Low-temperature specific heat of amorphous and crystalline Te0.81Ge0.15As0.04

Journal of Non-Crystalline Sohds 27 (1978) 1-8 © North-Holland Pubhshmg Company

LOW-TEMPERATURE SPECIFIC HEAT OF AMORPHOUS AND CRYSTALLINE Teo 8tGeo. I sAso.o4 M. JIRMANUS, J.A. GERBER * and H.H. SAMPLE ** Department o f Phystcs, Tufts Umversity, Medford, Massachusetts 02155, USA and L.J. NEURINGER Francts Bitter National Magnet Laboratory, Massachusetts Institute o f Technology, Cambridge, Massachusetts 02139, USA Recewed 2 February 1977 Revised manuscript received 17 May 1977

We have measured the specific heats of amorphous and crystalline specimens o! Teo. 81Ge0.15As0.04 between 0.2 and 20K, and of crystalhne Te0.93As0.07 between 1 and 20K Amorphous Te0.81Ge0.15Aso.04 shows a low-temperature hnear specific heat anomaly whose magnitude, 0 027 mJ/mol-K2, is similar to that of other amorphous insulators. Crystalhne Teo.81Ge0. I sAs0.04 exists as a two-phpse material comprised of GeTe and As-doped Te The specific heat of this materml is analyzed in terms of a weighted average of the properties of its two constituents.

1. Introduction The semiconducting ternary alloy Te0.81Geo.lsAso.oa (hereafter referred to as TGA) can exist in either an amorphous or crystalhne phase. The electrical properties o f the two phases are quite different; the amorphous phase is highly resistive while the crystalline phase is a relatively good conductor [1,2]. Thin-film devices made from this material have been shown to exhibit reversible electronic memory switching behavior by apphcation o f suitable voltage pulses [3] which convert small regions o f the f'llm from the amorphous to the crystalline phase. In bulk specimens, either the amorphous or the crystalline phase can be stabilized throughout the entire sample by the appropriate heat treatment [2]. Extensive studies by the present authors [4,5] and by others [6,7] have been made in order to understand the * Present address: Department of Physics, Umversity ol Nebraska, Lincoln, Nebraska 68588, USA. ** Visiting Scientist, Francis Bitter National Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

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M Jirmanus et al / LTspeciJic heat of amorphous and crystalline TGA

structural and electrical properties of this material and of similar bistable alloys. In many systems which have both amorphous and crystalline phases (e.g. SiO2, Ge, Se, etc.) it has been found that the short-range structural differences between the two phases are slight. This is not the case, however, in bulk specimens of TGA or in other T e - G e - A s alloys. While the amorphous phase of TGA is believed to be an approximately random arrangement of atoms, the crystalline phase has been shown to consist of alternating laminas of GeTe and Te, with the As occurring primarily in the Te regions [5,6,8]. The widths of these laminas are on the order of 0.1/am, depending on heat treatment. Thus the physical properUes of crystalhne TGA might be expected to approximate a weighted average of the properhes of GeTe and As-doped Te, and to bear little relationship to the properties of the amorphous phase. In this paper we report specific heat measurements made on bulk specimens of both amorphous and crystalline TGA in the temperature range 0.2 ~< T~< 20 K. The results for the amorphous phase are compared to those for other amorphous sohds both below and above 1 K. The crystalline phase results are analyzed m terms of a composite GeTe-Te structure. To accomplish this analysis it was necessary to measure the specific heat of Teo.93Aso.oT, a composition close to that of the Te-reglons of crystalline TGA. We note that crystalline TGA Is a superconductor below T = 0.87 K. The superconducting properties are discussed in detail elsewhere [8].

2. Experimental 2.1. Samples

Samples were prepared from 99.999% purity starting materials in fused silica ampoules. Sample preparation procedures have been discussed in detail previously [5,8]. The amorphous specimens of TGA, produced by water quenching of the melt, are very brittle. They show no evidence of crystallinity on the basis of their scanning electron micrographs (SEM) and X-ray powder patterns [5]. The electrical resistivity of the material is about 3 × 104 ~-cm at room temperature and is greater than 107 ~-cm below 77 K [8]. The crystalline TGA specimens are produced by heat-treating amorphous material [8]. X-ray and SEM examination show these samples to consist of alternating Te and GeTe laminas about 0.1 /am wide. While the Te X-ray lines agree well with accepted values [9], the GeTe lines indicate that these regions have undergone an approximately uniform rhombohedral lattice distortion. In our crystalline T G A specimens the GeTe rhombohedral angle is 86.5 + 0.5 ° as compared to 88.35 ° for bulk GeTe [8]. At 4.2 K, the electrical resistivity of the crystalline material ~s about p = 4.8 × 10 -4 ~-cm and the Hall coefficient is Rrl = 7.4 × 10 -2 cm3/C. X-ray powder patterns of the Teo.93Aso.o7 sample yielded sharp Te lines with a few faint lines produced by As2Te3. No SEM or electrical measurements were made

M Jtrmanus et al. / L Tspecific heat o] amorphous and co,stalhne TGA Table 1 Low-temperature specific heat parameters for TGA and Te0.93As0.07. Sample amorphous TGA No. 1 a) No 2 a) crystalhne TGA No 3 No. 4 crystaUlne Teo 93As0.07

Mass (g)

Measurement range (K)

3, (mJ/mol-K 2)

A (mJ/mol-K4)

811 13.1 6.13 5.36

02 - 22

0027-+ 0005

1.22-+006

1.2 -20

0.000 +- 0 03

1.22 -+ 0.06

11.0 16.6

0.27- 2.5 b) 1.1 -20

0.47 +- 0.02 0.52 -+ 0 02

0.47 -+ 0.03 0.47 -+0.03

17.4

1.2 -20

0 04 +-0 02

0.54 +-0.02

a In each temperature range, two &lferent amorphous samples prepared m the same ampoule gave identical specific heat results and are not dlstingmshed For sample No. 2, the data do not extend to sufficiently low temperature to make a rehable determination of 3'. b bor temperatures less than 0.87 K, measurements were carried out m an apphed magnetic field of 1 T m order to suppress the superconducting anomaly (ref. [8]). on this sample. However, resistivity and Hall coefficient experiments performed on a specimen of composition Te0.9sAs0.0s at 4.2 K yielded values o f p = 2.5 × 10 - 3 I2-cm and R H = 0.28 cm3/C [4]. The various samples used for the specific heat measurements are hsted in Table 1. Sample Nc 3 is one of the samples used previously for study of the superconducting properties of crystalline TGA [8]. 2.2. Measurement techniques Specific heat measurements were made in two separate cryostats, depending on the temperature range. Measurements in the range 1 - 2 0 K were made in a cryostat [10] using a standard pulse technique with heat pulse durations of 3 0 - 6 0 s. Thermometry for this cryostat is based on specific heat measurements of high-purity copper specimens (see ref. [10] for details). For the present series of measurements, the separately measured addenda heat capacity always constituted less than 50% of the total. The resulting accuracy of the present specific heat data taken in this cryostar is estimated to be 5% at the lowest measurement temperatures, improving to better than 2% above 1.5 K. For measurements in the temperature range 0 . 2 - 2 . 5 K a calorimeter employing a modified heat-pulse technique was used [8]. The operation of this cryostat was checked by first measuring the specific heat of pure copper. The results agreed with accepted values to within 5%. In addition, we measured a 6.67 g specimen of SiO~ * Spectrosd B, Thermal American Fused Quartz Co.

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M. Jtrmanus et al / LTspecific heat o] amorphous and crystalline TGA

m the temperature range 0.25-2.5 K. Our SiO2 results agreed with those of Zeller and Pohl [11 ] to within 5% at all temperatures. On the basis of these two checks, an accuracy of 5% is assigned to all specific heat measurements made in this lowtemperature cryostat. This error estimate includes the negligible uncertainty introduced by the 0.03 g addenda, which was measured in a separate experiment (see ref. [8] for details). 3. Results

At the lowest temperatures the specific heat data for each of the samples were fit to equations of the form (1)

Cp= 3"T + A T 3 .

The coefficients 3' and A obtained from eq. (1) are listed in table 1. For the values in table 1, 1 mol is defined as the average gram-atomic weight of the alloy, namely 117.2 g for Teo.stGeo.lsAso.o4 and 123.9 g for Teo.93Aso.o7 . From table 1 it is apparent that there is good agreement between the results for similar samples measured in the two cryostats. The lattice specific heats for crystalline and amorphous TGA are plotted over the entire temperature range m fig. 1 as (Cp - 3"T)/T 3 versus T. The value of 3' listed in table 1 were used in making this plot, except for sample No. 2, where a value 3' = 0.027 mJ/mol-K 2, as for sample No. 1, was assumed. On this plot, the error bars correspond to an uncertainty of +5% in the total specific heat. The dashed lines indicate the extrapolations to T = 0 implied by the coef-

q

2.2 -- 2.C "~ 1.8 I

(u 1.6

i

[Teo,81Geo.15

1

i

I

i

ASo.04] #itJ~l%%

Amorphous /

•

7-

'~°6r°4r°.... o21-i- ~~Crystalllne o.I

0.2

0.5

I

T(K)2

5

Io

2O

Fig. I. (Cp - ?T)/T 3 for amorphous and crystalline TGA. +, sample No. 1 ; o, sample No. 2; D, sample No. 3; m, sample No. 4. The dashed lines are extrapolations to T = 0; the solid hne through the crystalline data is explained in the text.

M. Jirmanus et al / L T specifie heat o f amorphous and crystalhne TGA

085 ~080'

5

[ I [fL_.~ / \ ILTeo93Aso07] / # ~ t f

r

I

I

[

r

_oO ~'o 75 o7o i

7- o

65

-

~-,~" 0 60 ~0.55 050

i

I 2

I I I I IIII 3 4 5 678910 T (K)

i I 2O

Fig. 2. (Cp - ?T)/T 3 for Teo.93As0.07. Also shown are results for pure crystalline Te. - , ref. [12] and., ref [131, assuming 3' = 0. ficients A in table 1. The solid line through the crystalline data is discussed below. The specific heat results for the Teo.93Aso.07 sample are plotted in fig. 2 as (Cp - 3"T)/T 3 versus T, using the value of 1' in table 1. In fig. 2, we have included the results o f Smith [12] and of Slansky and Coulter [13] for pure crystalline Te. At low temperatures, Smith's value o f A = 0.542 mJ/mol-K 4 for pure Te is in excellent agreement with our value of A for Teo.93Aso.oT. Smith observed no linear 3'T term in his measurements down to 1 K. Consequently, we have taken 3' = 0 for both sets of pure Te results in plotting fig. 2. At higher temperatures, our Teo.93Aso.o7 results deviate from the Te curve by as much as 8%, although the general temperature dependence o f Cp is very similar for both materials. Some of this discrepancy may be due to inaccuracies in our scaling of Smith's results from his graph of the Debye temperature.

4. Discussion 4.1 A m o r p h o u s T G A

Linear specific heat anomalies have been observed at temperatures below 1 K in a variety of amorphous insulators [11,14], with values of 3' in the range 0.02-0.1 mJ/mol-K 2 * It has been suggested [11,14] that the existence of this anomaly, * We have converted the values of 3' (in erg/g-K2) for the materials listed in ref. [14] to mJ[ mol-K2 by multiplying them by the average gram-atomic weight of the substance. The 3" values so obtained thus specify the hnear heat capac]ty per average atom.

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M. Jirmanus et al / L T spect]~c heat o f amorphous and crystalline TGA

and an accompanying anomalous behavior of the low-temperature thermal conductivity, may be a universal feature of glass systems. Our measurements on amorphous TGA further support this suggestion. Moreover, our value of 7 = 0.027 mJ/mol-K 2 is comparable to those for the other amorphous solids. We note that if, as is common in the literature, units of erg/g-K 2 are used then TGA has one of the smallest values of 7(2.3 erg/g-K2) reported to date for an amorphous insulator. As indicated in fig. 1, the specific heat of amorphous TGA is well represented by eq. (1) for T ~ 1.3 K. At higher temperatures, a relatively rapid rise in (Cp - 7 T ) / T 3, typical of amorphous solids, [15] is observed. This rise is much more rapid than for the crystalline form. However, as mentioned earlier, the very large differences in structure between the two froms make it difficult to compare their properties. Stephens [14] and others have pointed out another salient feature of the specific heats of amorphous solids. Namely, they exhibit a T 3 contribution, which is greater than the value derived from the Debye model based on experimental sound velocities. Unfortunately, our attempts to measure sound velocities m amorphous TGA specimens were unsuccessful. This is probably due to the many microcracks and other imperfections which are present as a result of the quenching treatment used to prepare the specimens. 4.2. Crystalline TGA

We analyzed the crystalline specific heat as a simple weighted average of the specific heats of GeTe and As-doped Te. For this purpose we used previous measurements made on GeTe specimens both below [16] and above [17] 1 K as well as our own measurements on Te0.93Aso.o7. We also assumed that all the As ~s associated with the Te regions of crystalline TGA. Under these assumptions the specimen is comprised of 30 at% of GeTe and 70 at% of Teo.94Aso.o6. The latter composition is very close to that of the Teo.9aAso.o7 sample which we measured. We first consider the lattice contribution to the specific heat Cp - 7T. From his measurements on a Teo.siGeo.49 specimen in the temperature range 0.1 ~< T ~ 1.1 K Feingold [16] deduced a value 0D = 166 -+ 3 K for the Debye temperature of GeTe. This corresponds to value of A = 0.54 mJ/mol-K 4. For the As-doped Te regions, we use our experimental value of A = 0.21 mJ/mol-K4 obtained from the Teo.93Aso.o7 specimen. This value of A is the same as that for pure Te. Thus the calculated value of A for TGA is (0.30)(0.21) + (0.70)(0.54) = 0.44 mJ/mol-K4, m good agreement with our experimental value of 0 47 -+ 0.03 mJ/mol-K 4. Furthermore, we have used the GeTe results of Lewis [17] in the range 1 - 2 0 K and the Teo.93Aso.o7 results of fig. 2. The calculated weighted average specific heat of TGA we obtain is shown by the solid line in fig. 1. As may be seen there is good agreement with the data, especially at the higher temperatures. It thus appears that the lattice specific heat of TGA is well represented by a simple sum of the contributions from its constituents, GeTe and As-doped Te. A similar analysis of the electronic specific heat coefficient for crystalline TGA,

M Jlrmanus et al / L Tspeclflc heat o] amorphous and crystalhne TGA

7

taking account o f its two-phase nature, is not as successful. Goodman and Marcuccl [16] reported 3' values for Te-doped GeTe ranging from 0.57 to 0.67 mJ/inol-K 2 * The higher value corresponds to a Teo.siGeo 49 specimen having a carrier concentration p = 1.52 × I021 cm - 3 and a carrier effective mass m~] = 2.2 mo. We do not know the exact carrier concentration o f the GeTe regions in our TGA specimens. However, Hall coefficient measurements on various crystalline T e - G e alloys [4] indicate a maximum concentration o f p = 1.8 X 1021 cm -3, irrespective o f the Te doping. Assuming the GeTe regions have p less than or equal to this value, and assuming a one-band model as did Goodman and Marcucci, we calculate an upper limit o f 3' = 0.71 mJ/mol-K 2 for the GeTe regions o f our crystalline TGA speci. mens. For the As-doped Te regions we use the value 3' = 0.04 -+ 0.02 mJ/mol-K 2 obtained by direct measurement o f Teo.93Aso 07 (see table 1). Moreover, this value is qmte reasonable on theoretical grounds. To demonstrate this, we assumed (a) a parabohc band with masses mll ~- 0.25 mo and m i ~- 0.16 too, (b) a value for the carrier concentration p = 2.2 × 1019 cm -3 apphcable to Teo 95As0.o5 [4] and (c) 2.3 equivalent maxima m the Brillouin zone after Neurlnger et al. [18]. Under these assumptions, the calculated value of 3' is 0.03 mJ/mol-K 2, in excellent agreement with the experimental value for Te0.93Aso.07. Thus, the calculated upper hmlt for the electronic specific heat coefficient of crystalline TGA is 7 = (0.30)(0.71) + (0.70)(0.04) = 0.25 mJ/mol-K 2. This is a factor of two smaller than the experimental values in table 1. The reason for this discrepancy is not entirely clear. The Te regions contribute only a small amount to 3, in the above calculation, so we believe the discrepancy must be due to the GeTe regions. For the one-band model used by Goodman and Marcucci, 3' is proportional to pl/3. It would thus require an increase o f p by nearly an order of magnitude to ~ 1 . 4 × 1022 cm - 3 to account for the discrepancy m 3'. Such a large carrier concentration for the GeTe regions cannot be produced by excess Te doping [4]. Nor is it likely due to As doping o f the GeTe regions, since Adler et al. [6] have shown that the As in this material is associated primarily with the Te regions. We believe a more reasonable explanation is that the uniform GeTe lattice strain observed m the X-ray studies o f our specimens alters the electronic band structure sufficiently to increase the effective mass o f the carriers m* by a factor o f two. Since 3' is proportional to m*, this would account for the enhanced electronic specific heat in TGA. Further support for this view is given by the enhanced superconducting transition temperatures which are observed for TGA specimens [8].

* Since both refs. [16] and [17] define 1 mol of GeTe as Avogadro's number ofGeTe molccules (or 200.2 g) we have divided their reported specific heats by a factor of two to compare them with our results in which we take 1 mol to be Avogadro's number of atoms (or 100.1 g in the case of GeTe).

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M Jirmanus et al / L Tspectfic heat o] amorphous and crystalhne TGA

Acknowledgement The authors gratefully acknowledge the expert advice and assistance of Mr. James Alexander in all phases of the sample preparation procedures and X-ray analysis. The research was supported by the National Science Foundation, Grant No. DMR74-23480. The Francis Bitter National Magnet Laboratory is also supported by the National Science Foundation.

References [1] [2] [3] [4]

S.R. Ovshinsky, Phys. Rev. Letters 21 (1972) 1450. H. Fritzsche and S.R. Ovshinsky, J. Non-Crystalline Sohds 2 (1970) 148. E.J. Evans, J.H. Helbers and S.R. Ovshlnsky, J. Non-Crystalline Solids 2 (1970) 334. H.H. Sample, L.J. Neuringer, J.A. Gerber and J. deNeufville, m Conduction in Low Mobillty Materials, ed. N. Klein, D.S. Tannhauser and M. Pollack (Taylor and Francis, London, 1971), p. 329. [5 ] H.H. Sample, L.J. Neurmger, J.A. Gerber and J. deNeufvdle, 1. Non-Crystalhne Solids 8/9 (1972) 50. [6] D Adler, J.M. Franz, C.R. Hewes, B.P. Kraemer, D.J. Sellmyer and S.D. Senturia, J. NonCrystalline Solids 4 (1970) 330. [7] R. Pinto, J. Non-Crystalline Solids 6 (1971) 187. [8] J.A. Gerber, H.H. Sample and L.J. Neuringer, J. Appi. Phys. 47 (1976) 2134. [9] ASTM Powder Diffraction File (American Society for Testing and Materials, Philadelphia, 1963). [10] M. Jlrmanus, H.H. Sample and L.J. Neurmger, J. Low. Temp. Phys. 20 (1975) 229. [ 11 ] R.C. Zeller and R.O. Pohl, Phys. Rev. B4 (1971) 2029. [12] P.L. Smith, Conf. de Phys. de Basses Temperature (Institut International du Froid, Paris, 1955) p. 281. [13] C.M. Slansky and L.V. Coulter, J. Am. Chem. Soc. 61 (1939) 564. [141 R.B. Stephens, Phys. Rev. B8 (1973) 2896, and references thereto. [15] A.J. Leadbetter, J. Phys. Chem. Solids 9 (1968) 1. [16] L. Feingold, Phys. Rev. Letters 13 (1964) 233; B.B. Goodman and S.G. Marcuccl, Ann. Acad. ScL Fenn. A VI (1966) 86. [17] J.E. Lewis, Phys. Letters 47A (1974) 404. [18] C. Guthmann and J.M. Thuillier, Phys. Stat. Sol. 38 (1970) 635; L.J. Neurmger, E. Braun and G. Landwher, Proc. Int. Conf. on High Magnetic Fields and their Application, Nottingham, England, 1969 (The Institute of Physics and the Physical Society, London, 1969), p. 77; O. Betbeder-Matibet and M. Hulin, Phys. Stat. Sol. 36 (1969) 573.