Quantum Size Effects and Thermoelectric Transport in IV-VI – Based 2D-Structures

The present status of our studies on the observation of thickness oscillations of the thermoelectric and galvanomagnetic properties in IV-VI quantum wells (QWs) is reviewed. These oscillations are attributed to the quantum size effects (QSEs) due to electron or hole confinement in the QWs. The experimental values of the oscillation period are in good agreement with the results of the theoretical calculations using the effective mass approximation and a model of a rectangular potential well with infinitely high walls. The influence of various factors (carrier concentration, type of substrate, structural parameters, growth mechanism, etc.) on the observed oscillatory phenomena is analyzed. The effect of the size quantization on the thermoelectric power factor of thin film structures is considered. Introduction Electron confinement in low-dimensional structures leads to a radical change in physical properties of these systems as compared with bulk crystals and introduces new ways for controlling the properties of solids [1]. In QWs, charge carrier motion is confined in one direction, which results in the quantization of the electron quasi-momentum and energy spectrum in this direction. By now, the energy level structure of thin films and QWs has been determined by a number of experiments, mainly dealing with optical and tunneling techniques. Also sensitive to QSEs are the various transport properties, in particular thermoelectric (TE) properties. For thin film applications in thermoelectricity, it is necessary to take into account the QSEs, which can drastically change TE properties under thickness change. The interest in studying TE properties of 2D-structures has grown significantly since the possibility of a substantial increase in the TE figure of merit ZT in QWs and superlattices (SLs) under decreasing the QW width was predicted theoretically [2]. One of the possible manifestations of the QSEs in 2Dstructures is an oscillatory behavior of the thickness dependences of the transport and thermodynamic properties due to the quantization of the energy spectrum [3]. Quantum oscillations in the transport properties of thin films with changing film thickness were observed for the first time in studies on semimetallic Bi films [4]. Metallic films are not very convenient objects for studying QSEs through transport property measurements because their Fermi wavelength λF and the oscillation period ∆d are comparable to interatomic distances, which requires growing very thin films with a high degree of structural perfection. Semiconductors, which have significantly lower charge carrier concentrations and, consequently, larger λF, represent more convenient systems for studying QSEs by measuring their transport properties [5]. By choosing an optimal set of parameters, one can create conditions for the experimental studies of the oscillations even in rather thick films. However, up to now, the number of such investigations of semiconducting QWs has been very limited, which to all appearances is connected with the complexity of such studies. The authors of [6,7] observed oscillations in the ddependences of the galvanomagnetic properties of InSb [6] and CdAs2 [7] semiconducting thin films, and attributed their existence to quantization of electron spectrum. IV-VI-based materials are well known as promising thermoelectrics [8]. A sufficiently small effective mass in the direction perpendicular to the direction of growth, with transport along the film surface, and a high charge carrier mobility make IV-VI compounds convenient materials for QSEs studies using transport properties. However, the available works were devoted mainly to the QSEs in spacecharge accumulation or inversion [9,10] layers at the PbTe surface. Recently, interest in these compounds has grown due to the experimental observation of a substantial increase in ZT in IV-VI-based QWs and SLs [2,11,12] as compared with bulk crystals, which had been predicted earlier theoretically. All this stimulates further studies of the thermoelectric properties of IV-VI –based 2D-structures. To realize conditions necessary for the observation of quantum oscillations, it is necessary to overcome a number of problems connected with the preparation of high-quality QWs. In the experimental study of the quantum oscillations in thin Bi films deposited on mica substrates [4], air played the role of one of the barriers, surrounding Bi QW, because at relatively low temperatures the transport properties of Bi layer exposed to air practically do not change. Unfortunately, oxygen in lead chalcogenides acts as an acceptor, causing the appearance of p-type charge carriers, whose presence can radically change the transport properties of crystals and thin films [13]. With decreasing film thickness d, a surface layer with p-type behavior becomes increasingly important in determining the thin film transport properties. However, until very recently the available results on the oxidation of IV-VI compound semiconductors were obtained for relatively thick (d = 0.1-10 μm) films, whereas there are practically no results yet available on nanosized film thicknesses. Our studies [14-16] of the effect of near surface oxidation on the transport properties of freshly prepared n-type IV-VI films on KCl and mica substrates showed that the appearance of an oxidized layer on the nPbTe, n-PbSe and n-PbS freshly grown thin films surface in air at room temperature causes a strong d-dependences of the TE properties, including inversion of the dominant carrier sign from n to p at a certain critical thickness, depending on the chalcogenide species and carrier concentration. A twocarrier model for very thin films and a two-layer model for more thick films provide an explanation of the observed experimental dependences of the TE properties on the film thickness [16]. It follows from the results obtained in those works that establishing the true thickness dependences of the TE properties of IV-VI QWs with a view toward revealing the physical effects occurring at a nanosize level, or controlling the properties of thin films, or using the films in TE and other devices is impossible without taking special measures for protecting the films from oxidation. In the present paper, a review of the works of our research group on studying dependences of thermoelectric properties of IV-VI–based quantum wells on QW width with a view toward observing thickness oscillations is given. Experimental details IV-VI (PbTe, PbSe, PbS and SnTe) monocrystalline thin films were prepared by the thermal evaporation of IV-VI crystals from tungsten "boats" in an oil-free vacuum (10 – 10) Pa and the subsequent deposition onto (001) KCl or (111) mica surface at (520±10) К. For thin film preparation, we used only substrates of high quality, without steps. The condensation rate was 0.1 – 0.3 nm/s. The film thickness and the condensation rate were controlled using a calibrated quartz resonator. The epitaxial growth and structure of the samples were studied by electron microscopy and electron diffractometry. Transport measurements were carried out on freshly grown epitaxial IV-VI thin films covered with a ~ 30 nm EuS or Al2O3 layers prepared by electron-beam evaporation. Being wide-gap semiconductors, these cover layers, on the one hand, protected the IV-VI thin layers from oxidation and, on the other hand, acted as barrier layers making a negligible contribution to the electrical conductivity. The Hall coefficient RH and the conductivity σ were measured using a conventional dc method and a magnetic field of 0.8 T. Six ohmic contacts were prepared by soldering indium to the film surface. The error in the RH and σ measurements did not exceed 5 %. The Hall mobility was calculated as μH = RH ⋅ σ, and the electron concentration n was determined as n = A/(RH⋅e), assuming the Hall factor A to be 1. The Seebeck coefficient S was measured relative to copper with an accuracy of ≈ 3 %. Experimental results It is known that lead chalcogenides grow by the VolmerWeber mechanism on dielectric substrates, such as KCl, NaCl, etc., however the character of film overgrowth depends principally on the technological parameters of the growth. The results of our electron microscopy and electron diffraction studies showed that PbS, PbSe, PbTe, and SnTe thin films grow epitaxially on (001) KCl according to the vapor-crystal mechanism in the (001) orientation. The film growth starts with the formation of islands, which increase in size as d increases. At d ~ 4 – 10 nm, the films have a channel structure. Thin PbTe films grow on mica also epitaxially in an island like fashion predominantly in the (111) orientation [17]. SnTe and PbTe grow on one another in a layer-by-layer fashion. At the critical thickness of the growing layer dC~ 2 nm, misfit dislocations are introduced in the interface [18]. In Fig. 1, the thickness dependences of n, S, and σ for (001)KCl/PbS/EuS and (001)KCl/PbSe/EuS QWs are presented [19-21]. It should be noted that although σ, n, and S were measured independently, all the dependences exhibited oscillatory behavior with similar oscillation periods, which allows us to draw a single curve through experimental points for both PbS and PbSe QWs. The positions of the first minimum in the S(d) curve and the first maxima in n(d) and σ(d) curves correspond to d = 17±3 nm. The distances ∆d between the two first extrema in the σ(d), S(d) and n(d) curves are (30±5) nm.