A. G. Zabrodskii

Coulomb Gap and the Metal–Insulator Transition

Critical collapsing of the recently discovered multielectron Coulomb gap (CG) in moderately compensated neutron transmutation doped (NTD) Ge:Ga and the metal–insulator (MI) transition in this system had been under investigation. The results obtained are compared with those received for strongly and weakly compensated Ge, where single electron CG takes place far from the MI transition. Independently of the single- or multielectron origin all the gaps, as deduced by the variable range hopping (VRH) spectroscopy procedure, turned out to be collapsing in the critical point of the MI transition just the same where the low temperature metallic conductivity vanishes. One can consider such MI transition as the CG collapsing phenomenon and describe it in the frame of scaling theory as a second-order phase transition. In compensated semiconductors it is characterised by the critical index for a correlation length nearly equal to unity.

Electrostatic models of insulator-metal and metal-insulator concentration phase transitions in Ge and Si crystals doped by hydrogen-like impurities

Two electrostatic models have been developed that allow calculation of the critical concentration of hydrogen-like impurities in three-dimensional crystalline semiconductors corresponding to the insulator-metal and metal-insulator transition in the zero temperature limit. The insulator-metal transition manifests itself as a divergence of the static permittivity observed in lightly compensated semiconductors as the concentration of polarizable impurities increases to the critical level. The metal-insulator transition is signaled by the divergence of the dc electrical resistivity in heavily doped semiconductors as the compensation of the majority impurity increases (or its concentration decreases). The critical impurity concentration corresponds to the coincidence of the percolation level for the majority carriers with the Fermi level. The results of the calculations made with these models fit the experimental data obtained for n-and p-type silicon and germanium within a broad range of their doping levels and impurity compensation.

Atomic-force-microscopy visualization of Si nanocrystals in SiO2 thermal oxide using selective etching

The topography and local hardness of the etched surfaces of layers of SiO2 thermal oxide that contained Si nanocrystals in its bulk were studied using atomic-force microscopy. The Si nanocrystals were obtained by implanting Si+ ions into the oxide with subsequent high-temperature annealing. It is shown that the use of selective etching that removes the oxide material makes it possible to reveal Si nanocrystals that appear in the profile of etched surfaces in the form of nanohillocks with a height of up to 2–3 nm. These values are in satisfactory agreement with the average radius of Si nanocrystals in the SiO2 oxide layer. Independent confirmation of the Si-nanocrystal observation was obtained by comparing the topography of etched surfaces with the local-hardness maps obtained for the same surfaces; in these maps, the hillocks appear as sites at the surface with a reduced hardness. The phase precipitation of implanted Si is also observed in the form of extended flat clusters oriented in the oxide bulk parallel to the oxide surface. The suggested method for revealing the Si nanocrystals and clusters incorporated into the oxide provides a convenient way to study the specific features of nucleation growth and spinodal decomposition in the Si solid solution in the SiO2 oxide.

Thermopower of transmutation-doped Ge:Ga in the region for hopping conductivity

The low-temperature thermopower of transmutation-doped Ge:Ga is investigated experimentally and theoretically. The large values of the thermopower observed in the region for ɛ1 conduction and its sharp drop upon the transition to conduction between impurities are interpreted as manifestations of the phonon drag of free holes and its suppression in the region for hopping transport. The positive sign of the thermopower and its magnitude in the hopping-conduction saturation region can be explained theoretically under the assumption that the classical ɛ2 conduction channel, which is not manifested explicitly in the electrical conductivity, makes a contribution to the thermopower in the narrow temperature range associated with the transition from ɛ1 conduction to hopping conduction. After the transition to variable-range hopping (T⩽2 K), the thermopower decreases sharply and takes anomalous, vanishingly small values. They can be explained within the standard theory of hopping thermopower only under the condition that the contribution caused by the asymmetry of the density of states of the impurity band in the vicinity of the Fermi level and the correlation contribution are compensated.

Model of hopping dc conductivity via nearest neighbor boron atoms in moderately compensated diamond crystals

Abstract Expressions for dependences of the pre-exponential factor σ 3 and the thermal activation energy e 3 of hopping electric conductivity of holes via boron atoms on the boron atom concentration N and the compensation ratio K are obtained in the quasiclassical approximation. It is assumed that the acceptors (boron atoms) in charge states (0) and (−1) and the donors that compensate them in the charge state ( + 1 ) form a nonstoichiometric simple cubic lattice with translational period R h = [ ( 1 + K ) N ] − 1 / 3 within the crystalline matrix. A hopping event occurs only over the distance R h at a thermally activated accidental coincidence of the acceptor levels in charge states (0) and (−1). Donors block the fraction K / ( 1 − K ) of impurity lattice sites. The hole hopping conductivity is averaged over all possible orientations of the lattice with respect to the external electric field direction. It is supposed that an acceptor band is formed by Gaussian fluctuations of the potential energy of boron atoms in charge state (−1) due to Coulomb interaction only between the ions at distance R h . The shift of the acceptor band towards the top of the valence band with increasing N due to screening (in the Debye–Huckel approximation) of the impurity ions by holes hopping via acceptor states was taken into account. The calculated values of σ 3 ( N ) and e 3 ( N ) for K ≈ 0.25 agree well with known experimental data at the insulator side of the insulator–metal phase transition. The calculation is carried out at a temperature two times lower than the transition temperature from hole transport in v -band of diamond to hopping conductance via boron atoms.

Calculation of capacitance of self-compensated semiconductors with intercenter hops of one and two electrons (by the example of silicon with radiation defects)

Low-frequency electrical capacitance of silicon crystals in the case of hopping migration of both electrons and bipolarons (electron pairs) via the defects of one type, which stabilizes the Fermi level near the midgap, is calculated. The crystals with two-level defects in three charge states (+1, 0, or −1) with a negative correlation energy are considered. It is shown that, as the absolute value of the external potential is increased, the capacitance of silicon containing defects with positive correlation energy increases, while that with defects with negative correlation energy decreases. The expression for the drift and diffusion components of current density for bipolarons hopping from defects with the charge state −1 to defects with the charge state +1 was derived for the first time.

Distinctive features of the magnetoresistance of degenerately doped n-InAs and their influence on magnetic-field-dependent microwave absorption

Magnetic-field-dependent microwave absorption and electron spin resonance are used to investigate magnetoresistive effects in strongly doped n-InAs. It is shown that these effects can be traced back to negative, positive, or oscillatory magnetoresistance (i.e., the Shubnikov-de Haas effect). While the experimental data are in agreement with the predictions of theory in the latter two cases, for the negative magnetoresistance there are features that are difficult to interpret, especially the absence of any effect at very small fields, much smaller than the characteristic field Hϕ that appears in the theory of quantum corrections, and the two-dimensionality of bulk samples in fields much larger than Hϕ implied by the observed dependences on temperature and to some extent on the magnetic field.

Investigation of dislocations in Czochralski grown Si1−xGex single crystals

Dislocations in p-type Si1−xGex single crystals (2‐8 at% Ge) grown with the Czochralski technique are investigated by synchrotron white beam topography in transmission geometry. As the Ge concentration increases, the dislocation structure evolves from individual dislocations to slip bands and sub-grain boundaries, and the dislocation density increases from <10 2 cm −2 to 10 5 ‐10 6 cm −2 at 8at%. We discuss the effect of dislocations on the electrical characteristics such as resistivity ρv, Hall hole mobility µp, carrier lifetime τe and I‐V characteristics. Here τe and I‐V characteristics are measured from the diodes fabricated by bonding the p-Si1−xGex to n-Si wafers. I‐V characteristics are not deteriorated in spite of a five times decrease in τe with the Ge concentration.

Electron spin resonance of interacting spins in n -Ge: II. Change in the width and shape of lines

The effect of spin interaction on the width and shape of the electron spin resonance line in compensated and uncompensated n-Ge:As has been studied. It is shown that, in the case of a magnetic field oriented along the [100] axis, the width of the resonance line decreases irrespective of the degree of compensation as the critical concentration of the insulator-metal transition is approached, owing to enhancement of the exchange interaction of spins and to an increase in the spin relaxation time. When the magnetic field is directed along other axes, an additional line broadening appears in compensated samples. This broadening is determined by the influence exerted on the g factor by fluctuations of the internal electrostatic field via the stresses generated by these fluctuations. For well-conducting samples, in which the thickness of the skin layer becomes smaller than that of the sample, the line takes on an asymmetric (Dysonian) shape. In this case, the ratio between the wings of the derivative, characteristic of this line shape, is determined by the ratio between the rates of spin diffusion and spin relaxation.

Specific features of electron spin resonance in 4H-SiC in the vicinity of the insulator-metal phase transition: II. Analysis of the width and shape of lines

The variation in the width and shape of the ESR line of nitrogen in 4H-SiC in the concentration range corresponding to the insulator-metal phase transition was investigated. It is shown that the spin relaxation in the region of hopping and metal conduction occurs at electrical multipoles (clusters) whose sizes decrease from rather large to small (characteristic of interimpurity distances) as the concentration of impurity centers increases. Analysis of the temperature dependences of the resistance made it possible to estimate the critical concentration for the insulator-metal phase transition (ND-NA)c≈1.5×1019 cm−3. The values of other characteristic concentrations that determine the effects of electron-electron interaction in the system under study were also found.