Measurement 45 (2012) 133–139

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Measurement

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Simple apparatus for the multipurpose measurements of differentthermoelectric parameters

Biplab PaulMaterials Science Centre, Indian Institute of Technology, Kharagpur 721 302, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 24 March 2011Received in revised form 31 July 2011Accepted 10 September 2011Available online 28 September 2011

Keywords:Thermoelectric measurementDifferential methodSeebeck coefficientResistivityHall coefficientNernst–Ettingshausen coefficient

0263-2241/$ - see front matter � 2011 Elsevier Ltddoi:10.1016/j.measurement.2011.09.007

E-mail address: biplabpaul2006@yahoo.co.in

A simple apparatus for the simultaneous measurement of Seebeck coefficient (a) and elec-trical resistivity (q) in the temperature range 100–600 K, Hall coefficient (RH) and trans-verse Nernst–Ettingshausen coefficient (N) in the temperature range 300–600 K of thebar shaped samples has been fabricated. The instrument has been designed so simply thatthe sample can be easily mounted for the fast measurements of different thermoelectricparameters. The sample holder assembly of the apparatus has been designed so cleverlythat any part of that section can be replaced in case of any damage; and so it can beregarded as a modular based system. The apparatus is relatively cheaper in cost and alsoportable.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Search for a material for thermoelectric application in awide temperature range must be associated with the abilityto measure the Seebeck coefficient of the material in bothhigh and low temperature regimes. In thermoelectric mate-rials, scattering of carriers tunes its thermoelectric proper-ties. So, different scattering mechanisms are intentionallyintroduced into the materials for the enhancement of theirthermoelectric efficiency. Thermoelectric efficiency of amaterial is defined in terms of a dimensionless parameter,thermoelectric figure of merit ZT = a2T/qk, where T and kare the absolute temperature, and thermal conductivity,respectively. For the measurement of Seebeck coefficientin a bar shaped sample, with dimension typically of the or-der of 1.3 � 1.0 � 10 mm3, a temperature difference (DT)is produced along its length and the corresponding voltagedeveloped between the ends is measured (DV). Seebeckcoefficient being the ratio of DV

DT , a small error in the measure-ment of DT will introduce a large error in the value of a. So,the accuracy of the measurements of the temperature

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gradient is a major concern for any measuring system. Fur-ther, the measurement of temperature dependent electricalresistivity simultaneously with the Seebeck coefficientmakes it easy for electrical characterization and causesmuch reduction in time consumed by the measurement pro-cess. Both the integral [1–6] and differential methods [7–17]have been implemented by the researchers to measure theSeebeck coefficient in both high and low temperatureregimes. However, the integral method is suitable for verylong samples. Usually the samples used by the investigatorsare generally very small in dimension. So, differential meth-od has become more popular one. However, there are fewreports giving details of the instrument, which capable ofhigh temperature transport property measurements [7,9–11]. Ponnambalam et al. [9] and Burkov et al. [10]developed an apparatus for the measurement of Seebeckcoefficient and electrical resistivity at high temperatures.However, their design is somewhat complex and not costeffective. Zhou and Uher [7] developed an instrument forhigh temperature measurement of Seebeck coefficient andresistivity. However, here the drilling on the sample surfaceto insert the thermocouple tips and electrical leads do notallow nondestructive characterization of sample. Dasgupta

134 B. Paul / Measurement 45 (2012) 133–139

and Umarji [11] reported the fabrication of an apparatus forthe measurement of high temperature value of thermal con-ductivity and Seebeck coefficient. More recently a review onthermoelectric apparatus was presented by Martin et al.[18]. However, no apparatus can fulfill the purpose of mea-suring all the four parameters a, q, RH, N alone. In thisscenario I have designed and fabricated an apparatus forthe nondestructive evaluation of the thermoelectric materi-als. The instruments are very simple in design, where thesample can be easily mounted to carry out the fast measure-ments of resistivity and Seebeck coefficient. Sample holderassembly of the instruments has been designed so cleverlythat any parts of this section can be easily replaced in caseof any damage. Further, the instruments are relativelycheaper in cost and portable. The most advantage of thisinstrument is that the same apparatus can be used for thesimultaneous measurement of Seebeck coefficient andresistivity of any sample in the temperature range 100–600 K. However, with the present simple design where theaccommodation of the cryostat is not straightforward, themeasurement of Hall coefficient and Nernst–Ettingshausencoefficient can be done using the same apparatus in thetemperature range 300–600 K.

2. Apparatus description

Fig. 1 shows the schematic diagram of the instrumentalarrangement for the measurement of Seebeck coefficient in

Fig. 1. Schematic representation of the whole instrumental arrangementfor the measurement of Seebeck coefficient and electrical resistivity in thetemperature range 100–300 K.

the temperature range 100–300 K. Here, to reduce the tem-perature of sample environment below room temperaturethe main apparatus is inserted into a liquid nitrogen con-tainer. Fig. 2 describes schematically the different partsof the sample holder assembly. In Fig. 2 the copper blocks(1 and 2) in sample holder assembly have diameter slightlyless than 6 mm, into which very thin (0.08 mm) type-Kthermocouples to sense the temperature and copper wires(3) of diameter 0.06 mm for the measurement of thermo-emf are embedded. These copper blocks are heated to raisethe temperature from 100 K onwards. The sample (4) isplaced between the heating copper blocks.

The copper blocks are kept inside the quartz tubes (5and 6) with inner diameter of 6 mm of thickness 1 mmhaving a length 11 mm onto which 180 X of kanthal (ofdiameter 0.1 mm) heaters (7 and 8) are wounded. Theheaters are wounded by mica sheets (9 and 10) of width10 mm, which are pressed-fit inside the other two quartztubes (11 and 12) of inner diameter 15 mm and outerdiameter 17 mm. The quartz tube (5) is suspended by theforce of compressive strain developed by the mica sheets.The length of the quartz tubes (11) and (12) are 22 and10 mm, respectively. Quartz tubes (11) and (12) are placedinside the quartz tube (13) of inner diameter 17 mm andouter diameter 19 mm with length 60 mm. The quartz tube(11) is attached along the inner wall of (13) by the springaction (14). The quartz tube (11) can be easily moved coax-ially up and down. Similarly, the copper block (1) can eas-ily pass through the tube (5). This mechanism has beenemployed so that the sample of different length can besupported between the copper blocks.

Two slits of dimension 13 � 12 mm2 are cut at the dia-metrically opposite side of the bottom portion of quartz

Fig. 2. Schematic diagram of the sample holder assembly of theapparatus.

B. Paul / Measurement 45 (2012) 133–139 135

tube (13) for the purpose of mounting the sample and con-necting the sensors and other electrical wires. Quartz tube(13) is squeezed between two ceramic plates (15 and 16)and placed inside a brass frame. The ceramic plates (15and 16) prevent the direct conduction of heat from the hea-ter to the brass frame. The brass frame consists of two par-allel plates (17 and 18) of diameter 37 mm each and ofthickness 6 mm. The plates are separated by a distance of75 mm by four brass pillars (19) of diameter 6 mm each.The brass plate (17) is kept fixed on the brass pillars bythe nuts. The four holes of diameter 3 mm drilled and towhich fine bored ceramic beads (20) attached and throughwhich all the sensors and electrical wires are passed.

In order to establish good thermal contact the sample (4)is squeezed between the copper blocks. For this purpose,pressure is applied on the copper block (1) by a brass screwof diameter 4.5 mm (21), which is supported by the brassframe. To keep the brass screw (21) to be thermally isolatedfrom the copper block (1) the pressure on the copper blockis transmitted through a ceramic bead (22), which isattached to the extreme end of the screw through a stain-less steel spring (23). Here, the spring action implies aconstant force on the sample during the entire experiment.

The sensors and all the wires for electrical measure-ment are Teflon coated and hence electrical insulationand isolation is maintained. The brass frame is attachedto the closed end of a brass tube (shown in Fig. 2) of outerdiameter 22 mm having an inner thickness of 2 mm. Thelength of the brass tube is 70 mm, whose open end is fixedto a Teflon rod of diameter 25 mm by the press fitting andscrewing method as shown Fig. 1. The Teflon rod is passedthrough a Teflon frame, which supports a quartz tube ofouter diameter 41 mm of thickness 2 mm and length31 mm by compressive strain. The quartz tube encapsu-lates the whole sample holder assembly and remains airtight with the inner wall of the Teflon frame by a thin rub-ber band. A steel pipe of diameter 6 mm is passed throughthe Teflon frame for evacuating the sample chamber. Tomeasure the electrical resistivity and Seebeck coefficientin the temperature range 300–600 K the main apparatusis kept out of the liquid nitrogen container. Two steel pipesof diameter 3 mm passed through the Teflon rod inside thebrass tube as shown in Fig. 1. The water is passed throughthe steel pipes to avoid the degradation of Teflon rod adja-cent to the open end of brass tube during high temperaturemeasurements.

Fig. 3. Schematic representation of the principle of (a) Seebeck coefficientand (b) electrical resistivity measurements.

3. Measurement procedures

Two p-type PbTe bar samples, viz. specimen-I and spec-imen-II, with room temperature hole concentration of3.97 � 1018 and 4.07 � 1018 cm�3, were taken and eachwas placed between the two heating blocks and samplechambers evacuated to 5 � 10�5 Torr to avoid the oxida-tion during high temperature measurements. To ensurethe good thermal contact of the sample faces with theheating blocks sample is squeezed between the blocks bythe press screw (21) driven by the steel spring (23) throughthe ceramic bead (22). The advantage of the spring loadingmechanism is that by which a constant force can be

employed at all the temperatures throughout the measure-ment runs.

3.1. Seebeck coefficient measurement

To measure the Seebeck coefficient either dc or acmethod are generally used [19–21]. The dc method isrelatively easier method for the transport measurements,which is used here to measure the Seebeck coefficient. Inthis technique a thermal gradient is established along thesample and both thermoelectric voltage (DV) and temper-ature difference (DT) across the length of the sample aremeasured. The Seebeck coefficient is obtained from

a ¼ � dVdT¼ �DV

DTð1Þ

The basic principle of measuring the Seebeck coefficientis shown in Fig. 3a. Thermal gradient is generated by produc-ing a temperature difference, across the sample. To producethe thermal gradient the temperature of the heaters raisedslowly, typically at a rate of 1.5 �C/min, which allows thesteady state condition to be sustained during data collectionand negate the error arising from temperature drift. Ther-mometer attached to the copper block very close to the sam-ple faces indicates the temperature T1 and T2. To measurethe temperature Kiethley 2182 nanovoltmeters are usedby which thermocouple signal can be converted directlyinto temperature values with a resolution of 0.001 �C. Dueto the temperature difference of DT = T1 � T2 a voltage DVS

is developed across the sample, which can be either negativeor positive depending on the type of the majority carriers(either hole or electron) in the sample. To measure ther-mo-emf across the sample Keithley 2001 voltmeter is usedwhich can easily measures up to the resolution of 0.01 lV.

As already mentioned the Seebeck voltage is measuredwith the aid of thin copper wires that are embedded in thecopper blocks close to the sample faces. So, both the tem-perature difference (DT) and developed thermoelectricvoltage (DVS) are measured between the same two points.However, the voltage detected by the nanovoltmeteracross the sample is somewhat different from the valueDVS and given by

DV ¼ DVS þ DV2 þ DV1 ð2Þ

Here, DV2 is the voltage developed in the copper wireattached to the cold end because of the fact that its oneend is at temperature T2 while the other end is at the

136 B. Paul / Measurement 45 (2012) 133–139

atmospheric temperature (Tatm). Similarly, due to a tem-perature difference T1 � Tatm across the copper wire at-tached to the hot end a voltage DV1 is developed. If aCu isthe Seebeck coefficient of copper wire then the aboveequation can be written as

DV ¼ DVS þ aCuðT2 � T1Þ ð3Þ

where DV2 + DV1 is replaced by aCu (T2 � T1). So, the See-beck coefficient can be written as

a ¼ �DVS

DT¼ DV

T2 � T1� aCu ð4Þ

To reduce the error in the measurement of Seebeckcoefficient, it is taken as the slope of the linear plot of ther-moelectric voltage against the temperature differenceacross the samples. However, it is to be ensured that thetemperature difference DT across the sample must besmall (3–8 K) so that the Seebeck coefficient falls in the lin-ear range. This practice of measuring Seebeck coefficienteliminates the error introduced by the offset voltages aris-ing from the inhomogeneities in thermocouple and non-equilibrium contact interfaces [7,9]. It also avoids theassumption that the curves must pass through the point(DV = 0, DT = 0). The obtained Seebeck coefficient is notthe absolute one but it is the Seebeck coefficient relativeto copper. To obtain the absolute Seebeck coefficient ofthe sample the contribution arising from the copper hasbeen corrected. The accuracy of the Seebeck coefficient de-pends on the accuracy in the measurement of temperaturegradient and voltage difference. It is estimated that theuncertainty in the measurement in temperature gradientof 3–8 K to be within ±0.4%. The accuracy in the voltagegradient measurement is found to be within ±0.6%, whichis mainly originated from the noise in voltage developedacross the sample. The total error in the measurement ofSeebeck coefficient is estimated to be within ±1%. Fig. 4aand b show the temperature dependent Seebeck coefficientin the temperature range 100–600 K of the specimen-I andspecimen-II. The Seebeck coefficient measurement of thesample was performed several times both in heating andcooling mode and the discrepancy between the individualdata points was found not to exceed ±1%. The obtained val-ues of Seebeck coefficient of the PbTe specimens are wellmatched with the values obtained from Pisarenko plot[22] for similar carrier concentration.

3.2. Electrical resistivity measurement

The basic principle of electrical resistivity measurementis shown in Fig. 3b. Here, a constant current I is passedthrough the sample by the copper wires attached to thecopper block. Two more ends of the copper wires areattached at the middle of the sample using silver paint,which are used to measure the potential drop V1 whereV1 = VIR + VTE, VIR being the resistive voltage due to currentI1 and VTE is the contribution from the thermo-emf. To nul-lify the thermo-emf VTE the current (I2) is suddenlyreversed in direction (negative) to measure the voltage V2

where V2 = VIR + VTE. The sample resistance can be obtainedfrom the relation

R ¼ V1 � V2

2Iav¼ ðV IR þ VTEÞ � ð�V IR þ VTEÞ

I1 � I2¼ V IR

Iavð5Þ

where Iav=(I1 � I2)/2. However, for the accuracy of the elec-trical resistivity measured by this method care should betaken that VIR must be greater than or comparable to VTE.In the present study for the determination of electricalresistivity a current of I = 10 mA is passed through thesample. The sample resistivity is calculated by using theequation

q ¼ RALV

ð6Þ

where A is the cross sectional area of the sample and LV isthe distance between the center of the voltage contacts.However, the electrical resistivity obtained by this methodcan be somewhat different from the actual resistivity of thesample. This is because when a current is passed throughthe metal/semiconductor interfaces of the sample, due toPeltier effect, heat is liberated at one current contact andis absorbed at the other, which results in a thermal gradi-ent and consequent thermoelectric voltage across the sam-ple. Unfortunately voltage developed due to Peltier effectcannot be nullified by averaging the readings for forwardand reverse current direction. This is because the reversalof current reverses the direction of both the temperaturegradient and its corresponding thermoelectric voltage.However, the fast switching of current polarity and reduc-tion in measurement time can negate the Peltier effect asthe thermal gradient requires finite time to propagate. Inthe present study the switching of sample current and datacollection time are faster than the propagation time ofthermal gradient and thus the voltage arising from the Pel-tier effect is very much reduced. In time duration of datacollection a fluctuation of only ±0.01 �C in the value ofDT is observed, which is attributed to the Peltier effect, giv-ing rise to an error of ±0.3% in the measurement of volt-ages. Other source of error in estimation of electricalresistivity is the uncertainty in the measurement of sampledimension. The uncertainty in the measurement of Lv(measured under the microscope) is within ±0.4%. Theuncertainty in estimation of sample cross-section is±0.5%. The total error in the measurement of resistivity isestimated to be within ±1.2%. However, if the sample isnot uniform then the error in the measurement of electri-cal resistivity may exceed ±1.2%. Electrical resistivity mea-surement was performed several times on the samesample both in heating and cooling mode and discrepancybetween the individual data points was not found toexceed ±1.2%. Fig. 4c and d show the temperaturedependent electrical resistivity of the specimen-I andspecimen-II in the temperature range 100–600 K.

3.3. Hall coefficient measurement

By the above described instrument the Hall coefficientof the sample in the temperature range 300–600 K can eas-ily be measured. For the measurement of Hall coefficient ofthe specimens the sample holder assembly is placed verti-cally between two magnetic pole pieces. When a current Iis passed through the sample along the x-direction and a

Fig. 4. Temperature dependent Seebeck coefficient of (a) specimen-I and (b) specimen-II and electrical resistivity of (c) specimen-I and (d) specimen-II inthe temperature range 100–600 K.

Fig. 5. Schematic representation of the principle of (a) Hall coefficientand (b) Nernst coefficient measurements.

B. Paul / Measurement 45 (2012) 133–139 137

magnetic field BZ is applied along the z-direction an elec-tromotive force (EH) is generated along the y-direction,which is schematically shown in Fig. 5a. The Hall coeffi-cient (RH) is defined by the equation

EH ¼ RHJxBz ð7Þ

where Jx is the current density along the x-direction. For themeasurement of Hall voltage, two electrical leads of copperis attached at the mid of the opposite faces perpendicular tothe y-direction. To avoid the error in the measurements,introduced by the theromagnetic effect, sufficient careshould be taken to ensure that there arise no thermal gradi-ents across the length of the sample at the high tempera-tures, i.e. the temperature at the upper end of the sample(T1) must be equal to the temperature (T2) at its lowerend. However, it is difficult to maintain the isothermal con-dition while measuring the Hall voltages. Because of Peltiereffect a thermal gradient is developed along the length ofthe sample, which through Nernst–Ettingshausen effectgives rise to a voltage, often called the Nernst voltage, per-pendicular to both current and magnetic field direction. Inthe present study measurement is performed quickly thatthe thermal gradient does not get sufficient time to propa-gate and hence reducing the magnitude of Nernst voltagedeveloped across the sample. It is found in time durationof Hall data collection only a temperature difference of±0.01 �C to develop along the length of the sample, whichcontributes an error of ±1.7% in the measurement of Hallcoefficient. The Hall coefficient was taken as the slope atzero magnetic field of the transverse Hall resistivity withrespect to the field. This method is significant to nullify

the spurious voltages developed in the circuit. Other sourceof error is the uncertainty in the measurement of sampledimension, which contributes an error of ±0.9% in estima-tion of Hall coefficient. The total error in the measurementof Hall coefficient is estimated to be within ±2.6%. Hallmeasurements was performed several times both in heat-ing and cooling mode and the discrepancy between individ-ual data points was not found to exceed ±2.6%. Holeconcentration, p, was determined by p = 1/eRH, where e is

Fig. 6. Temperature dependent hole concentration of (a) specimen-I and (b) specimen-II and hole mobility of (c) specimen-I and (d) specimen-II in thetemperature range 300–600 K.

Fig. 7. Temperature dependent Nernst coefficient of specimen-I and specimen-II in the temperature range 300–500 K.

138 B. Paul / Measurement 45 (2012) 133–139

the electronic charge. Fig. 6a and b show the temperaturedependent hole concentration of specimen-I and speci-men-II in the temperature range 300–600 K. The tempera-ture dependent mobility of hole l of specimen-I andspecimen-II, calculated from the equation 1/q = pel, wheree is the electronic charge, is shown in Fig. 6c and d. Themobility of hole has been found to vary as l/T�m withm = 2.43 and 2.48 for specimen-I and specimen-II, respec-tively, which is in consistent with the results as reported

elsewhere [23] confirming the accuracy of the Hallmeasurements.

3.4. Nernst–Ettingshausen coefficient measurement

When a thermal gradient dT/dx exists in a conductoralong the x-direction and a magnetic field Bz is appliedalong the z-direction, an electromotive force (ENE) is devel-oped in the conductor in y-direction, which is schematically

B. Paul / Measurement 45 (2012) 133–139 139

described in Fig. 5b. The field ENE is called the Nernst fieldand expressed as

ENE ¼ �NBzdTdX

� �ð8Þ

where N is the Nernst–Ettingshausen coefficient and oftenabbreviated as Nernst coefficient. The above-describedapparatus can be used easily to measure the value of N inthe temperature range 300–600 K. For the measurementof N, sample holder assembly is placed vertically betweenthe two magnetic pole pieces. Nernst voltages were mea-sured at the low-field condition (lB� 1, where l is theelectron mobility) by reversing the sign of the magneticfield quickly and taking the differences in transverse volt-ages. Nernst coefficient was obtained from the slope of thelinear plot of Nernst voltage against the magnetic field.During the measurement of Nernst coefficients a tempera-ture gradient is developed along the direction of Nernstfield and so the value measured here is called the adiabaticNernst coefficient. Nernst coefficient measurement wasperformed several times both in heating and cooling modeand the discrepancy between the individual data pointswas found not to exceed ±3%. Fig. 7 shows the temperaturedependent Nernst coefficient of specimen-I and specimen-II in the temperature range 300–500 K.

4. Summary

An apparatus has been designed so that it can be usedfor the multipurpose measurements of different thermo-electric parameters. It is noted that the accuracy of themeasurements of the temperature gradient is a major con-cern for such measurements. So, care has been taken toimplement this design aspect relating to measurement oftemperature gradient. Further, the measurement of tem-perature dependent electrical resistivity simultaneouslywith the Seebeck coefficient with this equipment makesit easy for electrical characterization and causes muchreduction in time consumed by the measurement process,particularly due to quick mounting of the samples in theholder.

Acknowledgments

The authors acknowledge technical support from Mr.Ratanlal Mukherjee and Mr. Pijush Chakroborty.

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