Evidence of Phonon Condensers at Nanoscale

Evidence of Phonon Condensers at Nanoscale Abhay Abhimanyu Sagade, A. Ghosh, R. A. Joshi and Ramphal Sharma Thin Film and Nanotechnology Laboratory, Department of Physics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, MS, India. Abstract. The values of thermovoltage are observed to enhance in metal chalcogenide materials after heavy ion irradiation. The physical basis behind this process is unclear. Here we treated thermal and electrical currents equally and replaced two dimensional thermal system by electrical network incorporating resistors, connected in series and capacitors, connected in parallel. The physical essence, however, and units of the terms of the equations are different. This scheme is called as ‘electro-thermal’ analogy and it explains qualitatively the hampered motion of phonons from hot end to cold end. Restricting phonons in thermoelectric materials paves the way to enhancement of Seebeck coefficient. Keywords: Thermoelectricity, Seebeck coefficient, Phonons, Metal chalcogenides. PACS: 61.80.-x, 71.55.-I, 72.10.Bg, 73.50.Lw, 72.20.Dp, 72.20.Pa, 73.63.Bd, 73.90.+f

INTRODUCTION Transfer of phonons from hot end to cold end with charge carriers during thermoelectric measurement is the major threat for reduction of Seebeck coefficient (S) in thermoelectric materials. The use of nanowires and quantum superlattices are the better solutions, since the diffuse interface scattering inside the nanostructure materials cannot only reduce the phonon mean free path but can also destroy the coherence of phonons. The possibilities and probabilities of electron-phonon decoupling have been discussed in more details by Ziman [1]. The enhancement in such metal chalcogenide structures (Bi2Te3/Sb2Te3, PbSeTe etc.) have been demonstrated successfully in the past years [1, 2, 3]. Phonons are quantized travelling elastic waves associated with the displacement of atoms from their equilibrium lattice positions. Zuckermann and Lukes [4] described the means of scattering of phonons from nanoparticles and methods to control the process. The obstacles for scattering includes other phonons, grain boundaries, impurity atoms, structural defects such as vacancies and dislocations, changes in atomic mass isotopes. In general, any features that change the bond stiffness, bond orientation, or mass of adjacent atoms from those of the host lattice are restricting phonon motion. This approach will reduce thermal conductivity by increasing scattering for a wide spectral range of phonons. Therefore we need a matrix with such a scattering centres (Fig. 1) which hamper phonons forward motion and propagate the electrons from hot end to cold end. The absorption of phonons through such a matrix has been investigated using molecular dynamics by Norris [5] on the basis of Mur’s absorbing boundary conditions. CPU 47, Transport and Optical Properties ofNanomaterials—ICTOPON - 2009, edited by M. R. Singh and R. H. Lipson © 2009 American Institute of Physics 978-0-7354-0684-l/09/$25.00

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FIGURE 1. The process of breaking a coupling between electron (arrow) and phonon (wave packet). During the motion of their coupled system through the matrix containing embedded nanoparticles, phonons get scattered from the scattering centers (red cubes) and finally at the right end we get single electron, coupled and decoupled system of e-p with same or reduced coupling factor.

The best options available in creating such a matrix are the growth of material using molecular beam epitaxy of desired material with suitable scattering centers. Unfortunately it is a tiresome and tedious job to be performed. The other option is embedding single elemental atom/ion in the matrix using ion beam implantation. In this case the embedded atom forms its own deforming potential and bonding in the matrix causing unexpected changes in transport properties. Also low energy ions generate collision cascades, which disturbs periodicity of lattice. On the other hand swift heavy ion (SHI) bombardment method is useful in creating different zones (tracks) in the matrix with equal/different properties of same material. In the present study, phenomenological model of restricting phonon forward motion through such ion tracks in metal chalcogenide materials is discussed.

EXPERIMENTAL RESULTS The irradiation experiments were carried out on cadmium sulfide (CdS) and bismuth sulfide (Bi2S3) thin films using 100 MeV gold SHI. The detailed experimental work and modifications in materials properties have been reported elsewhere [6]. 80

Pristine 11

70

5X10

60 50 40 30 20 10

a

0 320

340

360 380 400 Tempe r at ur e ( K)

420

280

440

300

320

340

360

380

Temperature

400

420

440

(K)

FIGURE 2. The variation of thermovoltage in CdS (a) and Bi 2 S 3 (b) thin films with irradiation fluence.

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It is observed that particle size, electrical resistivity and thermovoltage of these metal chalcogenide films are function of irradiation fluence. Generally irradiation causes diffusion of atoms across the grain boundaries and appends those two grains to form one bigger grain [6]. The increase in grain size plausibly decreases the electrical resistivity and increase carrier mobility. This task fulfills the requirements to enhance thermovoltage in the material. Fig. 2 shows the variation of thermovoltage as a function of irradiation fluence and temperature in CdS and Bi 2 S 3 thin films. The irradiation of 100 MeV gold ions at 10 11 ions/cm2 fluence starts to increase thermovoltage in CdS and Bi2S3 from 2 to 6 mV and 80 to 90 mV, respectively. This behavior continues up to fluence of 5 × 1012 ions/cm2 and after it there is sudden drop in thermovoltage at 1013 ions/cm2 fluence in both the films.

DISCUSSION Metal chalcogenides of bismuth (BiX) and cadmium (CdX, X = S, Se and Te) are very promising materials in solar cells, photodetectors, laser etc. applications. There thermoelectric materials have been extensively studied [7]. The main reason behind conductivity in these materials is the presence of X vacancies making them potential n-type semiconductors. The effects of SHI on their opto-electronic properties have been recently reported [6]. When SHI pass through a solid they loss their energy during their path into the matrix and create tracks of diameter ~ 10 nm. Figure 3 shows the schematic of heavy ion irradiation on solid matrix. The left part shows a passage of heavy ion and track created by it in solid (not to the scale).

FIGURE 3. Schematic of thermal spike generation in solids.

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The dark shaded area is the actual track with radius R from center O. Thermal spike generation in this nanodimensional region will reduce the viscosity of that region in comparison to the solid matrix around it. The temperature distribution in track is a Gaussian one; it has maximum at center O and decays out in the solid matrix near the track. If, for time being, the viscosity of matrix around the track is infinite, then the viscosity of this nanodimensional region is sufficiently less that it can be declared as a liquid. This nanodimensional region is explored in the right part of the figure. Because of high temperature, this region consists of single and ionized atoms, thermalized electrons, defects, etc., species. Hence there is a finite probability of heat exchange between all of these species and formation of new bonds. When cooling down occurs, due to frozen in, all the physical properties of this region get modified. The use of sufficient fluence will modify the whole solid matrix. If the fluences are increased excessively, an overlapping of tracks takes place and this phenomenon occurs for a number of times in particular nanodimensional regions [6]. Therefore, irradiated target consists of matrix/track/matrix (MTM) layered structure perpendicular to its thickness as shown in Fig. 4. These tracks may have smooth or rough interface with matrix in addition to same or different bonding between the atoms. Let us assume that these tracks may be formed at equal distance along X-axis so during thermoelectric measurement this layered structure may act as a quantum superlattice and hamper the motion of phonons from hot end to cold end. This can be explained by using a phenomenological model. •* L(~80nm) *\ x2 ...

—•

FIGURE 4. Schematic of (a) thermal system used in thermovoltage measurement and (b) equivalent electrical circuit of (a).

The thermal system is thus replaced by an electrical network incorporating resistors, connected in series and capacitors, connected in parallel (Fig. 2). A quantitative analysis at nanoscale is performed by treating both thermal and electric conduction processes equally. The physical essence, however, and units of the terms of the equations are different. This scheme is called as electro-thermal analogy. The phenomena of heat and electrical conduction obey the following equations dQ = -A(dT/dnt)dAt

and dl = -a(BE/dne)dAe

… (1)

where dQ and dl are elementary heat flow and electrical current per unit time per unit area dAt, dAe, in the direction of the perpendiculars nt and ne; J and £ are temperature and electrical potential; X and a are the thermal and electrical conductivity. Here subscripts t and e indicate thermal and electrical phenomena, respectively.

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An application of these equations to a two-dimensional problem of steady state conduction in time, in which the physical properties (A ando) are independent of temperature, leads us to the following Laplace differential equations: (d2T /dx2) + (d2T /dy2) = 0

… (2)

(5 2E/ dx2) + (5 2E/ dy2) = 0

These equations expressing temperature and electrical potentials are of identical structure. Analogous phenomena should develop in geometrically similar systems. The boundary conditions may be stated in following ways: -AVT = aAT or -VT = AT /(A/a) = AT/£t and similarly, -VE = AE/£e. The quantitative relationship between analogous physical parameters may be established by reducing their mathematical descriptions to the dimensionless form. For this purpose a certain value At0 can be taken as a scale for the temperature difference, Auo for the electrical potential and for the linear dimensions ito and te0. Then the quantities expressed in a relative scale are xt I

Xt; — = Yt;

I,

L;

At

©

£ 0/

0/

Having substituted these relationships, eq. (2) acquire the dimensionless form AL

d2&

d2& +

dX,

0

dYt j

and

Ae

520 520 — + —2 dX 2 BY e J

0

… (3)

which are identical at any choice of similar scales for the temperature and electrical potentials. In investigating transient processes for 2D problems, the differential equations of thermal and electrical conduction have the form dT drt

zz (J

dE

d2T d2T dx2 + dy22 1

d2E

… (4)

d2E

zz

dze

ReCe

Here Re is the electrical resistance per unit length; Ce is the “electrical condenser”. Comparison of these equations shows that analogy sets in only if the condition a = 1/Re Ce is observed. Therefore, variation of electrical current is proportional to the capacity and variation in voltage

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dl = C

dr ,

… (5)

variation in heat flow is proportional to the variation of “heat condenser” or “phonon condenser” of the system and the variation of temperature in time, i.e. by an analogy dT , dQ = C, dr, ' dr, '

… (6)

Considering graded thermoelectric materials with the thermal conductivity (X), the Seebeck coefficient (S), and the electrical conductivity (a) changing with position x, the heat equation at steady state is [8], d dT(x) k(x) dx dx

J

dS(x) + JT(x)—

cr(x)

… (7)

dx

where J is the electrical current density. If we assume that l(x) and power factor S(x)2a(x) are constant in a finite range of electrical conductivity values, then even though average S and a do not change, the local thermoelectric efficiency (ZT) could become larger. The corresponding optimal Seebeck profile includes three sections, S0, Sop,(x)

0