PHYSICAL REVIEW B VOLUME 51, NUMBER 15 15 APRIL 1995-I

Low-temperature transport propertIes ofp-type CoSb3

D. T. MorelliPhysics Department, Genera/ Motors Research and DeUelopment Center, 8'arren, Michigan 48090

T. Caillat, J.-P. Fleurial, A. Borshchevsky, and J. VandersandeJet Propulsion Laboratory, California Institute of Technology, Pasadena, California 90210

B.Chen and C. UherDepartment of Physics, University ofMichigan, Ann Arbor, Michigan 48109

(Received 27 October 1994)

Single crystals of the skutterudite CoSb3 exhibit large hole mobilities (up to 3000 cm V ' s ' at roomtemperature), intrinsic lattice thermal conductivity down to 10 K, and pronounced drag effects in thethermoelectric power. The dependence of the mobility and diffusion thermopower on hole density is

consistent with recent band-structure calculations, which indicate that CoSb3 possesses a highly nonpar-abolic valence-band structure.

I. INTRODUCnoN

Skutterudite compounds have recently been identifiedas strong candidates for advanced thermoelectric materi-als. ' These compounds derive their name from the natu-ral cubic mineral CoAs3, the structure of which was in-vestigated by Oftedal in 1928. The skutterudite familyconsists of compounds of the form AB3, where A is Co,Ir, or Rh, and B is As, P, or Sb. In this structure, shownin Fig. 1, the pnictide atoms constitute four-memberedrings located at the centers of cubes formed by the metalatoms. ' Very little is known about the physical proper-ties of these materials. In a series of papers in the late1950's and early 1960's, Dudkin and co-workers in-vestigated the transport properties of CoS13 above roomtemperature. From the activated nature of the resistivitythey concluded that this material was a semiconductorwith a band gap of approximately 0.5 eV. Hulliger' alsoconcluded that skutterudites were semiconductors basedon his observations of diamagnetism and large Seebeckcoefficients. It should be mentioned that all of the aboveexperiments were performed on pressed powders. Acker-

W wwxY5

'IP %I

~ Co Q Sb

FIG. 1. The skutterudite structure.

mann and Wold" prepared single crystals of Co skutteru-dites and found that while all three were diamagnetic,only CoP3 exhibited an optical band gap; their samples ofCoSb3 and CoAs3 displayed a metallic electrical resistivi-ty below room temperature. Finally, Kliche and co-workers, ' ' based on far-infrared measurements, con-cluded that CoP3, CoAs3, CoSb3, and RhSb3 were seIni-conductors; on the other hand, they observed metallicconduction in RhSb3 and a zero crossing in the Hallcoe%cient of CoAs3, behavior which they suggested wasextrinsic in origin.

The brief summary of the physical properties of skut-terudites given above serves to show that our knowledgeof these materials is at best sketchy and controversial innature, in particular with regard to the question of sem-iconductivity in these compounds. This fact, togetherwith the renewed interest in their thermoelectric proper-ties, would be reason enough to undertake a detailed andsystematic investigation of their transport properties.This situation, however, has been rendered even morethought provoking by the recent' band-structure calcu-lations for CoAs3, CoSb3, and IrS13 by Singh and Pickett(SP). These workers found that, in agreement with theearlier band-structure calculations of Jung, Whangbo,and Alvarez, ' a relatively large ( —1 eV) gap formsaround the Fermi level in these compounds„but that asingle valence band crosses the gap, touching the conduc-tion band in IrSb3 and CoAs3, and nearly doing so inCoSb3. Thus SP concluded that these materials are actu-ally zero- and narrow-gap semiconductors, with a highlynonparabolic band structure in the case of the an-timonides. We feel that the combination of the recentstrong interest in these materials, the controversial andincomplete nature of existing experimental data, and theband-structure predictions of SP, call for a detailed inves-tigation of the low-temperature transport properties ofskutterudites. We have chosen to begin with CoSb3 be-cause this compound is the easiest to fabricate in single-crystal form.

0163-1829/95/51(15)/9622(7)/$06. 00 51 Qc 1995 The American Physical Society

LOW-TEMPERATURE TRANSPORT PROPERTIES OF p-TYPE CoSb3 9623

II. EXPERIMENT

Starting constituents for the growth of our sampleswere Co (99.998% pure) and Sb (99.9999% pure). An im-purity analysis of the cobalt detected only Al, Ca, Mg,and Ag, all at levels of less than 1 ppm. Single crystalswere grown using the gradient freeze technique frommelts with 93-at. % Sb in sealed quartz ampoules, thelatter having been coated with graphite and providedwith a pointed tip. A temperature gradient of approxi-mately 50'Cern was maintained at the growth inter-face. Typical ingots obtained after the growth were com-posed of two parts, the bottom part corresponding to thecompound CoSb3 and the upper part to the Sb-rich eutec-tic. Single-crystalline samples were obtained as indicatedby Laue patterns. Selected samples were polished, andtheir microstructure examined, under an optical micro-scope. Microprobe analysis was also performed on thesame samples to determine their composition. Finally,some samples were ground for x-ray-diffractometryanalysis. These experiments showed that the sampleswere single phase with a lattice constant indicative of aCo:Sb ratio of 1:3. The density of all samples was mea-sured by the immersion technique using toluene as theliquid. The measured densities were found to be approxi-mately 99.5% of the theoretical density of 7.69 gcrnconfirming the stoichiometric ratio of 1:3. We havefound, in agreement with Dudkin, that all unintentional-ly doped material is p type. Several samples wereprepared with hole concentrations in the range2.6 X 10' —4. 1 )& 10' cm

Therrnopower, van der Pauw, and thermal conductivi-ty measurements were carried out at room temperatureon these samples at Jet Propulsion Laboratory as de-scribed earlier. ' Four of these samples, as shown inTable I, were large enough for the low-temperature mea-surements described in this paper. One of these, desig-nated 52NB14, was not large enough to carry out low-temperature thermal conductivity and thermoelectricpower measurements, but low-temperature galvanornag-netic data were obtained on this sample.

Thermal transport measurements were carried out bythe four-probe steady-state technique which has been de-scribed in detail elsewhere. ' ' Samples were cut with ahigh-speed diamond saw in the shape of parallelepipedswith heat Row along the longest axis. Since the CoSb3

structure is cubic, the lattice thermal conductivity, whichas we will see is the predominant contribution, is essen-tially isotropic. Heat input to the sample was made via ametal film heater epoxied to the free end of the crystal.The temperature difference along the sample was mea-sured with either Chromel-Constantan or AuFe-Chromelthermocouples above 20 K and with carbon glass ther-mometers at lower temperatures, and results differed byless than 5% in the overlap region. For Seebeck probes,we used either Pb or Cu wires, the absolute thermopowerof each having been previously calibrated. ' In eithercase the absolute Seebeck coefticients of these probes donot exceed 1.5 pVK ' in the temperature range of in-terest.

Measurements of thermal conductivity sc and thermo-power S were carried out in a closed-cycle helium re-frigerator with a base temperature of 11 K. In order toextend data on one sample (71NB13) to lower tempera-ture, this sample was remounted in a liquid-helium cryo-stat. We estimate the absolute error in our measurementsof Ir and S as 10%, which arises from the error in measur-ing the geometrical factor of these small samples.

The electrical resistivity, carrier concentration, andmobility were measured on disks of material using thevan der Pauw technique with sample currents in therange 1 —30 mA. Care was taken to insure that no heat-ing of the samples occurred during the course of a mea-surement. The hole concentration p was determinedfrom the Hall coefficient RH (which was independent offield to within 5% up to 6 T) using RH=1/pe, i.e., as-suming a scattering factor equal to 1 and a single-carriermodel. On one sample (71NB13) Hall measurement wasrepeated on the parallelepiped using the standard Hallgeometry, and the results agreed with those using the vander Pauw technique to within 10%. The hole mobility vwas determined from the zero-field resistivity p and thecarrier concentration p using p = 1/(pe v).

Finally, magnetic-susceptibility measurements werecarried out between 4 and 300 K using a QuantumDesign superconducting quantum interference device(SQUID) magnetometer. The samples were placed insideof a polyethylene capsule and straw, and the backgroundsusceptibility was independently measured and accountedfor. Due to the small susceptibility of the samples, we es-timate an error in this measurement of approximately10%.

52N1B4 o71NB 13 ~2NB14 01NB14 4

2.6x10"1.2x10"3.6x10"4. 1x10"

2775 —4.1 98002445 0.115 216 —7.7 73002175 0.129 167 —8.7 67001746 0.102 130 —8.9 5600

TABLE I. Parameters of p-type CoSb3 crystals. p is the holeconcentration (cm ) at 300 K; v is the hole mobility(cm V ' s ') at 300 K; ~ is the thermal conductivity(Wcm ' K ') at 300 K; Sis the thermoelectric power (pV K ')at 300 K; y is the magnetic susceptibility (10 ' emu G ' mol '}at 300 K; and Pz is the low-temperature saturation value of themobility (crn V ' s ').

Sample

III. RESULTS

A. Hole concentration and hole mobility

Table I indicates the room-temperature hole concen-tration, hole mobility, thermal conductivity, Seebeckcoefticient, and magnetic susceptibility of four nominallyundoped samples of p-CoSb3. The large hole mobility isconsistent with the predominantly covalent bonding inthis compound. For comparison, Slack and Tsoukalafound a mobility of 1320 cm V 's ' on an IrSb3 samplewith a hole concentration of 1.1 X 10' cm . Thethermal conductivity is fairly small due to the large atommasses and complex unit cell. This combination of large

9624 51

the lowest do eoped sample, the m' '

eac ee mobility reacheeac es nearly 10carrier mob'11 Ity and fairl s

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Tememperature (K)

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1000 I I s ~ I ~ I I ~ I I ~ s s I I I ~ s s h ~ I Temmperature (K)

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Tememperature (K)

FICx. 2. (a) HoleCoSb ' ine in (b)

(I ion is given in Table I.

1000 FICx. 3. Thererma1 conduc'

is given in Table Ie I. Curve 3

rve B includes the eh(I1 presents h h-ig -temperature

I.OW-TEMPERATURE TRANSPORT PROPERTIES OF p-TYPE CoSb3 9625

is essentially absent in these materials, and apparently theconcentration of other types of defects and impurities isvery small. What is surprising is that the rapid rise inthermal conductivity occurs despite the fact that thesematerials are electrically conducting. We are aware of noprevious such observation on an electrically conductingmaterial except the semimetal bismuth, another elementwith only a single isotope. While there is some sampledependence of ~ near the peak in CoSb3, it does not scalewith hole concentration.

C. Seebeck coef5cient

0EU

E

CL

40

lO

1.10+

s.iO-5

~ ~ ~ ~ ~ ~ ~ ~ I

0 oo oooo«0

Figure 4 exhibits the thermoelectric power of our threesamples of CoSb3. The magnitude of the thermopowerscales inversely with hole concentration and decreasesroughly linearly with temperature down to 100 K, indica-tive of the predominance of hole diffusion thermopower.Below 100 K S( T) rises dramatically and develops a peakat approximately the same temperature as the peak in thethermal conductivity. This coincidence of maxima inS ( T) and ~( T) is evidence that this feature in the Seebeckcoefficient is a strong phonon drag effect (we eliminate aKondo phenomenon as the source of this peak, sincethere is no evidence of magnetic impurities in these sam-ples; see Sec. III D).

100 200 300

Temperature (K)

temperature-independent contribution from the carriers,and leave this subject without further analysis.

FIG. 5. Magnetic susceptibility of four samples of p-typeCoSb3, with the sample designation given in Table I. The solidline indicates the estimated ion core contribution.

D. Magnetic susceptibility IV. DISCUSSION

hC

200ctD

~~6tDOO

100

th

op~ o oo oo oo

o oo

ooo o

o

~ ~

o 0

50 100 150 200 250 300

Temperature (K)

FICx. 4. Thermoelectric power of three samples of CoSb3,' thesample designation is indicated in Table I.

Figure 5 exhibits the magnetic susceptibility of p-typeCoSb3 after correcting for the background susceptibilityof the sample holder. We see that the susceptibility issmall, diamagnetic, and essentially temperature indepen-dent, in agreement with previous studies. ' ' The solidline indicates the ion core contribution to y(T) estimatedfrom the atomic susceptibilities of the constituents.Due to the inaccuracy of estimating this latter contribu-tion, it is dificult to say anything quantitative about themagnetic susceptibility; we simply note that there ap-pears to be a small diamagnetic and essentially

As indicated above, the temperature dependence of thehole mobility is suggestive of a combination of scatteringby phonons at high temperature (above 100 K) and neu-tral impurities below 100 K. In fact the data in Fig. 2(b)can be fit using the empirical relation

v '=v '+v 'ni

with the phonon-limited mobility vz =p&T ' and theneutral-impurity-limited mobility v„;=p2. The best fitoccurs for p&=1.8X10 cm V 's 'K ~ and for thevalues of P2 given in Table I. The absence of ionized im-purity scattering (as evidenced by the lack of a T ~

dependence of mobility at lower temperatures) is quitesurprising given the relatively large hole concentration inthese materials. One might surmise that this is due to astrong screening effect. While the dielectric constant ofCoSb3 is indeed fairly large (e „=25;Ref. 26), it is rough-ly the same as that in InSb ( —18), a material in whichionized impurity scattering is known to be quite strong,and it is much smaller than in PbTe ( -2000 at low tem-perature), the prototypical material in which ionized im-purity scattering is suppressed due to screening. On theother hand, if the holes were intrinsic and excited acrossa gap of 50 meV (such as that suggested by the SP band-structure calculation), their intrinsic density at 300 Kwould be about 10' cm; thus these samples are mostlyextrinsic in the temperature range studied here. Thesmall variation in hole concentration with temperature inthe two most lightly doped samples is in fact consistentwith a gap on the order of 100 meV. Given the lack ofionized impurity scattering, the origin of the extrinsiccarriers in this material is an open question, the answer

9626 D. T. MORELLI et al.

100000

V)

E

10000

O

0)0

10001p17 1P18

Hole Concentration (cm )

1019

FIG. 6. Low-temperature saturation value of the hole mobili-ty as a function of hole concentration for p-CoSb3. The solidline is the v-p ' ' behavior.

to which awaits further investigation.One of the predictions of the SP band-structure model

is that when the constant scattering time approximationholds, i.e., when the scattering of holes is energy indepen-dent, the hole mobility, which is normally independent ofdoping level under these conditions, will vary as pNow the scattering time is energy independent forscattering from neutral impurities, which is just the casein CoSb3 at low temperatures. Thus we can comparedirectly the low-temperature saturation value of the mo-bility with the predicted behavior according to SP. Fig-ure 6 shows the low-temperature hole mobility as a func-tion of hole concentration. Indeed, the p

' law isreasonably closely followed for this material, in goodagreement with the SP band-structure model.

We turn now to a discussion of the thermal conductivi-ty and thermoelectric power. As discussed above, thethermal conductivity is due almost entirely to the lattice,and we can attempt a fit to the data using the Debye mod-el and assuming only phonon-phonon umklapp scatter-ing and boundary scattering. The frequency co and tem-perature dependence of the U-process scattering rate 7 pp'

in principle can be determined if one has knowledge ofthe phonon dispersion curves, for instance using the pro-cedure of Han and Klemens. Unfortunately no infor-mation is available with regard to the phonon-dispersionrelations in CoSb3. Therefore, we shall make use of theempirical relation r '-co T exp( —9/3 T), where 0 is theDebye temperature. This form for the umklapp scatter-ing rate has been used with success for a variety of co-valently bonded semiconductors, including Si and Ge(Ref. 29) and diamond. Berman has shown that, atleast for the temperature range considered here, the par-ticular values chosen for the frequency and temperatureprefactors in this equation are somewhat arbitrary, since

the temperature dependence is determined largely by theexponential; we have chosen the above form simply onthe basis that it has been used successfully for theaforementioned materials over very wide temperatureranges. For the boundary scattering rate we takerb '=v/L, where u is an average phonon velocity and Lis a characteristic sample dimension. The Debye temper-ature and phonon velocity are related to each other by

0=297. 72( U /5 ), (2)

where 5 is the average volume occupied by an atom.Curve A in Fig. 3 is the best fit to the data of sample2NB 14 using L = 1 mm and yields 0=287 K andv =2700 m s '. These values are in good agreement withthe values 0=306 K and v =2930 m s ' determined fromour ultrasonic measurements, and are to be comparedwith values of 0=308 K, v&,„g

=4675 m s ', andV„,„,=27 17 m s ' for IrSb3 ~ Thus the measured latticethermal conductivity of CoSb3 above the maximum isnearly what one expects given the crystal structure andelastic constants of this compound If we were to assumethat the holes observed in the electrical transport ori-ginated from charged vacancies, one would expect thatthe thermal conductivity would be reduced due tophonon-vacancy point-defect scattering. For a vacancyconcentration of 1 X 10' cm (sufficient to produce3 X 10' cm holes, each vacancy providing threeholes ), the resultant thermal conductivity would be thatindicated by curve B in Fig. 3, which exhibits a muchslower rise and smaller peak value than that observed.This curve was derived using the vacancy-phonon-scattering rate of Ratsifaritana and Klemens, ' whichtakes into account both the mass and elastic constantdifferences due to the presence of the vacancy. The ac-ceptor impurity which would produce the least amountof phonon scattering is Sn substituting for Sb; in this casethe mass difference is only 3%, and Sn impurities at aconcentration of 3 X 10' cm would produce, assumingno strain effect, practically no phonon scattering. How-ever, trace impurity analysis reveals a Sn concentration atleast two orders of magnitude smaller than necessary toproduce the observed hole concentrations, and in addi-tion such an argument cannot explain the difference inthermal conductivity at the peak between samples 2KB 14and 11'14. Taken together, these observations againstress the inexplicable origin of the holes in this material.Finally, it is possible that the thermal conductivity ofsample 1%8 14 is limited by other types of defects, suchas dislocations, but we have not undertaken a detailedstudy along these lines.

Another point to be noted is that the phonon mean freepath at low temperatures takes on a very large value.This very large phonon mean free path at low tempera-tures manifests itself in the occurrence of phonon dragthermopower in this material in this temperature range.From our measured values of thermal conductivity andmobility it is possible to make a rough estimate of themagnitude of the phonon drag component Spd of thethermopower. We have

S~d = (k~ /e)(m *U/k~ T)(L~ /Th&)

51 LOW-TEMPERATURE TRANSPORT PROPERTIES OF p-TYPE CoSb3 9627

1000

hC

4)~~0

~00

CJ0)

OP(h

1017 1018 1019

Hole Concentration (cm )

1020

which S-p . Note that Eq. (4) contains no adjust-able parameters, the thermopower depending only on theslope of the band, which is fixed by the band-structurecalculation, and the measured hole concentration. Figure7 shows the room-temperature thermoelectric power(where the phonon drag effect is negligible) versus carrierconcentration for a variety of p-type CoSb3 samples, in-cluding three Sn-doped samples measured by Zobrinaand Dudkin. The solid line is the predicted value of Eq.(4) for CoSb3, and the agreement is quite remarkable,especially in light of the fact that there are no adjustableparameters. SP also found that the one sample of Slackand Tsoukala was consistent with their calculation.These findings thus lend strong support to the SP band-structure model of antimonide skutterudites.

FIG. 7. Room-temperature thermoelectric power as a func-tion of hole concentration in p-CoSb3. Sample designation: ,this work; A, Ref. 9. The solid line is the relation predicted byEq. (4) for CoSb, .

In this expression, rn *=0. 1m 0 is the hole effectivemass, ' I, the phonon mean free path, and ~h„ the hole-phonon scattering time. For T = 10 K, we estimateI. =0. 1 mm. The hole-phonon scattering time can be es-timated from the phonon-limited mobility determinedfrom the fit to our experimental mobility as given above:

wh~=rn*ale =m*P&T ' /e=3X10 " s at this tem-perature. Thus from Eq. (3) at 10 K we find S d=300pV K ', in reasonable agreement with the observedvalues, given the very approximate nature of the scatter-ing parameters.

Finally, we wish to compare the room-temperaturethermoelectric power of our samples with that predictedby the SP band-structure model. In this model, the ther-moelectric power is predicted to be

V. SUMMARY

We have performed a detailed set of low-temperaturetransport measurements on CoSb3 in order to clarify thenature of transport in this skutterudite and to comparethe results with the recent band-structure model of Singhand Pickett. ' High-quality single crystals exhibit largehole mobilities, intrinsic lattice thermal conductivitydown to 10 K, and pronounced phonon drag effects in thethermoelectric power. A comparison of the results withthe predicted band structure seems to lend support to thepicture that these skutterudites possess a highly nonpara-bolic valence band. On the other hand, based on the ab-sence of ionized impurity scattering and the observationof an exponentially rising thermal conductivity at lowtemperature, the origin of the highly mobile holes in thismaterial remains a mystery. We are planning furthermeasurements of the low-temperature transport proper-ties of both p- and n-type samples in order to further elu-cidate their behavior.

S= (2rrktt T/3ect)(tr/3p)' (4) ACKNOWLEDGMENTS

0where cx= —3. 1 eV A is the slope of the linear dispersingband as calculated by SP. This expression has a differentdoping dependence than the normal parabolic band, for

The authors would like to acknowledge useful discus-sions with Dr. J. Herbst, Dr. J. Heremans, Dr. G. Meis-ner, Dr. D. Singh, and Dr. G. Slack.

T. Caillat, A. Borshchevsky, and J.-P. Fleurial, in Proceedingsof the XIth International Conference on Thermoelectrics, University of Texas at Arlington, 1992, edited by K. R. Rao (Uni-versity of Texas at Arlington Press, Arlington, 1993),p. 98.

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