Polarons in crystalline and non-crystalline materials

The current state of polaron theory as applicable to transition metal oxides is reviewed, including problems such as impurity conduction where disorder plays a role. An estimate is given of the conditions under which polaron formation leads to an enhancement of the mass but no hopping energy. The binding energy of a polaron to a donor or acceptor in narrow-band semiconductors is discussed. The experimental evidence about the conductivity of TiO₂ and NiO is reviewed. Impurity conduction in NiO and conduction in glasses containing transition metal ions is discussed and it is emphasized that the activation energy for hopping nearly all vanishes at low temperatures. Pollak's theory of a.c. impurity conductivity is reviewed and applied to the problem of dielectric loss in these materials.     

Electrical properties of flash-evaporated V2O5 films

Electrical properties of vanadium-pentoxide flash-evaporated films are reported. Transport parameters are investigated as functions of growth conditions and post-deposition treatments. The conduction mechanism is analyzed using the small polaron hopping model. The main features of the electrical conductivity such as the polaron hopping energy, the disorder energy term and the density of states are determined. Paper presented at 3rd Euroconference on Solid State Ionics, Teulada, Sardinia, Italy, Sept. 15–22, 1996     

Superconductor-insulator transition in (PbzSn1−z )0.84In0.16Te

The superconductor-insulator transition that occurs at liquid helium temperatures in the (Pb_zSn_1?z )_0.84In_0.16Te semiconductor system with varying lead concentration z = 0.5–0.9 is experimentally investigated. The transition is attributed to the change in the energy characteristics of In impurity centers due to the variation in the amount of lead. The insulator state appears with the transition from the mixed band-impurity conduction, which is characterized by resonant scattering of carriers into the quasilocal indium impurity states, to the hopping conduction between indium impurity states. The sample with z = 0.8 is found to exhibit a variable range hopping conduction described by Mott’s law. Factors that lead to the hopping conduction via impurity states are considered.     

Electrical conduction properties of Si δ-doped GaAs grown by MBE

The temperature dependent Hall effect and resistivity measurements of Si δ-doped GaAs are performed in a temperature range of 25–300 K. The temperature dependence of carrier concentration shows a characteristic minimum at about 200 K, which indicates a transition from the conduction band conduction to the impurity band conduction. The temperature dependence of the conductivity results are in agreement with terms due to conduction band conduction and localized state hopping conduction in the impurity band. It is found that the transport properties of Si δ-doped GaAs are mainly governed by the dislocation scattering mechanism at high temperatures. On the other hand, the conductivity follows the Mott variable range hopping conduction (VRH) at low temperatures in the studied structures.     

New Energy Spectra Structure of Polaron in Trans-Polyacetylene

In the weakly coupled electron-phonon systems, the existing theory pointed out that the energy spectra of polaron include four electronic bound states. Our work shows that, due to the non-nearest neighbor hopping interactions, the electron-hole symmetry of the energy band structure implied by SSH model is broken, and the numbers of the bound electronic states are changed. For a negative charged polaron, one new bound state is found near the bottom of conduction band, and the original two bound states below the bottom of the valence band and above the top of the conduction band disappear. For a positive charged polaron, five bound states have been found: one of them is an additional bound state at the top of the conduction band, the others are just the states found in the SSH model. Besides, the energy gap 2Δ is slightly shifted by turning on the long-range hopping interactions.     

Sr-doping effects on conductivity,charge transport,and ferroelectricity of Ba_(0.7)La_(0.3)TiO_3 epitaxial thin films

Sr-doped Ba_0.7La_0.3TiO₃(BSLTO)thin films are deposited by pulsed laser deposition,and their microstructure,conductivity,carrier transport mechanism,and ferroelectricity are systematically investigated.The x-ray diffraction measurements demonstrate that Sr-doping reduces the lattice constant of BSLTO thin films,resulting in the enhanced phonon energy in the films as evidenced by the Raman measurements.Resistivity-temperature and Hall effect measurements demonstrate that Sr can gradually reduce electrical resistivity while the electron concentration remains almost unchanged at high temperatures.For the films with semiconducting behavior,the charge transport model transforms from variable range hopping to small polaron hopping as the measurement temperature increases.The metalic conductive behaviors in the films with Sr=0.30,0.40 conform to thermal phonon scattering mode.The difference in charge transport behavior dependent on the A-site cation doping,is clarified.It is revealed that the increasing of phonon energy by Sr doping is responsible for lower activation energy of small polaron hopping,higher carrier mobility,and lower electrical resistivity.Interestingly,the piezoelectric force microscopy(PFM)results demonstrate that all the BSLTO films can exhibit ferroelectricity,especially for the room temperature metallic conduction film with Sr=0.40.These results imply that Sr-doping could be a potential way to explore ferroelectric metal materials for other perovskite oxides.     

Halleffekt und Leitfähigkeitsmessungen an Zinkoxid-Einkristallen mit Sauerstofflücken als Donatoren

The electrical conductivity and Hall effect of pure zinc oxide single crystals have been measured from 5 to 300 K. The temperature dependence of the conductivity and the charge carrier concentration is similar to silicon and germanium. The low temperature conduction mechanism depending on the impurity concentration is explained by means of hopping conductivity and impurity band conduction. The impurity band is supposed to be built up of overlapping wave functions of the excited donor states. The results have been discussed supposing that the donors are oxygen vacancies occupied by one or by two electrons.     

Electrical properties of a-antimony selenide

This paper reports conduction mechanism in a-Sb₂Se₃ over a wide range of temperature (238 to 338 K) and frequency (5 Hz to 100 kHz). The d.c. conductivity measured as a function of temperature shows semiconducting behaviour with activation energy ΔE=0.42 eV. Thermally induced changes in the electrical and dielectric properties of a-Sb₂Se₃ have been examined. The a.c. conductivity in the material has been explained using modified CBH model. The band conduction and single polaron hopping is dominant above room temperature. However, in the lower temperature range the bipolaron hopping dominates.     

Non-adiabatic polaron hopping conduction in CaMn1−xCrxO3 (0?x?0.3)

DC electrical conductivity (σ_dc) of electron-doped antiferromagnetic CaMn_1−xCr_xO₃ (0?x?0.3) has been discussed elaborately in the light of polaron hopping conduction. The increase in Cr doping concentration increases the conductivity and decreases the activation energy. Non-adiabatic polaron hopping conduction is observed in all the manganites at high temperatures. The analysis of σ_dc data shows that small polarons are formed at lower concentrations (?5%) of Cr doping and undoped samples. However, large polarons are materialized at higher doping (?10%) concentrations. This is consistent with the fact that doped Cr³⁺ has larger ionic size compared to that of Mn⁴⁺. Again, strong electron-phonon (e-ph) interaction is perceived in undoped and 5% Cr-doped samples but not in manganites with larger doping concentration. This also confirms the formation of larger polarons with the increase of x. Mott's variable range hopping (VRH) model can elucidate the dc conductivity at very low temperatures. It has been detected that single phonon-assisted hopping is responsible for the dc conduction in the Cr-doped CaMnO₃ manganites.     

Konzentration und Beweglichkeit von Elektronen in Zinkoxidkristallen mit Indium-Dotierung

The electrical conductivity and Hall effect of zinc oxide single crystals doped with indium has been measured from 5 to 300 K. Similar results to other semiconductors such as silicon and germanium are found. The temperature dependence of the measured quantities was discussed in terms of impurity band conduction and hopping conductivity.     

Cation defects and conductivity in transparent oxides

High quality doped zinc oxide and mixed transition metal spinel oxide films have been deposited by means of sputter deposition from metal and metal oxide targets, and by spin casting from aqueous or alcoholic precursor solutions. Deposition conditions and post-deposition processing are found to alter cation oxidation states and their distributions in both oxide materials resulting in marked changes to both optical transmission and electrical response. For ZnO, partial reduction of the neat or doped material by hydrogen treatment of the heated film or by electrochemical processing renders the oxide n-type conducting. Continued reduction was found to diminish conductivity. In contrast, oxidation of the infrared transparent p-type spinel conductors typified by NiCo₂O₄ was found to increase conductivity. The disparate behavior of these two materials is caused, in part, by the sign of the charge carrier and by the existence of two different charge transport mechanisms that are identified as free carrier conduction and polaron hopping. While much work has been reported concerning structure/property relationships in the free carrier conducting oxides, there is a significantly smaller body of information on transparent polaron conductors. In this paper, we identify key parameters that promote conductivity in mixed metal spinel oxides and compare their behavior with that of the free carrier TCO’s. PACS 61.72.C.; 71.38.-k; 81.15.-z; 77.84.Bw; 73.61.-r     

Electronic transport mechanisms in tetraphenyleprophyrin thin films

Thermally-evaporated thin films of tetraphenylporphyrin, TPP, with thickness range from (175 to 735) nm had been prepared. Annealing temperatures ranging from (273–473) K do not influence the amorphous structure of these films. The influence of environmental conditions: film thickness, temperature and frequency on the electrical properties of TPP thin films had been reported. It was found that dc conductivity increases with increasing temperature and film thickness. The extrinsic conduction mechanism is operating in temperature range of (293–380) K with activation energy of 0.13 eV. The intrinsic one is in temperatures >380 K via phonon assisted hopping of small polaron with activation energy of 0.855 eV. The ac electrical conductivity and dielectric relaxation in the temperature range (293–473) K and in frequency range (0.1–100) kHz had been also studied. It had been shown that theoretical curves generated from correlated barrier hopping (CBH) model gives the best fitting with experimental results. Analysis of these results proved that conduction occurs at low temperatures (300–370) K by phonon assisted hopping between localized states and it is performed by single polaron hopping process at higher temperatures. The temperature and frequency dependence of both the real and imaginary parts of dielectric constant had been reported.     

Optical and electrical properties of binary WO3–Pb3O4 glasses

A glass system of the composition xWO₃+(100−x)Pb₃O₄, with x=5, 10, 20 and 30 mol.% was prepared. The optical absorption, ac and dc conductivities are the subject of the present work. The optical absorption indicates that the electronic transition is indirect and is associated with phonon assisted transition. The exponential dependence of the absorption coefficient as a function of the incident photon energy suggests that the Urbach rule is obeyed, and indicates the formation of a band tail. On the other hand, ac conductivity measurements are performed in the frequency range 0.1–100 kHz, and in the temperature range 300–600 K. The results of the electrical conductivity are discussed on the basis of electronic glass conduction models. Correlated narrow-band limit for random sites and single polaron hopping model are found to describe the experimental results effectively. The dielectric constant was correlated to the optical band gap and a satisfactory relation was found. It was also possible to calculate the thermochromic properties from independent ac and dc measurements, and it was possible to evaluate the optical gap at 0 K by extrapolation.     

Anomalous Hall effect in ferromagnetic semiconductors in the hopping transport regime

We present a theory of the anomalous Hall effect in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous Hall conductivity in this system can be attributed to a phase that a hole gains when hopping around closed-loop paths in the presence of spin-orbit interactions and background magnetization of the localized Mn moments. Mapping the problem to a random resistor network, we derive an analytic expression for the macroscopic anomalous Hall conductivity sigma(AH)(xy). We show that sigma(AH)(xy) is proportional to the first derivative of the density of states varrho(epsilon) and thus can be expected to change sign as a function of impurity band filling. We also show that sigma(AH)(xy) depends on temperature as the longitudinal conductivity sigma(xx) within logarithmic accuracy.     

The effect of sintering time and temperature on the electrical properties of MnZn ferrites

Polycrystalline samples of Zn_0.37Mn_0.58Fe_2.05O₄ have been prepared by the solid state reaction method. The structural characterization of the samples indicated that 1523 K is the most proper temperature for obtaining a single phase spinel structure. The DC electrical conductivity measurement was carried out by a two-probe method. Temperature dependent of DC electrical conductivity increases with increase in temperature ensuring the semiconductor nature of the samples. The drift mobility was estimated and found to be temperature dependant. The electrical conduction mechanism in these samples change from hopping, in the low temperature range, to polaron hopping in the high temperature range. The portion of energy Δε anticipated in hopping was determined. It decreases with increasing the sintering time and temperature. PACS 70; 71.20.Nr; 75.50.Gg     

Temperature and hydrogen-like impurity effects on the excited state of the strong coupling bound polaron in a CsI quantum pseudodot

With hydrogen-like impurity(HLI) located in the center of Cs I quantum pseudodot(QPD) and by using the variational method of Pekar type(VMPT), we investigate the first-excited state energy(FESE), excitation energy and transition frequency of the strongly-coupled bound polaron in the present paper. Temperature effects on bound polaron properties are calculated by employing the quantum statistical theory(QST). According to the present work's numerical results, the FESE, excitation energy and transition frequency decay(amplify) with raising temperature in the regime of lower(higher)temperature. They are decreasing functions of Coulomb impurity potential strength.     

Electrical properties and conductivity mechanism of LiCuFe2(VO4)3

This paper reports conduction mechanism in LiCuFe₂(VO₄)₃ over a wide range of temperatures (300 to 712 K) and frequencies (209 Hz to 5 MHz). The DC conductivity of the material is thermally activated with activation energy about 0.66 eV. In LiCuFe₂(VO₄)₃, the electrical conductivity is probably due to the hopping of alkali lithium ion along the channel [001]. Temperature dependence of AC conductivity is studied at different frequencies. Frequency exponent s is found to decrease with increase in temperature. The results have been explained on the basis of correlated barrier hopping (CBH) model. Numerical calculations agree well with experimental results. The results show that the frequency and temperature-dependent behavior of AC conductivity of the studied materials are predominantly due to single polaron hopping.     

Al-doped ZnO: Electronic, electrical and structural properties

Changes in structural, electrical and electronic properties of zinc oxide (ZnO) due to Al doping are studied using a quantum-chemical approach based on the Hartree-Fock theory. A periodic supercell of 128 atoms has been exploited throughout the study. The atomic parameters for Zn atom were obtained by reproducing the main properties of ZnO crystal as well as the first three ionization potentials of Zn atom. The perturbation imposed by Al atom incorporation leads to the atomic relaxation, which is computed and discussed in detail. A novel effect of electron density redistribution between different atomic orbitals within the same atom has been found. This phenomenon influences atomic rearrangement near Al impurity. The Al doping generates a free electron in the conduction band, which can be considered as a large radius electron polaron increasing the n-type electrical conductivity in the crystal in agreement with the known experimental data. The obtained small increase in the band-gap width due to the impurity incorporation resolves existing experimental debates on this point.     

A lattice model of nearest-neighbor hopping conduction and its application to neutron-doped Ge: Ga

A model of hopping conduction between nearest neighbors is developed in which the majority and compensating dopant atoms are assumed to form a unified simple cubic lattice in a crystalline matrix. The hopping of carriers occurs when thermally activated “equalization” of majority impurity levels takes place, while the compensating impurities block the corresponding sites. The range of relatively high temperatures is considered in which the interactions giving rise to a Coulomb gap can be neglected and the density of states of the majority impurity band is Gaussian. The concentration dependences of the activation energy for hopping conductivity ? ₃ (nonmonotonic and having a maximum) and the preexponential factor σ₃ are found. The results are compared with experimental data obtained by different authors for neutron-doped Ge: Ga.