Theory of electronic properties of disordered semiconductors and
systems with reduced dimensionality
Members of the group:
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
Some recent publications:
- 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/Al0.3Ga0.7As 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
1017cm-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,
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.
Physics of Semiconductors