Contains reports on four research projects.U. S. Navy (Office of Naval Research) under Contract Nonr-1841(51

Adler, Richard B.

Aigrain, P.

Dennis, Jane H.

Nelson, R. E.

Tavernier, J.

Contains research objectives and reports on four research projects.U.S. Navy (Office of Naval Research) under Contract Nonr-1841(51

Manley, O. P.

DSpace@MIT

V. THERMOELECTRIC PROCESSES AND MATERIALSProf. R. B. Adler Prof. P. AigrainttR. E. Nelson L. GodefroytJane H. Dennis J. Tavernier$O. P. ManleyRESEARCH OBJECTIVESWe are trying to understand the relationships between the structure of a solid andits relevant properties as a thermoelectric converter. Now, and for some time to come,we expect to remain interested primarily in compound semiconductors, and in mixedcrystals of them.Besides the very considerable matters of actually making and handling the materialsinvolved, the obvious properties of thermoelements which command immediate attentionare: the thermoelectric power (Seebeck coefficient) or Peltier heat (Peltier coefficient),the electrical conductivity, and the thermal conductivity. The first two properties aredependent upon the electronic energy-band structure of the solid and the electronicscattering mechanisms in it. Underlying the third property are the dynamics andmechanical perfection of the crystal lattice.Collateral features of interest in thermoelectric applications are such device-oriented topics as the diffusion (or other transport) of contact materials in the semi-conductor and the performance of completed coolers or generators.A little progress has been made during the past year on selected parts of eachtopic mentioned above. We have learned how to grow good single crystals of the well-understood material Bi 2 Te 3 , and the group in France has struggled with new compoundsof Mo and W, and they have made successfully polycrystalline solid solutions in theSe-Te system.We have also helped Professor David C. White's Energy Conversion Group,of the Electronic Systems Laboratory, M. I. T., with their preparation of polycrys-talline HgTe and mixed polycrystals in the HgTe-CdTe system. A great deal ofeffort has been expended in developing our ability to cut, etch, make contact to,and conduct the necessary thermal and electrical measurements on the various mate-rials.As for the thermoelectric parameters, we have made some theoretical speculationson the connection of the anisotropic thermoelectric power in iodine-doped Bi2Te 3 withmultiple electronic scattering mechanisms in nondegenerate (probably compensated)material, and experiments to pursue these ideas have been carried out at the same time.The band-structure investigation of HgTe has just been started by conducting meas-urements of Hall effect and resistivity over a moderately broad temperature range.Professor Aigrain's group, in Paris, has perfected its thermal-diffusivity equip-ment and used it to measure the thermal conductivity of germanium, silicon, andcompounds in the Se-Te system. They have gone quite far in pursuing Tavernier'stheory of the thermal conductivity produced by random mass fluctuations in the lattice,and they have checked it successfully in many cases against their own experimentaldata and the results of others.The diffusion of copper in Bi Te 3 at room temperature has been observed in apreliminary way, it having been previously determined that the copper seizes telluriumThis work was supported in part by the U.S. Navy (Office of Naval Research) underContract Nonr-1841(51). Reproduction in whole or in part is permitted for any purposeof the United States Government.tPart-time visiting professor in the Department of Electrical Engineering, M.I. T.$Laboratoire Central des Industries Electriques, Fontenay-aux-Roses, France.(V. THERMOELECTRIC PROCESSES AND MATERIALS)by chemical reaction at temperatures higher than approximately 3000C. Several con-tributions to the general theory of diffusion have been made, and papers have beenaccepted for journal publication. As by-products of this work, we hope to have soon aninteresting check of the effective mass in bismuth telluride from measurements onsamples into which copper has diffused.Finally, some amusing work on devices has been carried out by using bismuth tel-luride as a heat pump to cool a power transistor. Such efforts are worth while to keepus abreast of both the more practical fabrication problems and the theory of the per-formance of devices.In the coming year, most of the current programs are expected to continue, but itis clear that the group at Research Laboratory of Electronics needs to learn much moreabout thermal conductivity, so that we can help to carry forward the very effective workbeing done on this key problem by Prof. Aigrain and his associates.R. B. AdlerA. MERCURY TELLURIDE EVALUATIONIngots of mercury telluride have been prepared by the Bridgman method from astoichiometric ratio of mercury and tellurium. Single crystals, approximately 1 cm3in volume, have been obtained. Hall data on three wafers cut from the ingots indicatethat the mercury telluride measured thus far is p-type. Because of a high electron-to-hole mobility ratio (b~50-70), room-temperature electronic Hall mobilities of20,000 cm /volt sec have been measured. Room-temperature thermoelectric powers,are n-type, and approximately 120 [v/C in magnitude. From the Hall data at 4. 2K,18 3acceptor densities of the order of 10 per cm , and hole mobilities ranging from 50to 250 cm /volt sec, have been computed. Hole mobilities appear to be affected bythe acceptor density, since the higher hole mobility was measured in the more lightlydoped sample.An ingot of mercury telluride has been prepared with gold as principal impurity.But the gold segregated to the top of the ingot, where the material was distinctly poly-crystalline. No measurements were made on this portion except for those on thethermoelectric power at room temperature, which was found to be p-type and 160 v/oCin magnitude.R. E. NelsonB. THERMOELECTRIC TEMPERATURE CONTROL OF ELECTRONICCOMPONENTSA joint report with P. E. Gray and J. Blair, of the Energy Conversion Group,M.I.T., on the static and dynamic performance of a bismuth telluride Peltier coolerwas presented at the Northeast Electronics Research and Engineering Meeting, heldin Boston, November 19, 1959.This device had a heat-pumping capacity of 10 watts and a maximum unloaded(V. THERMOELECTRIC PROCESSES AND MATERIALS)temperature drop of 53°C below heat-sink temperatures, in the range 00 C-100°C. Thecomplete description of, and experimental results obtained with, the thermoelectriccooler will be published in the proceedings of the meeting.R. E. NelsonC. TRANSPORT OF CONTACT MATERIALS IN BISMUTH TELLURIDEWhen copper enters p-type Bi 2 Te 3 , the semiconductor changes into n-type if theconcentration of copper is high enough. In a homogeneous starting material the locationof the p-n junction will correspond to a fixed concentration of copper. Thus, by fol-lowing the motion of the p-n junction, the transport parameters for Cu in Bi2Te 3 maybe determined.Preliminary measurements indicate that the width of the p-n junction region isseveral millimeters. Since, furthermore, the Debye radius for Bi 2 Te 3 is generallya few lattice parameters, it is permissible to perform meaningful 4-point probe meas-urements in the junction region. It can be demonstrated that, because of compensationin that region, the conductivity goes through a fairly sharp minimum. If it is assumedthat the charge-carrier mobility is relatively independent of charge-carrier concentra-tion - an assumption justified by the absence of ionized-impurity scattering at or nearroom temperature - then it can be shown that the difference between acceptor and donorconcentrations is given byNd +nd - NA - PA = 2e (b-) (b+1) 1 - 2 1/2whereN d = concentration of ionized donorsnd = concentration of un-ionized donorsN A = concentration of ionized acceptorsnA = concentration of un-ionized acceptors4n = electron mobilityb = ratio of electron to hole mobilities0- = conductivity at the point of interest"min = minimum conductivityThe plus sign is to be used whenN +n - N - P < min (b-1)nSince NA Ais presumed to be known and constant throughout a homogeneous2eSince N A + PA is presumed to be known and constant throughout a homogeneous(V. THERMOELECTRIC PROCESSES AND MATERIALS)starting sample, N d + nd, the donor concentration, and hence the Cu concentration, canbe determined from conductivity data. Moreover, it can be shown that, subject to thestated assumptions, at the point where the conductivity has its minimum value, -min'the thermoelectric power, a, is given bymk 3 1a = n ln be 2mnwhere m and m are the density-of-states effective masses of holes and electrons,p nrespectively, and k is Boltzmann's constant. Thus, there exists a good possibility ofdetermining the ratios of the pertinent effective masses in Bi2Te 3 .Inspection of the equations given above reveals that in order to exploit fully theconductivity and thermoelectric-power data, it is necessary to locate, as well as meas-ure accurately, the minimum in the electric conductivity. It is also necessary to meas-ure accurately the thermoelectric power in the region where it has a very small value.To fulfill these objectives, a four-point probe system with approximately 0. 3 mm probeseparation was constructed for conductivity measurements; and a new thermoelectricprobe is now being completed. This probe is designed around a Keithley microvolt-meter which will permit accurate determination of small values of the thermoelectricpower a.O. P. ManleyD. THERMAL CONDUCTIVITY STUDIES1. Theory and MeasurementsThermal conductivity measurements have been carried out on solid solutionsMg Pb Sn at room temperature, in order to test our theoretical predictions. Pre-2 x 1-xliminary results cover the range 0 < x < 30 per cent.If the coefficient A in the formulaK 5/4 -5/4 1/2 -1/2 T1/2 (1)giving the thermal conductivity caused by mass fluctuations (1), is chosen to fit theexperimental data for x = 10 per cent, then the results obey the theory fairly well,except for x < 5 per cent (Fig. V-l). The discrepancy can be explained if we assumethat for low Pb concentrations, Umklapp processes may also contribute to the thermalThis work is being performed at Laboratoire Central des Industries Electriques,Fontenay-aux-Roses, France.(V. THERMOELECTRIC PROCESSES AND MATERIALS)resistivity. Then the total thermal resistivity is of the formK-1 = A- 1 T-5/4 M5/4 -1/2 E1/2 T1/2 + B-1 T3/2 M7/6 p-2/3 Tf f (2)where B is the coefficient giving the thermal conductivity caused by Umklapp processesalone.It turns out that the factors Tf5/4M 5/4p-1/2 and Tf M3/ 7/6 p-2/3 have verysimilar variations, and so we can write Eq. 2 in the formK- 1 =(A-1 T1/2 1/2 + B-1 T)F (3)whereF T-5/4 5/4 -1/2If (KF) - 1 is plotted against E1/2, the points actually fall roughly on a straight line(Fig. V-2), which supports the theory.The thermal conductivity, K, of a sample is compared with that of Constantan (Ko),as shown in Fig. V-3. The sample and the reference rod are placed end to end betweena heating element and a thermostat. The system is evacuated. A silver pad keeps theheat flux uniform at the boundary between the sample and the reference rods. Thetemperature gradients are measured with two thermocouple circuits; the position of thejunctions on the rods is accurately measured. The temperature differences AT and0 150.10.05OEXPERIMENT oTHEORY10 20 30 40 50x(ATOMIC PER CENT Pb)Fig. V-l. Thermal conductivity, K, as a function ofin the material Mg 2 PbxSn 1 -xcomposition, x,(V. THERMOELECTRIC PROCESSES AND MATERIALS)HEATERREFERENCE10% (CONSTANTAN)- AgSAMPLEFig. V-2. Effect of mass fluctuation onthermal conductivity of thematerial Mg 2 PbxSn 1 -x.Fig. V-3. Experimental arrange-ment for measurementof thermal conductivity.(AT)o are deduced from the thermal emf's V and Vo, which are measured with 2-4Vaccuracy by a zero-current method.If the radiation losses are disregarded, the heat flux D in the system is conserved,and thusAT (AT) 0I k - I oKS K SO O(4)where S and S are the cross sections of the rods, measured beforehand. From Eq. 4owe obtain(AT) o  SoK=K 0 0o AT SOWe have investigated the influence of radiation losses under the pessimistic hypo-thesis that the thermal resistance contributed by radiation losses is in parallel with thatof the sample (p= K where K, f, S are the thermal conductivity, the length and crosssection of the sample, respectively). The resistance associated with radiation losses,if we assume that sample and container behave as black bodies, isATS[ (T +AT) -Twhere E is the side area of the sample.150010005xl-02 IOxO2 15x -1021/2(V. THERMOELECTRIC PROCESSES AND MATERIALS)Under our assumptions, it is easy to show that the true thermal conductivity Ktrueis related to the measured conductivity Km byK =K 1-4 Gf T 3 6uET 2 AT .. (6)true =Km K S o K S o (6)m mThe first corrective term in Eq. 6 yields a systematic error of approximately10 per cent for usual sample dimensions and room temperature; the second yields anadditional error that varies linearly with AT, which was verified by our measurements.In any event, the radiation losses are unimportant when the thermal conductivity ofthe sample is approximately 0. 1 w/ocm.2. Preparation of SamplesThe solid solutions of Se-Te, which were previously prepared, proved heterogeneous.To improve this situation, a zone-leveling apparatus has been built and is in operation.Efforts are also continuing to prepare new compounds such as WTe2, WSe2, MoTe2,MoSe 2 , and so on.P. AigrainReferences1. P. Aigrain, Thermal conductivity studies, Quarterly Progress Report No. 53,Research Laboratory of Electronics, M.I.T., April 15, 1959, p. 39; see Eq. 2.

Thermoelectric Processes and Materials

V. THERMOELECTRIC PROCESSES AND MATERIALSProf. R. B. Adler Prof. P. AigraintjR. E. Nelson L. GodefroyfJane H. Dennis J. Tavernier$O. P. ManleyA. ANISOTROPIC THERMOELECTRIC EFFECTS IN BISMUTH TELLURIDE1. TheoryIn Quarterly Progress Report No. 55 (pages 48-49), an analysis was made of aniso-tropic thermoelectric power produced in nondegenerate semiconductors by two simulta-neously competing scattering mechanisms that act upon a single type of charge carrier.Since the writing of that report, the possibility that anisotropy may arise in two-carrier systems, from mixed conduction in bands that differ in their detailed structure,has been studied carefully. The 2:1 anisotropy in bismuth was computed from the theory,with results that are in agreement with accepted experimental values, and are substan-tially identical to those published recently by Chandrasekhar (1).2. ExperimentApparatus was developed to measure thermoelectric power at room temperature insamples of Bi 2 Te 3 oriented parallel and perpendicular to the cleavage planes. Precisionof approximately lptv/°C, which is better than 1 per cent for most samples, has beenachieved.By using iodine-doped material prepared in a Bridgman furnace, it was possible toprepare a melt from which quite uniform n-type single crystals may be drawn in a crys-tal putter.Preliminary measurements of thermoelectric power at room temperature, madeon the crystals described above, show thermoelectric powers parallel to the cleavageplanes ranging from 118 to 125v/OC in different samples, and from 89 to 104 v/°Cperpendicular to the cleavage planes in the same samples. These results are reconcil-able with Goldsmid's report of a 25v/OC difference between the thermoelectric powersin the two directions for a more heavily doped zone-refined single crystal with meanthermoelectric power of 220p.v/oC.The temperature dependence of thermoelectric power and resistivity will be*This work was supported in part by the U. S. Navy (Office of Naval Research) underContract Nonr-1841(51). Reproduction in whole or in part is permitted for any purposeof the United States Government.tPart-time visiting professor in the Department of Electrical Engineering, M. I. T.SLaboratoire Central des Industries Electriques, Fontenay-aux-Roses, France.(V. THERMOELECTRIC PROCESSES AND MATERIALS)investigated along both directions in the crystals, in order to distinguish between thetwo sources of anisotropic thermoelectric power which are being considered.Jane H. DennisReferences1. S. Chandrasekhar, J. Phys. Chem. Solids 11, 268 (1959).B. MERCURY TELLURIDE EVALUATIONThe determination of the temperature dependence of thermoelectric power in mer-cury telluride is now in progress. The sample holder and heaters required for themeasurement have been designed to minimize differences between the temperaturesat the ends of the sample and at the thermocouples employed to measure these tempera-tures.Preliminary results show an n-type thermoelectric power of 130v/OC at roomtemperature, which decreases approximately linearly in magnitude as a function ofinverse temperature. The zero value occurs at approximately 200'K.R. E. NelsonC. TRANSPORT OF CONTACT MATERIALS IN BISMUTH TELLURIDEThis study was carried out by Oscar P. Manley. The results, submitted to theDepartment of Electrical Engineering, M. I. T. , May 1960, as a thesis in partial ful-fillment of the requirements for the degree of Doctor of Science, will also appear in asummary technical report of our project.R. B. AdlerD. THERMAL CONDUCTIVITY STUDIES1. TheoryAn account of the theory of thermal conductivity at temperatures above the Debyetemperature, upon which we have been reporting, is now available in a report entitled"Contribution a 1'Etude de la Conductivite Thermique de Reseau dans les Solides," byThis work is being performed at Laboratoire Central des Industries Electriques,Fontenay-aux-Roses, France.X/p =f (T)/$3 X40101-300V-I. Resistivity of Cd3As 2.RH= f(I/T)Fig.40040-30 -20-5II I I I I 15 10 10 0Fig. V-2Hall effect for CdFig. V-2. Hall effect for Cd 3 As 2.I I(V. THERMOELECTRIC PROCESSES AND MATERIALS)J. Tavernier, May 15, 1960. [A few copies are on file in the Document Room of theResearch Laboratory of Electronics. Copies are available for distribution, upon requestfrom Laboratoire Central des Industries Electriques.]2. Measurement of Thermal ConductivityThe heat-wave method of determining thermal conductivity, outlined in previousquarterly progress reports, is discussed at length in a report entitled "Mesure desConductivites Thermiques en Regime Variable," by J. C. Perron, May 15, 1960.[Copies may be obtained as indicated above.]3. Preparation and Properties of Cd3As 2An investigation of the compound Cd 3 As 2 has been initiated. This material seemsespecially promising from the thermoelectric standpoint because its electric conduc-tivity is high, whereas its thermal conductivity is expected to be rather low. The crys-tal structure of this compound, determined by Passerini, is, except for cadmiumvacancies, similar to that of Mg 2 Sn. The electrical and thermal properties of Cd 3 As 2are probably related to this special crystallographic arrangement.The compound has been prepared by cofusion of the elements in a sealed tube, witha slight excess of cadmium to prevent the formation of CdAs 2 . Rhombohedral rods andthin platelets, metallic in appearance, presumably Cd 3 As 2 , accumulated on the wallsof the tube. These small crystals, properly crushed, were used to obtain back-reflection powder patterns that confirmed Passerini's results.Electrical measurements (resistivity (p), Hall effect (R), and thermoelectric power(Q)) have been made on polycrystalline samples obtained by re-melting the crystallitesmentioned above in vacuum, at approximately 700'C.Nickel was electroplated on the electrode areas, and conventional tin soldering wasused to fix the electrodes on the nickel-plated areas.Table V-1. Properties of Cd 3 As2'T = 80'K T = 273 0 Kp(ohm-cm) 18 X 10- 6 62 x 10- 6R(cm3/coulomb) 0. 16 0. 33N = 1/Re(cm - 3 ) 4 X 101 9  2 X 1019J = R/p(cm2/v-sec) 8, 900 5, 300Q(pV/degree) 50(V. THERMOELECTRIC PROCESSES AND MATERIALS)The results obtained with one of the most recent samples prepared are shown inTable V-l and plotted in Fig. V-l (p versus T), and Fig. V-2 (R versus i/T).The carrier concentrations N and mobilities 4 in Table V-1 were calculated underthe assumption that only one type of carrier is present.It should be noted that the carriers appear to be electrons from the sign of thethermoelectric power, whereas the Hall effect would indicate a p-type material. Thisanomaly, together with the anomaly concerning the carrier concentration, is now beinginvestigated. At least, the high mobility that has been reported by others has beenconfirmed.Much more work is needed to understand the electrical properties of this especiallyinteresting compound.J. Tavernier, P. Aigrain

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Thermoelectric Processes and Materials

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