Thermoelectric properties of BiSbTe alloy nanofilms produced by DC sputtering: experiments and modeling
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Abstract
Thermoelectricity refers to the conversion of thermal energy into electrical energy and vice versa, which relies on three main effects: Seebeck, Peltier and Thomson, all of which are manifestations of heat and electricity flow. In this work, we investigate the deposition of nanometric films and the effect of a thermal treatment on their thermoelectric properties. The films are based on BiSbTe ternary alloys, obtained by deposition on a substrate using the DC sputtering technique. We produced sputtering targets with repurposed materials from commercial thermoelectric modules. In this way, we explore an environmentally responsible destination for discarded devices, with in situ preparation and manufacture of film-based thermoelectric modules. Film samples show an improvement trend in thermoelectric efficiency as the annealing temperature is increased in the range 423–623 K. The experimental data regarding thermal conductivity, electrical resistivity (or electrical conductivity), and the Seebeck coefficient were analyzed with the theory of q-deformed algebra. Applying a q-deformation to our system, we can model the effect of the annealing temperature on the thermal and electrical conductivities, as well as the Seebeck coefficient, and argue that the q-factor must be related to structural properties of the films. We believe that our work could pave the way for future developments in the modeling of experimental measurements via the formalism of q-deformation algebra.
Notes
Acknowledgments
We would like to thank CAPES, CNPq (Grants 309961/2017-3, 436859/2018-1, 312104/2018-9) and PNPD/PROCAD-CAPES, for financial support.
References
- 1.de Groot SR (1952) Thermodynamics of irreversible processes. N. Holland Publishing Co., AmsterdamGoogle Scholar
- 2.Rowe DM, Bhandari CM (1983) Modem thermoelectrics, Holt TechnologyGoogle Scholar
- 3.Cooke-Yarborough EH, Yeats FW (1975) Efficient thermo-mechanical generation of electricity from the heat of radioisotopes. In: Proceedings of Xth IECEC, 1033Google Scholar
- 4.Huang B, Kaviany M (2010) Filler-reduced phonon conductivity of thermoelectric skutterudites: ab initio calculations and molecular dynamics simulations. Acta Mater 58:4516–4526CrossRefGoogle Scholar
- 5.Kim MY, Oh TS (2009) Electrodeposition and thermoelectric characteristics of \({\text{ Bi }}_2{\text{ Te }}_3\) and \({\text{ Sb }}_2{\text{ Te }}_3\) films for thermopile sensor applications. J Electron Mater 38:1176–1181CrossRefGoogle Scholar
- 6.Harman TC et al (2002) Quantum dot superlattice thermoelectric materials and devices. Science 297:2229–2232CrossRefGoogle Scholar
- 7.Venkatasubramanian R et al (2001) Thin-film thermoelectric devices with high room-temperature figures of merit. Nature 413:597–602CrossRefGoogle Scholar
- 8.Harman TC et al (2002) Nanostructured thermoelectric materials. J Eletron Mater 34:L19–L22CrossRefGoogle Scholar
- 9.Shakouri A (2006) Nanoscale thermal transport and microrefrigerators on a chip. Proc IEEE 94:1613–1638CrossRefGoogle Scholar
- 10.Gross AJ (2010) Low power, integrated, thermoelectric micro-coolers for microsystems applications. University of Michigan, Ph.D. dissertationGoogle Scholar
- 11.Vining CB et al (1991) A model for the high-temperature transport properties of heavily doped n-type silicon–germanium alloys. J Appl Phys 69:331–340CrossRefGoogle Scholar
- 12.Fano V (1994) CRC handbook of thermoelectrics. In: Rowe DM (ed) CRC Press, Boca Raton, p 257Google Scholar
- 13.Cope RG, Penn AW (1968) The powder metallurgy of n-type \({\text{ Bi }}_2{\text{Te}}_{2.55}{\text{Se}}_{0.45}\) thermoelectric material. J. Mater. Sci. 3:103–109. https://doi.org/10.1007/BF00585476
- 14.Felix IM, Pereira LFC (2018) Thermal conductivity of graphene-hBN superlattice ribbons. Sci Rep 8:2737CrossRefGoogle Scholar
- 15.Takashiri M et al (2008) Structural and thermoelectric properties of fine-grained \({\text{Bi}}_{0.4}{\text{Te}}_{3.0}{\text{Sb}}_{1.6}\) thin films with orientation deposited by flash evaporation method. Thin Solid Films 516:6336–6343CrossRefGoogle Scholar
- 16.German RM (1998) Powder metallurgy of iron and steel. Wiley, New YorkGoogle Scholar
- 17.Bouville F, Studart AR (2017) Geologically-inspired strong bulk ceramics made with water at room temperature. Nat Commun 8:14655CrossRefGoogle Scholar
- 18.Dughaish ZH (2002) Lead telluride as a thermoelectric material for thermoelectric power generation. Physica B Cond Mater 322:205–223CrossRefGoogle Scholar
- 19.Goldsmid HJ (2014) Bismuth telluride and its alloys as materials for thermoelectric generation. Materials 7:2577–2592CrossRefGoogle Scholar
- 20.Kim H et al (2012) Effects of \({\text{ Bi }}_2{\text{ Se }}_3\) nanoparticle inclusions on the microstructure and thermoelectric properties of \({\text{ Bi }}_2{\text{ Te }}_3\)-based nanocomposites. J Electron Mater 41:3411–3416CrossRefGoogle Scholar
- 21.Muller E et al (1996) Determination of the thermal band gap from the change of the Seebeck coefficient at the pn-transition in \({\text{ Bi }}_{0.5}{\text{ Sb }}_{1.5}{\text{ Te }}_3\). In: Proceedings of the IEEE, Pasadena CA USA, pp 26–29Google Scholar
- 22.Goldsmid HJ et al (1988) High-Tc superconductors as passive thermo-elements. J Phys D 21:344–348CrossRefGoogle Scholar
- 23.Hicks LD, Dresselhaus MS (1993) Effect of quantum-well structures on the thermoelectric figure of merit. Phys Rev B 47:12727–12731CrossRefGoogle Scholar
- 24.Gentile G (1940) Osservazioni sopra le statistiche intermedie. Nuovo Cimento 17:493–497CrossRefGoogle Scholar
- 25.Green HS (1953) A generalized method of field quantization. Phys Rev 90:270–273CrossRefGoogle Scholar
- 26.Polychronakos AP (1996) Probabilities and path-integral realization of exclusion statistics. Phys Lett B 365:202–206CrossRefGoogle Scholar
- 27.Biedenharn LC (1989) The quantum group \(SU_{q}(2)\) and a q-analogue of the boson operators. J Phys A Math Gen 22:L873–L878CrossRefGoogle Scholar
- 28.Macfarlane A (1989) On q-analogues of the quantum harmonic oscillator and the quantum group \(SU(2)_q\). J Phys A Math Gen 22:4581CrossRefGoogle Scholar
- 29.Pharthasarathy R, Viswanathan KS (1991) A q-analogue of the supersymmetric oscillator and its q-superalgebra. J Phys A Math Gen 24:613–617CrossRefGoogle Scholar
- 30.Chaichian M, Gonzales Felipe R, Montonen C (1993) Statistics of q-oscillators, quons and relations to fractional statistics. J Phys A Math Gen 26:4017–4033CrossRefGoogle Scholar
- 31.Fuchs J (1992) Affine Lie algebras and quantum groups. Cambridge University Press, CambridgeGoogle Scholar
- 32.Gavrilik AM, Rebesh AP (2012) Deformed gas of \(p,q\)-bosons: virial expansion and virial coefficients. Mod Phys Lett B 26:1150030CrossRefGoogle Scholar
- 33.Lavagno A, Swamy PN (2000) Thermostatistics of a q-deformed boson gas. Phys Rev E 61:1218–1226CrossRefGoogle Scholar
- 34.Lavagno A, Swamy PN (2002) Generalized thermodynamics of q-deformed bosons and fermions. Phys Rev E 65:036101CrossRefGoogle Scholar
- 35.Hatami N, Setare MR (2016) The q-deformed Dirac oscillator in \(2+1\) dimensions. Phys Lett A 380:3469–3472CrossRefGoogle Scholar
- 36.Algin A, Senay M (2016) General thermostatistical properties of a q-deformed fermion gas in two dimensions. J Phys Conf Ser 766:012008CrossRefGoogle Scholar
- 37.Algin A, Senay M (2016) Fermionic q-deformation and its connection to thermal effective mass of a quasiparticle. Physica A 447:232–246CrossRefGoogle Scholar
- 38.Algin A, Arikan AS (2017) Effective approach for taking into account interactions of quasiparticles from the low-temperature behavior of a deformed fermion-gas model. J Stat Mech Theory Exp P043105Google Scholar
- 39.Chung WS, Algin A (2017) Duality of boson and fermion: new intermediate-statistics. Phys Lett A 381:3266–3271CrossRefGoogle Scholar
- 40.Algin A, Olkun A (2017) Bose–Einstein condensation in low dimensional systems with deformed bosons. Ann Phys 383:239–256CrossRefGoogle Scholar
- 41.Hoyuelos M (2018) From creation and annihilation operators to statistics. Physica A 490:944–952CrossRefGoogle Scholar
- 42.Gavrilik AM et al (2018) Condensate of \(\mu \)-Bose gas as a model of dark matter. Physica A 506:835–843CrossRefGoogle Scholar
- 43.Tsallis C (1988) Possible generalization of Boltzmann–Gibbs statistics. J Stat Phys 52:479–487CrossRefGoogle Scholar
- 44.Plastino AR et al (2014) Stationary and uniformly accelerated states in nonlinear quantum mechanics. Phys Rev A 90:062134CrossRefGoogle Scholar
- 45.Brito S, da Silva LR, Tsallis C (2016) Role of dimensionality in complex networks. Nat Sci Rep 6:27992CrossRefGoogle Scholar
- 46.Ourabah K, Tribeche M (2014) Planck radiation law and Einstein coefficients reexamined in Kaniadakis \(\kappa \) statistics. Phys Rev E 89:062130CrossRefGoogle Scholar
- 47.Mohammadzadeh H, Adli F, Nouri S (2016) Pertubative thermodynamic geometry of nonextensive ideal classical, Bose, and Fermi gases. Phys Rev E 94:062118CrossRefGoogle Scholar
- 48.Rovenchak A (2018) Ideal Bose-gas in nonadditive statistics. Low Temp Phys 44:1025–1031CrossRefGoogle Scholar
- 49.Adli F et al (2019) Condensation of nonextensive ideal Bose gas and critical exponents. Physica A 521:773–780CrossRefGoogle Scholar
- 50.Chung WS, Gavrilik AM, Nazarenko AV (2019) Photon gas at the Planck scale within the doubly special relativity. Physica A 533:121928CrossRefGoogle Scholar
- 51.Ernst T The History of \(q\)-calculus and a new method. (Dep. Math., Uppsala Univ. 1999–2000)Google Scholar
- 52.Floratos EG (1991) The many-body problem for q-oscillators. J Phys Math 24:4739CrossRefGoogle Scholar
- 53.Patthria RK (1972) Statistical mechanics. Pergamon Press, OxfordGoogle Scholar
- 54.Reif F (1965) Fundamentals of statistical and thermal physics, TokyoGoogle Scholar
- 55.Huang K (1987) Statistical mechanics. Wiley, New YorkGoogle Scholar
- 56.Kittel C (1996) Introduction to solid state physics. Wiley, New YorkGoogle Scholar
- 57.Ziman JM (1960) Electron and phonons: the theory of transport phenomena in solids. Oxford University Press, OxfordGoogle Scholar
- 58.Bourgault D et al (2008) Thermoelectric properties of n-type \({\text{ Bi }}_2{\text{ Te }}_{2.7}{\text{ Se }}_{0.3}\) and p-type \({\text{ Bi }}_{0.5}{\text{ Sb }}_{1.5}{\text{ Te }}_{3}\) thin films deposited by direct current magnetron sputtering. Thin Solid Films 516: 8579–8583Google Scholar
- 59.Huang H et al (2009) Influence of annealing on thermoelectric properties of bismuth telluride films grown via radio frequency magnetron sputtering. Thin Solid Films 517:3731–3734CrossRefGoogle Scholar
- 60.Marinho AA, Brito FA, Chesman C (2012) Thermal properties of a solid through q-deformed algebra. Physica A 391:3424–3434CrossRefGoogle Scholar
- 61.Tristant D, Brito FA (2014) Some electronic properties of metals through q-deformed algebras. Physica A 407:276–286CrossRefGoogle Scholar
- 62.Marinho AA, Brito FA, Chesman C (2014) Application of Fibonacci oscillators in the Debye model. J Phys Conf Ser 568:012009CrossRefGoogle Scholar
- 63.Marinho AA, Brito FA, Chesman C (2016) Thermal and electrical properties of a solid through Fibonacci oscillators. Physica A 443:324–332CrossRefGoogle Scholar