, making the uniform distribution unstable. For GaAs/GaAlAs superlattices the estimate of the critical conditions for the loss of stability of the homogeneous state at T=0 K correspond to doping concentrations of about 10^{17}cm^{-3}. Inhomogeneous ground states are discussed. - I.P. Zvyagin and M.A. Ormont. Anisotropy in hopping conductivity of
quasi-one-dimensional systems.
**Fiz. Tech. Poluprov**, 1999, v.33, p.79-82.

We calculate the energy spectrum of doped semiconductor superlattices with intentional disorder taking account of the Coulomb interaction, originated from redistribution of electrons over the quantum wells. Using the density functional theory, we study numerically the effect of screening on vertical disorder, in particular, on the distribution of size quantization levels in these structures. We show that screening gives rise to a shift of the maximum of the level distribution and appreciable decrease of its width; this can produce delocalisation of electron states that determine vertical conductivity of the structure. - I.P. Zvyagin. Recombination via defect complexes in hydrogenated
amorphous silicon. In:
**Solid State Phenomena**, 1995, v. 44-46, p.765-772.