Size effects in lead telluride thin films and thermoelectric properties

The influence of thickness d on thermoelectric properties (the Seebeck coefficient S, electric conductivity σ, the Hall coefficient RH, charge carrier mobility μН) of films d = 8 – 170 nm in thickness, prepared by vacuum evaporation of PbTe crystals with lead excess onto (001) KCl substrates coated with Al2O3 layer has been studied. It has been established that films with d 75 nm carrier transport is determined by n-type charge carriers. The inversion of conductivity sign close to d ≈ 75 nm is attributed to a change in thermodynamic equilibrium conditions in the films as compared to crystal, as well as to material evaporation and condensation features. Oscillations on the d-dependences of the kinetic coefficients of films with p-type conductivity are attributable to quantization of the hole gas of carriers. Calculation of oscillation period Δd using a model of infinitely deep rectangular potential well is in good agreement with the experimentally determined Δd value. For n-type conductivity films the values of kinetic coefficients increase with increase in d, which points to manifestation of a classical size effect

Quantum Size Effects and Transport Phenomena in PbSe Quantum Wells and PbSe/EuS Superlattices

It is established that the room-temperature dependences of transport properties on the total thickness of PbSe layers d in PbSe/EuS superlattices exhibit an oscillatory behavior. It is shown that the oscillation period Δd practically coincides with the period of the thickness oscillations observed earlier in single PbSe/EuS quantum well. The non-monotonic character of these dependences is attributed to quantum size effects. The theoretically estimated and experimentally determined Δd values are in good agreement

Size Effects in Transport Properties of PbSe Thin Films

This paper presents an overview and analysis of our earlier obtained experimental results on the dependences of kinetic properties of single PbSe quantum wells and PbSe-based superlattices on the PbSe layer thickness d. The observed oscillatory character of these dependences is attributed to quantum size effects due to electron or hole confinement in quantum wells. Some general regularities and factors that determine the character of these quantum size effects are established. The influence of the oxidation processes and doping on the d-dependences of the transport properties is revealed. A periodic change in the conductivity type related to quantum size oscillations is detected. It is shown that the experimentally determined values of the oscillation period Dd are in good agreement with the results of theoretical calculations based on the model of a rectangular quantum well with infinitely high walls, taking into account the dependence of the Fermi energy eF on d and the availability of subbands below eF. It is established that the Dd value for the superlattices is practically equal to the Dd value observed for the single PbSe thin film

Size effects in thin PbSe films

The objects of the study are thin PbSe films with thicknesses d in the range of d = 5.5 – 410 nm, grown by thermal evaporation in vacuum of stoichiometric p-PbSe crystals on KCl substrates and covered with a EuSe layer. The room-temperature d-dependences of the Seebeck coefficient, Hall coefficient, electrical conductivity, charge carrier mobility, thermoelectric power factor are obtained. When d increases to ~ 20 nm, an inversion of the conductivity sign from p to n is observed. In the d-dependences of the transport properties one can isolate a monotonic and oscillatory components, whose presence is attributed to the manifestation of classical and quantum size effects, respectively. The oscillation periods Δd for electronic and hole gases are determined. Theoretically calculated Δd, assuming a size quantization of the electronic and hole spectra, and our estimate of the monotonic component of the electrical conductivity, using the Fuchs-Sondheimer theory, are in good agreement with the experimental data

Size effects in chlorine doped PbSe thin films

The possibility of obtaining strongly degenerate (≈ 3·10²⁰ сm⁻³) PbSe thin films (d = 5 – 220 nm) with n-type conductivity by thermal evaporation in vacuum of PbSe crystals doped with PbCl₂, with subsequent condensation onto (001) KCl substrates was established. It was shown that the films had high homogeneity degree, no grain structure was observed. The thickness dependences of thermoelectric properties (the Seebeck coefficient S, the Hall coefficient RH and the electric conductivity σ) of thin films were obtained. In the thickness range d ≈ 5 ÷ 30 nm, oscillation properties were observed with growth of d that are attributable to electron gas quantization. The calculation of S(d) dependence on the assumption of size quantization with regard to contribution of several subbands and the thickness dependence of the Fermi energy was shown to be in agreement with the experimental data. In the region of d > 30 nm there was growth of S and σ with thickness, which is attributable to manifestation of classical size effect and interpreted in the framework of Fuchs-Sondheimer and Mayer theories

Dependences of thermoelectric properties on the thickness of thin films of indium doped lead telluride

Dependences of thermoelectric properties (the Seebeck coefficient S, the electric conductivity σ, the Hall coefficient RH, the carrier mobilityμ and the thermoelectric power P = S²·σ) on the thickness d (d = 10 – 255 nm) of thin films prepared by vacuum evaporation of indiumdoped PbTe crystals and subsequent condensation on (111) BaF₂ substrates were obtained. With decreasing thickness of films to d ≈ 40 nm, there is n- to p-type inversion of conduction which is related to a change in thermodynamic equilibrium conditions and partial reevaporation of lead and/or indium atoms. Extremes were found on the thickness dependences of properties at d₁ ≈ 20 nm which is indicative of hole gas quantization. In the range of thicknesses with n-type conduction there is a smooth change in thermoelectric properties with thickness which testifies to manifestation of classical size effect and is sufficiently well described in the framework of the Fuchs-Sondheimer theory

Vacuum fluctuation forces between ultra-thin films

We have investigated the role of the quantum size effects in the evaluation of the force caused by electromagnetic vacuum fluctuations between ultra-thin films, using the dielectric tensor derived from the particle in a box model. Comparison with the results obtained by adopting a continuum dielectric model shows that, for film thicknesses of 1-10 nm, the electron confinement causes changes in the force intensity with respect to the isotropic plasma model which range from 40% to few percent depending upon the film electron density and the film separation. The calculated force shows quantum size oscillations, which can be significant for film separation distances of several nanometers. The role of electron confinement in reducing the large distance Casimir force is discussed

Prediction of Anisotropic Single-Dirac-Cones in Bi1−x{}_{1-x}Sbx{}_{x} Thin Films

The electronic band structures of Bi${}_{1-x}$Sb${}_{x}$ thin films can be varied as a function of temperature, pressure, stoichiometry, film thickness and growth orientation. We here show how different anisotropic single-Dirac-cones can be constructed in a Bi${}_{1-x}$Sb${}_{x}$ thin film for different applications or research purposes. For predicting anisotropic single-Dirac-cones, we have developed an iterative-two-dimensional-two-band model to get a consistent inverse-effective-mass-tensor and band-gap, which can be used in a general two-dimensional system that has a non-parabolic dispersion relation as in a Bi${}_{1-x}$Sb${}_{x}$ thin film system