Thermoelectric and transport properties of -Ag 2 Se compoundsMarhoun Ferhat and Jiro Nagao

Citation: Journal of Applied Physics 88, 813 (2000); doi: 10.1063/1.373741 View online: http://dx.doi.org/10.1063/1.373741 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/88/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Thermoelectric properties of AgPb m SbTe m + 2 ( 12 m 26 ) at elevated temperature J. Appl. Phys. 105, 113703 (2009); 10.1063/1.3138803 Thermoelectric properties of Pt-doped - FeSi 2 J. Appl. Phys. 88, 5810 (2000); 10.1063/1.1322597 Room-temperature anisotropic, thermoelectric, and electrical properties of n -type ( Bi 2 Te 3 ) 90 ( Sb 2 Te 3 ) 5 ( Sb 2 Se 3 ) 5 and compensated p -type ( Sb 2 Te 3 ) 72 ( Bi 2 Te 3 ) 25 ( Sb 2 Se 3 ) 3 semiconductor alloys J. Appl. Phys. 85, 7807 (1999); 10.1063/1.370589 Effect of nonstoichiometry on the thermoelectric properties of GeBi 4 Te 7 J. Appl. Phys. 85, 3207 (1999); 10.1063/1.369662 n -type electrical conduction in transparent thin films of delafossite-type AgInO 2 Appl. Phys. Lett. 72, 1036 (1998); 10.1063/1.120957

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JOURNAL OF APPLIED PHYSICS VOLUME 88, NUMBER 2 15 JULY 2000

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Thermoelectric and transport properties of b-Ag2Se compoundsMarhoun Ferhata) and Jiro NagaoMaterials Division, Hokkaido National Industrial Research Institute, AIST, MITI, Sapporo 062-8517, Japan

~Received 13 September 1999; accepted for publication 7 April 2000!

The Hall coefficient, electrical resistivity, and Seebeck coefficient ofn-type specimens ofb-Ag2Se,the low temperature polymorph of silver selenide, were measured over the temperature range from70 to 300 K. The results showed maxima in both Hall coefficient and the electrical resistivity justbelow the onset of the intrinsic conduction range. This anomaly was qualitatively explained by thedeviation of the Coulomb scattering from the usual assumption of independence due to thedegenerate nature of the samples. The estimated energy gap for different samples of about 160 meVseems to confirm the existence of the second low temperature phaseb2 . This second phase is aprobable reason for the relatively high thermoelectric figure of merit observed. ©2000 AmericanInstitute of Physics.@S0021-8979~00!00214-0#

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I. INTRODUCTION

Ag2Se is the only stable composition that occurs inphase diagram of the Ag–Se system.1 As for all other silverchalcogenides, this compound undergoes a first order ptransition around 407 K. The low temperature phab-Ag2Se, is a narrow band gap semiconductor2 with an en-ergy gap ofEg570 meV at 0 K. The most accepted cryststructure of b-Ag2Se is orthorhombic with theP212121

space group and lattice parametersa50.4333 nm,b50.7062nm andc50.7764 nm. Four molecules of Ag2Se are includedin the unit cell. The high temperature phase,a-Ag2Se, isobtained by heating above 407 K. The crystal structurecomes cubic, the conduction changes to metallic and theterial presents superionic characteristics.3

b-Ag2Se is a promising candidate for enhanced dimsionless thermoelectric figure of merit defined byZT5S2sT/k, whereS is the Seebeck coefficient,s the electri-cal conductivity, andk is the total thermal conductivity. Thisis becauseb-Ag2Se exhibits unusual low lattice thermal coductivity kL('5 mW/cm K!4 coupled with high electricaconductivitys~'2000 S/cm! and relatively high Seebeck coefficientS~'2150mV/K ! at 300 K.5–8 The recent discoveryof large positive magnetoresistance in both bulk9 and thinfilm10 forms suggests thatb-Ag2Se deviates from the conventional view established in the past.11 Thus, it is worth-while to reinvestigate this compound for thermoelectric aplications in the low temperature range. The optimizationits thermoelectric properties is intended to be different frthat adopted for usual thermoelectric materials.

This paper is devoted to the temperature dependencthe thermoelectric and the transport parameters ofb-Ag2Sein temperatures ranging from 70 K and 300 K. The anomlous maxima observed in the Hall coefficient and telectrical resistivity are discussed and the room temperathermoelectric figures of merit are calculated from theperimental data.

a!Author to whom correspondence should be addressed; electronicferhat@hniri.go.jp

8130021-8979/2000/88(2)/813/4/$17.00

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II. EXPERIMENTAL DETAILS

Silver selenide specimens were prepared by a directaction of the source elements~6N purity! in evacuated('1024 Torr! quartz tubes. The mixture was maintained atemperature of about 1273 K for 10 h. The melt was thcooled slowly to room temperature. Samples in the formdisks, typically about 8 mm in diameter and 1.5–1 mm thicwere cut from the polycrystalline ingot and then polishedvarious measurements. X-ray diffraction analysis confirmthe formation ofb-Ag2Se. Analysis of the intensities of thdiffraction lines does not suggest any preferential orientator texture.

The electrical resistivity and the Hall coefficient wemeasured by the standard van der Pauw technique. Therent was reversed for each measurement to prohibit anytribution from thermoelectric effects. The electrical contawere made by attaching thin Cu wires to the samples usAg paste. Samples were kept below 360 K during all tmanipulation steps, because this temperature is close totemperature of phase transition in Ag2Se. The ohmic natureof the contacts was confirmed by the linearI–V characteris-tics in the full temperature range studied. The error inmeasurements of the electrical resistivities and the Hallefficients does not exceed62%. The Seebeck coefficientwere measured by the conventional differential steady stechnique with an error of about65%. The thermal conductivity was measured at room temperature by laser flash tenique, where the overall error is in the order of610%.

III. EXPERIMENTAL RESULTS

The selected three samples ofb-Ag2Se are labeled AS1AS2 and AS3, respectively, in the order of growing residucarrier concentrationn. This concentration is calculated fromthe low temperature value of the Hall coefficientRH by usingthe usual formulan51/eRH , wheree is the electron chargeThe curves in Fig. 1 are the temperature variations ofil:

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814 J. Appl. Phys., Vol. 88, No. 2, 15 July 2000 M. Ferhat and J. Nagao

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Hall coefficientsRH for the three samples. They show twtypes of variations: one exponential at a high temperatthe other almost flat at a low temperature. The Hall effmaximum separates these two domains. The temperatuthe occurrence of this maximum increases with the residcarrier concentration. The temperature of the maxima ofRH

were found to beTmax15140 K, Tmax25180 K and Tmax3

5220 K, respectively, for sample AS1, AS2 and AS3.The temperature variations of the electrical resistivit

for the three samples are presented in Fig. 2. The cushow also two regions separated by maxima at apprmately the same temperatures of those observed for thecoefficient. The low temperature electrical resistivitysample AS2 (r53.2231024 V cm) is lower than that ofsample AS3 (r59.2331024 V cm) although sample AS3has a higher residual carrier concentration. For sample Athe maximum in the electrical resistivity is broader wipractically constant resistivity in the low temperature ranand an exponential increase at higher temperature. Attemperature, both the Hall coefficient and the electricalsistivity exhibit a plateau. The samples are highly degeneand all the impurities are ionized owing to a small effectimass7 and high dielectric constant. At higher temperaturthe onset of the intrinsic conduction is observed and

FIG. 1. The semilogarithmic plot of the Hall coefficientRH vs 103/T, show-ing the anomalous maximums and the activation type behavior for the tspecimens AS1, AS2 and AS3 ofb-Ag2Se.

FIG. 2. The semilogarithmic plot of the electrical resistivityr51/s vs103/T, showing the anomalous maxima just before the onset of the intriconduction range for the three specimens AS1, AS2 and AS3 ofb-Ag2Se.

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slope of these curves gives an energy gap value of aboutmeV.

The Hall mobility (mH) was calculated from the Halcoefficient RH and the electrical resistivity bymH5RH /r.As seen from Fig. 3 the Hall mobility of sample AS2essentially constant with a high value of 104 cm2/V s. Forsamples AS1 and AS3, the mobilities increase with tempeture, reach a broad maximum and finally decrease. Thishavior is reasonable for samples with a lattice and impuscattering. The maximum values of the Hall mobilities aabout 33103 cm2/V s and 53103 cm2/V s, respectively, forAS1 and AS3.

The temperature dependence of the Seebeck coefficis shown in Fig. 4. The Seebeck coefficients increase wtemperature and reach a saturation value or decrease deing on the sample. The linear increase of the Seebeck cficient with the temperature is consistent with the high dgeneracy of the samples. All samples are ofn type in thetemperature range studied. The room temperature valuethe Seebeck coefficients areS152154 mV/K, S252133mV/K and S352113mV/K, respectively, for AS1, AS2 andAS3. These values are relatively higher if compared to pviously reported results for the same carriers concentrati

IV. DISCUSSION

b-Ag2Se has cationic Frenkel type disorder with fulionized defects.3 The formation of these defects can be d

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FIG. 3. Temperature dependence of the observed Hall mobilitymH

5RH /r for the three specimens AS1, AS2 and AS3 ofb-Ag2Se.

FIG. 4. The temperature dependence of the thermopowerS for the threespecimens AS1, AS2 and AS3 ofb-Ag2Se.

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815J. Appl. Phys., Vol. 88, No. 2, 15 July 2000 M. Ferhat and J. Nagao

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scribed by the quasichemical reaction: AgAgx 1Vi

x5Agi°

1VAgx , where AgAg is the silver atom in normal site,VAg

represents the vacancy of silver atoms.Vi is the vacancy inan interstitial site and Agi indicates the silver atom in interstitial position. The superscripts ° andx indicate, respec-tively, an effective charge of11 and 0. The concentrationNd

of these defects in the presentb-Ag2Se samples is equal tthe residual carrier concentration previously calculated.

The absence of a clear correlation between the defconcentration and the thermoelectrical effects is dueanomalous maxima observed in the temperature variationthe Hall coefficient and the electrical resistivity as will bdiscussed below. The behavior observed in the temperadependence of the three samples ofb-Ag2Se is consistenwith a degenerate narrow band gap semiconductor. Howethe Hall coefficient and the electrical resistivity curves ehibit anomalous maxima just below the onset of the intrinrange, which vary in a systematic way with the impurconcentration. Although maxima in the resistivities habeen previously observed2,12,13 no explanations were proposed. Since both the Hall coefficient and the electricalsistivity are function of the relaxation timetc , the anoma-lous behavior can be connected to the scattering mechain b-Ag2Se. In the present case, the main scattering menism at low temperature is by ionized impurity. The usethe Born approximation for the calculation of the relaxatitime tc is valid only if the inequalityld@1 is fulfilled. Herel is the mean de Broglie wavelength of the electron and52(3/4pNd)1/3 is the radius of the polyhedra surroundineach impurity. For the present case, and as pointed ouKurusawa,14 the electrons are scattered by local fluctuatioof the impurity atoms rather than by individual ones. TCoulomb potential screened by charge carrier inThomas–Fermi approximation can be expressed byV(r )5(2e2/er )exp(2r/RTF), wheree is the dielectric constantThe Thomas–Fermi screening parameter (RTF)

21 is givenby15

~1/RTF!254pe2

« E0

`

D~E!S 2] f

]EDdE, ~1!

TABLE I. Calculated values of the potential rangeRTF0 and the wavelengthof the electrons (kF)21 at 0 K.

RTF03ANv ~cm! (kF)21 ~cm!

AS1 3.7331027 3.0531027

AS2 3.6031027 2.8431027

AS3 3.4631027 2.6131027

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and depends on temperatures as (RTF)225(RTF0)

22

3(T/TF)1/2F1/28 (h), whereD~E! is the density of states othe conduction band withNv valleys,f~E! is the Fermi func-tion, F1/28 (h) is the derivative of the Fermi–Dirac integral,hthe reduced chemical potential andRTF0 is the potentialrange at 0 K, which is given by

~RTF0!215A4NvkF

a* p, ~2!

wherea* is the effective Bohr radius andkF the wavelengthof the electron at the Fermi level:

~kF!215~3p2Nd!21/3. ~3!

The appearance of the maxima in both the Hall coefficiand the electrical resistivity can be understood as follows.0 K the wavelength of the electrons (kF)21 is greater thanthe potential rangeRTF0. As the temperature increases, tpotential rangeRTF becomes larger. Once the potential ranbecomes nearly equal to the average wavelength of the etrons, a scattering occurs in resonant fashion leading toappearance of the maxima observed. The calculated vaof RTF03ANv and (kF)21 for the three samples are listedTable I. From the previous works7,16,17 on this compound amodel with a single valley (Nv51) in b-Ag2Se does nothold. Using the value ofNv.1, gives smaller values ofRTF0

than those reported in Table I, which is reasonable withabove assumption.

In order to show the potentiality ofb-Ag2Se as thermo-electric material for applications in the low temperaturange, we calculated the power factor defined byPf5S2s.As seen from Fig. 5 the power factors of the three sampincrease with the temperature and value as high asmW/K2 is obtained for sample AS2 at 300 K givingZT

FIG. 5. The plot of the calculated power factorPf5S2s vs 103/T for thethree specimens AS1, AS2 and AS3 ofb-Ag2Se.

TABLE II. Transport and thermoelectric properties of the three samples AS1, AS2 and AS3 ofb-Ag2Se atroom temperature.

n300 K5Nd s mH S k S2s(cm21) (V cm!21 (cm2/V s) (mV/K) ~mW/cm K! (mW/K2 cm! ZTmax

AS1 1.5031018 770 3191 2155 12.5 18.5 0.44AS2 1.0731018 1988 11 610 2133 11.0 35.2 0.96AS3 1.4331018 826 3611 2113 9.6 10.6 0.32

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50.96 ~see Table II!. This value approaches that of state-othe-art material for room temperature applications. Simet al.7 stated that values higher than unity are possible ifenergy gap ofb-Ag2Se is increased. This conclusion is cosistent with the present finding for sample AS2 sincevalue of the energy gap (Eg5160 meV) is about twiceas high as previously reported.4,8 The existence of this second low temperature phase has been claimed by mauthors2,12 and seems to be the case from our results.

V. CONCLUSION

In this paper, the Hall coefficient, the electrical resistity and the Seebeck coefficient were measured as functiotemperature from 70 K to 300 K. The results revealed tthe compounds are degenerate and show anomalous main the Hall effect and the electrical resistivity. The observmaxima were attributed to the screening effect and leadthe conclusion that silver selenide is probably a multivalsemiconductor. The energy gap of 160 meV obtained frthe slope of the electrical resistivity suggest the presencthe second low temperature phaseb2 . The relatively highthermoelectric figure of merit is believed to be due to tsecond low temperature phase.

ACKNOWLEDGMENTS

The authors would like to thank Dr. H. TakeuchiHNIRI for useful discussion and M. Sasamori and S. Na

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hara for experimental assistance. The authors also thankfessor T. Koyanagi and Y. Nagamoto of Yamaguchi Univsity for supplying experimental facilities. One of the autho~M.F.! is grateful to Science and Technology Agency~STA!of Japan for awarding the research fellowship.

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