Hall Effect, Thermoelectric Power and Electrical ConductivityMeasurements in Vitreous CdGexAs2*BY R. CALLAERTS T, M, DENAYER, F. H. HASHMI AND P. NAGELSSolid State Physics Dept., S.C.K./C.E.N., B-2400 Mol, BelgiumReceived 6th July, 1970A series of measurements of Hall effect, thermoelectric power and electrical conductivity havebeen performed on the vitreous CdGexAs2 having a Ge content of 0.2,0.3,0.4,0.6 and 1 mol respec-tively. The electrical conductivity has an exponential behaviour in the temperature range 185-500 Konly for the 0.6 and 1 mol composition. It deviates from the exponential behaviour at lower tempera-tures for the 0.2, 0.3 and 0.4 compositions. The thermoelectric power is positive for CdGeo.2Asz,negative for CdGeo.6Asz and CdGeIsOAsZ, whereas it changes sign for CdGeo.3As2 and CdGeo.4Asz.The Hall coefficient is negative for all compositions except for the CdGel.oAs2.The Hall mobilitiesdiffer widely for the different compositions and have the values of 1.5 x to 1.3 x 10-1 cm2 V-l s-lat room temperature.The compound CdGe,As, has been obtained in the glassy state for a varyingGe content (x = 0.02-1.3).1* The compound belongs to a ternary system basedon CdAs,, which is able to form amorphous substances when elements (e.g., Ge, T1,Sb, Si) which prevent crystallization, are added to it within certain concentrationimilts.The electrical and optical properties of vitreous stoichiometric CdGeAs, havebeen investigated earlier, but there still seems to be some doubt about the origin ofelectrical conduction in the compound.The band gap E,, as determined byGoryunova and Kolomiets from the absorption edge and from the spectral distri-bution of the photoconductivity, was 0.6 eV at room temperature. Vaipolin et aL4have measured the electrical conductivity of vitreous CdGeAs, in the temperaturerange 80-670 K and have observed an exponential temperature dependence above200 K. They have obtained Eg = 1.1 eV, assuming that the conduction is intrinsic.The authors, however, conclude from the large difference in E;Pt and E;' that theintrinsic conduction does not set in till 670 K. Tauc and coworkers have reportedmeasurements on the electrical conductivity and the thermoelectric power of amor-phous CdGeAsa. They have observed that the thermoelectric power is positive atlow temperatures and negative above 220 K.The authors explain it as a transitionfrom extrinsic to intrinsic conduction.The basic parameters such as mobility and carrier concentration still remain tobe determined. This is due to considerable difficulty in measuring low carriermobilities in high resistivity materials. This paper reports the temperature depen-dence of electrical conductivity, thermoelectric power and Hall coefficient of a numberof CdGe,As, glasses over a relatively wide range of temperatures. The aim of thestudy was mainly to extend the available Hall effect data in amorphous semiconductors.* Work performed under the auspices of the association R.U.C.A.-S.C.K./C.E.N.-f Rijksuniversitair Centrurn Antwerpen, Antwerpen, Belgium.1 on leave from the Pakistan Institute of Nuclear Sciences and Technology, Rawalpindi, Pakistan.228 VITREOUS CdGe,As2EXPERIMENTALSAMPLE PREPARATIONCdGe,Asz glasses of five different compositions, having 0.2, 0.3, 0.4, 0.6 and 1 mol ofGe respectively, were prepared from 5 N grade elements. The weighed amount of eachelement was put in quartz ampoules of 12 mm diam. which were then evacuated and sealed.The total amount of the materials was approximately 15 g.To avoid high pressures in theampoules, the temperature was slowly raised to 900°C (which is about 200°C higher thanthe melting point of the compound), and held there for 6h. To produce a completehomogeneity of the melt the ampoules were then rotated in the furnace for 8 h.Sincevitrification of compounds based on CdAs2 requires a fast rate of cooling, therefore, themelts with 0.2, 0.3 and 0.4mol of Ge respectively were quenched in air, whereas the oneswith 0.6 and 1 rnol were quenched by rapid immersion of the ampoules in ice water.Nevertheless, the bulk samples of the latter compositions consisted of a glassy and a crystallineportion. Whenever these two phases were present the boundary between them was clearlydistinguishable and specimens of millimeter sizes could easily be cut from the vitreousportions. Electron microscope examination of these samples after appropriate thinning inCP, showed no sign of crystallinity.TECHNIQUESThe electrical resistivity and the Hall effect were measured by the four probe method ofVan der Pauw.6 Specimens for these measurements were plane-parallel platelets of about5 x 5 mm area and 0.7 ~ll~ll thickness.Electrical contacts were made by fusing heated thinPt wires into the samples. The contacts showed good ohmic behaviour even at the lowesttemperature used in the measurement.The d.c. electrical resistivity was measured between 180 and 500K. The potentialdifference across different contacts (for the calculation of specific resistivity according toVan der Pauw's method), was measured above room temperature by a Dynamco digitalvoltmeter 2022 S and below room temperature by a Keithley electrometer model 640. ASefram verispot galvanometer was used to measure currents higher than 10-IOA and forcurrents lower than lo-'' A the method of the potential drop across a standard resistor wasemployed.The Hall effect measurements were carried out only above 300K.A d.c. magneticfield of 25 OOO gauss, the direction of which was reversed every 30 s, was used for all themeasurements. The residual voltage between the Hall probes, which in general do notlie on an equipotential line, was compensated with a Diesselhorst-type potentiometer.The Hall voltage was amplified by a photo-cell galvanometer amplifier or by a Fluke micro-volt amplifier (model 845 AB), and was recorded on a Kipp micrograph BD 2. The Hallvoltages were extremely small (sometimes as low as 15 pV) and great care was taken to avoidthe influence of other effects. These are mostly of thermal origin, e.g., change in thethermoelectric power at the Hall probes.' It was checked by the absence of any voltage atthe Hall probes for zero current and when the magnetic field was reversed.The thermoelectric power measurements were performed between 210 and 400 K.The specimens in the form of parallelepipeds (1.5 x 1.5 mm area and 5 mm long) weresoldered with In between two small copper blocks.This unit was then mounted with twosapphire discs on to the two large copper blocks which could be heated separately. Thesapphire slices give a good thermal contact and a high electrical insulation. Two calibratedchromel-constantan thermocouples were soldered close to the interface of the small copperblocks and the specimen. The assembly was then mounted in the inner chamber of acryostat which was evacuated and then filled with argon.A temperature gradient varyingbetween 2 and 10°C was maintained across the specimen. The thermocouple voltages weremeasured by a Dynamco digital voltmeter type 2006/D4 of 0.1 pV sensitivity. The Seebeckpotentials, for higher temperatures, were measured by a Dynamco digital voltameter 2022 Sand for low temperatures a Keithley electrometer model 602 was empIoyed. The measuredvalues were corrected for the absolute thermoelectric power of the thermocouple probesR . CALLAERTS, M. DENAYER, F. H . HASHMI AND P . NAGELS 29The resistance of the specimen was also measured simultaneously with the thermoelectricpower measurements by the Keithley 602 electrometer. The values of the specific resistivitythus obtained were in complete agreement with the ones obtained from Van der Pauw’smethod.RESULTSThe conductivity a of a CdGeo.2As2 sample, cut from the quenched material,was measured between room temperature and 450K.The room temperatureconductivity did not have the same value when it was again measured after thisthermal cycle. A decrease in the room-temperature a-value of approximately 20 %was found. A similar and even more marked effect was observed for the stoichio-metric CdGel .oAs2 composition. The difference in room-temperature a-value beforeand after the thermal cycle was of a factor of two. Further repeated thermal cyclingof the samples had no effect on the a value. Therefore all the measurements weremade on samples which were annealed for 24 h at 200°C.1 14 51 0 3 / ~ ( ~ - 1)0.2 (0, e) ; 0.3 (A) ; 0.4 (+) ; 0.6 (0, U) ; 1.0 (V).FIG.1 .-Temperature dependence of the electrical conductivity of CdGexAs2 glases ; Ge content :The measurements made on a number of samples cut from the same ingot showedreproducible results. This is shown in fig. 1 where log a is plotted against thereciprocal temperature for CdGe,As, samples containing respectively 0.2, 0.3, 0.4,0.6 and 1 mol of germanium. Moreover, the conductivity data obtained by Van derPauw’s method were in complete agreement with the ones obtained from the sampleswhich were used for thermoelectric power measurements. The ohmicity of th30 VITREOUS CdGe,As2I-V characteristics was checked at different temperatures by applying voltages upto 24 V cm-l across the samples. The conductivity was field independent even atthe lowest temperature employed in the experiment.The conductivity decreases with the increasing Ge content (fig.1) which is inagreement with the results reported by Hrubk et a2.l The temperature dependenceof the conductivity differs, however, for the different glasses. The curves ofCdGe, .0A~2 and CdGe,. ,As, have a linear 1 /T dependence in the whole temperaturerange investigated. The activation energy deduced from their slope in both thecases is 0.55 eV. The curves of the CdGeoe3As2 and CdGeom4As2, which overlapeach other, start to deviate from the linear behaviour below approximately 290 K.The straight-line portion of the curves yields an activation energy of 0.55 eV, i.e.,the same as for the higher contents of Ge.An even more pronounced deviationfrom the straight line is observed for the glass of the composition CdGe,,,As,.The activation energy in this case is 0.52 eV which is slightly lower than the othervalues. A difference in absolute value of the conductivity is sometimes observedbetween samples with the same composition but from different ingots. This effectis especially observed for the 0.2 and 1 mol composition and illustrated in fig. 1 for-1500-CdGeo,,As2 only.3 4103 /T(K - 1)FIG. 2.-Thermoelectric power as a function of the reciprocal absolute temperature for vitreousCdGexAsp ; Ge content ; 0.2 (0, a) ; 0.3 (A) ; 0.4 (+) ; 0.6 (0) ; 1.0 (V).The temperature dependence of the thermoelectric power is shown in fig.2.The Seebeck coefficient and the form of its dependence on temperature vary markedlyfor the different compositions of the glasses used. The thermoelectric power oR. CALLAERTS, M. DENAYER, I;. H . HASHMI AND P . NAGELS 31CdGe,.,As, is positive in the whole of the temperature range. For CdGe,.,As,and CdGe,,,As, a change of sign occurs at about 320 K, which is nearly the sametemperature where the conductivity starts to deviate from its linear behaviour. Onthe other hand, the thermoelectric power of the glasses CdGe,.,As, and CdGelaoAs2is always negative.The Hall coefficient data plotted as a function of the reciprocal temperature areshown in fig. 3. These measurements were performed between 300 and 500K.Below room temperature the Hall voltage could not be detected precisely due to thehigh resistance of the sample.One important feature, observed in these measure-ments, was the opposite sign for the stoichiometric composition. The sign of theHall coefficient is negative for glasses with Ge content x = 0.2, 0.3, 0.4 and 0.6,whereas it is positive for CdGe,.,As,.5FIG. 3.-Temperature dependence of the Hall coefficient of CdGexAsz glasses ; Ge content :0.2 (0, @I; 0.3 (A); 0.4 (-4-1; 0.6 (0, W); 1.0 67).The Hall mobilities calculated from the conductivity and the Hall coefficient dataare plotted in fig. 4. Their values vary widely from composition to composition.The Hall mobilities pH of compounds containing 0.3, 0.6 and 1.0 mol of Ge areindependent of temperature, whereas pHincreases slightly for CdGe, .4A~2 and decreasesslightly for CdGe, .,As2 with increasing temperature.Repeated measurementscarried out on other samples of the same ingot gave reproducible results within thelimits of experimental accuracy32 VITREOUS CdGe,As,FIG. 4.-Hall mobility as a function of temperature for vitreous CdGexAs2 ; Ge content : 0.2 (0, 40.3 (A); 0.4 (+I; 0.6 (0, W ; 1.0 (V).DISCUSSIONThe properties of amorphous stiochiometric CdGeAs,, in most of the previcstudies, have been compared with those of the corresponding crystalline materiCdGeAs, crystallizes in the chalcopyrite structure with a tetrahedr31 arrangemtof atoms and covalent bonds between them. Recently, however, Cervinka et ~1have investigated the structure of two CdGexAs2 glasses (x = 0.1 and 1.1) by X-Idiffraction. From the radial distribution curves of the atomic density they conchthat the position of the first maximum could best be interpreted by the distantbetween the atoms as determined for crystalline CdAs,.This compound hastetragonal lattice and is composed of tetrahedra formed by four As atoms with aatom in the centre. The individual CdAs, tetrahedra are bound together with 1common atoms of As and form networks. Then these are held together by ibon_ds between the atoms of As.Cervinka et al. have assumed that CdAs, forms an amorphous substance wherforeign atom, e.g., Ge, is added to it. The Ge atom will be bound to four As at0which are responsible for the binding of the neighbouring networks in pure CdAThey consider, therefore, that the amorphous CdGeAs, belongs to a broader systtof amorphous substances based on CdAs,.It seems thus obvious to compare tproperties of the amorphous CdGe,As, with those of crystalline CdAs,. Howevlthere exists a structural similarity in the short-range order of crystalline CdAs, aCdGeAs,, i.e., the lattices of both substances are made of the same unit of CdPtetrahedra.The electrical properties of crystalline CdAs, differ markedly with those o f R . CALLEARTS, M. DENAYER, F. H . HASMI AND P . NAGELS 33CdGeAs,. The latter compound has a similar band structure to that of the A"' BVsemiconductors and has a three-fold splitted valence band, i.e., consisting of a heavyhole, a light hole and a second heavy hole band.On the other hand, its electroneffective mass is very small (m* = 0.027 m0)* yielding mobility of the electronsmuch higher than that of the holes. On the contrary in CdAsz the effective massof the electrons is somewhat higher than that of the holes and both are stronglyanisotr~pic.~ The Hall mobility of electrons at 300 K is 100 and 400 cm2 V-1 s-'along the a- and c-axis respectively. O Hall mobility for holes has not been reportedso far. The forbidden gap as determined by the optical absorption is much higherfor CdAs2 (- 1 .O eV at 300 K) than for CdGeAs, (0.53 ev).Cervinka et al. assumed intrinsic conduction and deduced from conductivitymeasurements the band gap Eg for different CdAs, glasses with different contents offoreign elements.By extrapolating the dependence of Eg on the composition tox = 0, they obtained E, = 1.05 eV at T = 0 K for amorphous CdAs, which theyconsider to be in good agreement with the band gap of crystalline CdAs,.From these considerations, it seems reasonable to assume that all the glassesused in our study (including the one with 1 mol of Ge), have the same basic structure.This is strengthened by the fact that the linear parts of all the conductivity curveshave nearly the same activation energy.For a discussion of our experimental results, we compare first the thermoelectricpower data of the different glasses with the behaviour of their electrical conductivities.The slope of the conductivity curves of the compound with x = 0.2, 0.3 and 0.4increases with increasing temperature, but remains constant at high temperature.Since the slope is representative for the position of the Fermi level inside the band gap,it follows that the Fermi level shifts towards the middle of the gap and remains fixedat higher temperatures.The latter situation is already reached at the lowest tempera-ture of measurement for the CdGe,.,As,.The Seebeck coefficients of the 0.2, 0.3 and 0.4 compositions are positive inapproximately the same temperature range in which the conductivity deviate fromthe linear 1/T dependence. The experimental findings are consistent to a semi-conductor containing localized levels acting as acceptors and donors. ThFe levelsmay be due to lattice defects.The existence of such defects was proved by Cervinkaet al. They have measured magnetic susceptibility of CdGexAs2 and have found ahigh number of paramagnetic centres varying from 3 x 1019 ~ r n - ~ for 0.2 mol Geto 1 x 2OZ0 ~ m - ~ for 1.0 mol of Ge. The positive sign of the Seebeck coefiicientindicates that the number of holes is higher than the number of electrons or that thedonor-like states are outnumbered by the acceptor-like states. At very low tempera-ture the Fermi level is localized near the energy state Ec- EA. The shift of theFermi level as the temperature rises is generally due to the commencement of intrinsicconduction. A similar situation where the Fermi level lies also in the middle of thegap occurs in a highly compensated system.One may, therefore, consider that theintrinsic conduction occurs in the temperature range where the conductivity curvesare straight lines.Tauc et al. have performed conductivity and thermoelectric power measurementsdown to 140 K. They found a reversal of the Seebeck coefficient at approximately220 K which they ascribed to the transition from extrinsic to intrinsic conduction.For an intrinsic semiconductor the Seebeck coefficient is given byProviding the energy gap E,, is known, it is possible to obtain the value of p J p ,34 VITREOUS CdGe,As,and m:/rn; from the slope and the intercept of S plotted against l/T. In the presentexperiments this calculation can best be done by using the conductivity and thethermoelectric power curves of CdGe,.-,As,, since these are the curves which arelinear in the whole of the temperature range and where the negative sign of the Seebeckcoefficient indicates a higher electron to hole mobility.Using Eg0/2 = 0.55 eV andAn exact calculation of the mass ratio m;/rn: is impossible due to the uncertainty inthe temperature dependence of Eg and because the scattering mechanism is notknown. The observation that pn>puo in the CdGe,As, glasses is opposite to thatin the crystalline CdAs,.Care must be taken in deducing the intrinsic gap from the slope of the conductivitycurve. When applying classical band theory, the intrinsic carrier concentration isgiven byni = (NvNc)) exp [ - Eg0/2kT].Since (NvNc)* varies as T3, therefore it is preferable to construct a graph In (oT-3)against l/T.When applying this temperature correction, the intrinsic gap is 1 .O eVfor the glasses with 1.0, 0.6, 0.4 and 0.3 mol of Ge and 0.95 eV for the glassCdGeo,,As2. A further correction may also be necessary because of the temperaturedependence of the mobility, which is, however, not known in OUT case.The higher electron mobility implies a negative sign of the Hall coefficient in theintrinsic range. This has indeed been observed for the glasses with 0.2, 0.3, 0.4 and0.6 mol Ge. For the three first compositions, the Hall coefficient remains negativedown to the temperatures where the Seebeck coefficient has not yet changed in sign.This can easily be understood when applying the formula of RH for mixed conduction :RH = - ( n e d - pep,2)/(nePn + p e ~ p ) ~ *This expression, whch contains squared values of the mobilities, shows the onset ofintrinsic conduction at lower temperatures (pn > pP).The compound CdGe, .oAszexhibits a positive Hall coefficient. Thrs is an unexpected result since the behaviourof S ando seems to indicate that intrinsic conduction is dominant in the whole tempera-ture range. No satisfactory explanation can be offered for this sign anomaly.The Hall mobilities of the different glasses differ strongly. Measurements ofmagnetic susceptibility by Cervinka et al. have indicated the presence of a greatnumber of electrically charged centres in the CdGe,As, glasses. One would normallyexpect that these defects will act as scattering centres, leading to a large reduction ofmobility. This deccease will then depend on the scattering centre concentration,which according to Cervinka’s results, may vary from composition to composition.A. Hrubi and L. gtourae, Mat. Res. Bull., 1969, 4, 745.L. eervinka, A. Hrubi, M. Matyag, T. SimeEek, J. Skacha, L. Stourat, J. Tauc and V. Vorlitek,J . Non-Cryst. Solids, 1970,4,258.N. A. Goryunova and B. T. Kolomiets, Zhur. T. F., 1958,28, 1922.A. A. Vaipolin, g. 0. Osmanov and Yu. V. Rud’, Fiz. Tuerdogo Tela, 1965,7, 2266.Moscow, (Nauka, Leningrad, 1968), vol. 2, p. 1251.L. J. Van der Pauw, Phil@s Res. Reports, 1958, 13, 1 .N. A. Goryunova, F. P. Kesamanly and E. 0. Osmanov, Fiz. Tverdogo Tela, 1963, 5, 2031.M. J. Stevenson, Pliys. Rev. Letters, 1959, 3, 464.* J. Tauc, L. StouraE, V. VorlfEek and M. Zgvetova, Proc. 9th Int. Con$ Physics Semiconductors,’ H. J. Van Daal and A. J. Bosman, Phys. Rev., 1967,158,736.lo W. J. Turner, A. S. Fischler and W. E. Reese, Phys. Rev., 1961,121.759