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 TiO 2 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.     

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.     

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.     

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.     

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     

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     

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     

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.     

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.     

Specific features of the electrical conductivity of V6O11

A study has been made of the electrical conductivity of V₆O₁₁ single crystals over a broad range of temperatures covering the regions of the metal phase, metal-insulator phase transition, and insulator phase. It has been shown that the electrical conductivity of the metal phase correlates with the Mott limit of minimum conductivity. To explain the temperature dependence of the electrical conductivity of the V₆O₁₁ insulator phase, the theory of hopping conduction taking into account the effect of thermal vibration of atoms on the resonance integral has been invoked.     

The study of electronic conduction in amorphous thin films of Al-In<Subscript>2</Subscript>O<Subscript>3</Subscript>-Al structure deposited by thermal evaporation

A discussion of electronic conduction in amorphous thin films of Al-In₂O₃-Al structure is presented. Particular attention is given to the question of film thickness, substrate temperature during deposition and post-deposition annealing, since these conditions are known to have a profound effect on the structure and electrical properties of the films. The effects of temperature on the V-I characteristics and effects of frequency on conductivity and capacitance of the Al-In₂O₃-Al structure are also reported. Activation energies for conduction processes are estimated and the results are discussed in terms of the hopping model. The conduction at higher temperature is seemingly a contact-limited, i.e. Schottky type process, so a transition from hopping to free-band conduction takes place. The capacitance decreases with the rise of frequency and the lowering of temperature. The values of dielectric constants are estimated and the results are discussed in terms of Schottky type of conduction. The increase in conductivity with the increase in temperature during measurements of electrical properties, film thickness, substrate temperature and post deposition annealing is reported and results are discussed in terms of current theory.     

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.     

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.     

Small-polaron versus band conduction in some transition-metal oxides

In this paper an attempt is made to establish the nature of free charge carriers and of charge carriers bound to centres in p-type NiO, CoO and MnO and in n-type MnO and α-Fe₂O₃.

For free charge carriers, d.c. conductivity, Seebeck coefficient and Hall effect are considered. Effects arising from inhomogeneous conduction and impurity conduction are discussed. Impurity conduction appears to have a strong influence on transport properties in the case of α-Fe₂O₃, less so in NiO, whereas no influence of this effect has been found in CoO and MnO. It is shown that NiO and CoO do not exhibit the features characteristic of small-polaron conductors but rather can be consistently conceived of as large-polaron band semiconductors. It is suggested that magnetic resistance due to exchange coupling between charge-carrier spin and cation spins plays an important role. The anomalous behaviour of the Hall effect in NiO and α-Fe₂O₃ is extensively discussed. In contradistinction to NiO, CoO and n-type MnO, free charge carriers in p-type MnO seem to have small-polaron character.

For charge carriers bound to centres, dielectric loss, high-frequency conduction and optical absorption are considered. The dielectric loss data relate to Li or Na centres in NiO, CoO and MnO and to Ti, Zr, Sn, Ta, Nb and presumably oxygen vacancy centres in α-Fe₂O₃. It is concluded from the dependence of dielectric loss on frequency and temperature that bound charge carriers are small polarons. It is shown for the cases of NiO and α-Fe₂O₃ that apart from small-polaron effects, disorder due to locally varying electric fields determines the nature of dielectric loss. The small-polaron character of bound charge carriers in NiO is corroborated by the behaviour of high-frequency conduction and optical absorption due to centres and also by the magnitude of impurity conduction.     

Rietveld refinement and impedance spectroscopy of calcium titanate

Single phase perovskite CaTiO₃ has been synthesized by conventional solid state reaction technique. The ceramic was characterized by XRD at room temperature and its Rietveld refinement inferred orthorhombic crystal structure with the space group Pbnm. The field dependence of dielectric relaxation and conductivity was measured over a wide frequency range from room temperature to 673 K. Analysis of Nyquist plots of CaTiO₃ revealed the contribution of many electrically active regions corresponding to bulk mechanism, distribution of grain boundaries and electrode processes. The dc conductivity depicted a semiconductor to metal type transition. Frequency dependence of dielectric constant (ε′) and tangent loss (tan δ) show a dispersive behavior at low frequencies and is explained on basis of Maxwell-Wagner model and Koop's theory. Both conductivity and electric modulus formalisms have been employed to study the relaxation dynamics of charge carriers. The variation of ac conductivity with frequency at different temperatures obeys the universal Jonscher's power law (σ_ac α ω^s). The values of exponent ‘s’ lie in the range 0.13 ≤ s ≤ 0.33, which in light of CBH model suggest a large polaron hopping type of conduction mechanism.     

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.     

Polaronic transport in TiO2 thin films with increasing Nb content

The temperature dependence of the charge transport in TiO₂ films was investigated to establish the correlation between the Nb content and electrical properties. It was identified that temperature-dependent conductivity of the films is dominated by a phonon-assisted small polaron hopping model in the non-adiabatic regime. Applying the polaron hopping models of Mott, Schnakenberg and Emin to describe the observed behavior, temperature-dependent conductivity data of the films were analyzed. A detailed analysis in terms of small polaron hopping parameters in the investigated temperature regime was used to correlate electrical properties with the percentage of Nb.     

Polaron formation and hopping conductivity in the Holstein-Hubbard model

On the basis of the Holstein-Hubbard model the formation of polarons at finite densities is investigated by means of a variational approach appropriate for describing squeezing and correlation effects. An effective Hubbard model for the polarons is derived, where the correlations are treated within the slave-boson saddlepoint approximation. For low enough phonon frequencies, with increasing coupling an abrupt self-trapping transition from light to heavy polarons is found. With increasing density the squeezing effect increases, and the transition is shifted to higher couplings. In the case of an effective Coulomb repulsion, the self-trapping transition is shifted to lower couplings with increasing Hubbard interaction, and the effective polaron mass below the transition is enhanced. In the heavy polaron regime, the frequency-dependent polaron hopping conductivity is calculated. There occur qualitative finite-density and correlation effects on the zero-temperature absorption spectrum which are discussed with respect to their possible relevance to the midinfrared absorption in high-T _c superconductors.     

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.