Glass transition temperature shift under pressure for some semiconducting glasses

Journal of Non-Crystalline Solids 21 (1976) 215-224 © North-Holland Publishing Company

GLASS TRANSITION TEMPERATURE SHIFT UNDER PRESSURE FOR SOME SEMICONDUCTING GLASSES B.A. J O I N E R * and J.C. THOMPSON University of Texas, Austin, Texas 78712, USA

Received 29 July 1975 Glass transition temperatures (Tg) were measured as a function of pressure for the semiconducting glasses As2S3, TelsGe2As3 and Cd6Ge3ASl 1, using changes in the transit time of an ultrasonic pulse to detect the glass transition. The measurements of Tg as a function of pressure were compared to the predictions of the free volume theory of the glass transition. For As2S3 and TelsGe2As3, Tg first increased and then levelled oft" with increasing pressure, as predicted by the free volume theory. The amorphous semiconductor Cd6GeaAs I 1 exhibited anomalous behavior: Tg first increased with pressure, but at the relatively low pressure of 1.5 kbar it began to decrease with increasing pressure

1. Introduction In recent years the electronic properties of amorphous semiconductors have attracted great interest, but relatively little research has been done on their properties as glasses. However, it has been pointed out by de Neufville and Rockstad [1 ], Kastner [ 2 - 4 ] and others that a relationship exists between the glass transition temperature (Tg) and the band gap of semiconducting glasses, providing a link between the mechanical properties typified by Tg, and the electronic properties of the glass. This paper seeks to examine this relationship using pressure as the experimental parameter, and to compare the pressure dependence of Tg with that of other glasses. We have measured Tg as a function of pressure for the semiconducting glasses As2S 3, Cd6Ge3ASll and TelSGe2As 3. We compare the pressure dependence of Tg with that of the band gap and with the pressure dependence of Tg of other materials.

* Robert A. Welch pre-doctoral Fellow.

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2. Experimental A Harwood * pressure vessel and a locally built intensifier were used for the pressure measurements. The pressure medium was nitrogen. The temperature was measured with a chromel-alumel thermocouple. The glasses were made from the appropriate elements (99.99% pure; Cd 99.9% pure) in evacuated quartz ampoules in a rocking tube furnace. The glasses were held for at least 24 h at 800°C for TelSGe2As 3 and 850°C for Cd6Ge3ASll before being rapidly quenched in air. Typical sample size was 2 0 - 3 0 g. The samples were then cut and polished to a cylinder with a length of approximately 1 cm. The As2S 3 samples were purchased from the Servo Corporation **. A standard ultrasonic pulse echo technique [5] was used to measure the transit time of a 10 MHz longitudinal sound pulse in the glass as a function of temperature at constant pressure. The quartz transducers were bonded to the glass sample with Permatex no. 2 * * * (a non-hardening automobile gasket compound) diluted slightly with ethanol. The glass transition was then located by the change in slope of the ultrasonic transit time as a function of temperature as previously reported by Litovitz and Lyon [6]. This procedure is illustrated in fig. 1, in which the transit time as a function of temperature is shown for Tel5Ge2As 3 at atmospheric pressure for a heating rate of l°C/min and a cooling rate of 2°C/min. The glass transition on the heating

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Fig. 1. Ultrasonic transit time as a function of temperature for TelsGe2As3 at atmospheric pressure. The arrows indicate heating and cooling cycles. * Harwood Engineering Co., Walpole, Massachusetts. ** Servo Corporation of America, Hicksville,New York. *** Distributed by Woodhill Chemical Sales Corporation, Cleveland, Ohio.

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curve is located by the increase in slope of the transit time as a function of temperature, using a straight-line approximation to the region on each side of the transition. The small region of flattening just below Tg occurs because the glass is being heated more slowly than the quench rate at which the glass was formed [7]. On the cooling curve Tg is located using the derivative of the transit time with respect to temperature as illustrated in fig. 2. Again, straight-line approximations to the region on each side o f the transition are to locate the glass transition. This procedure for locating Tg yields the low-temperature side of the transition rather than the middle. Hence, Tg's measured on the cooling curves will be lower than those

measured on the heating curves. In any case, the temperatures so measured may not agree with those measured by DTA, etc.

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Fig. 3. Ultrasonic transit time as a function of temperature for TelsGe2As a at 3.4 kbar (cf. fig. 1).

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Fig. 4. Ultrasonic transit time as a function of temperature for Te is Ge2 As3 at atmospheric pressure for a glass formed by cooling under a pressure of 3.4 kbar (cf. fig. 1). The change in behaviour from that shown in fig. 1 is due to expansion of the densified glass upon heating.

If the same material is then heated at 3.4 kbar, Tg can be found from the transit time as a function of temperature as shown in fig. 3. The downward trend in the transit time above 75°C is due to the densification of the glass. Above this temperature, the viscosity of the glass has been reduced to the point that the glass will increase in density toward the value it would have, had it been formed under that pressure. Since all the data were taken at a constant heating or cooling rate, and densification or expansion is a kinetic process, the transit time is a function of time as well as temperature. Thermal history is therefore an implicit parameter in figs. 1 - 3 . Again, Tg is located on the heating curve by the increase in slope of the transit time as a function of temperature and from its derivative curve upon cooling. When the sample is reheated at atmospheric pressure, the sample will expand back toward its original density. The transit times in fig. 4 demonstrate the increase in volume above ~75°C. Here, the glass transition is obscured by the simultaneous expansion of the sample. Using this procedure, Tg was determined in a consistent way as a function of pressure for the semiconducting glasses As2S3, Cd6Ge3As 11 and TelSGe2As 3.

3. Results In fig. 5, Tg measured as a function of pressure is shown for TelsGe2As 3 on both heating and cooling curves; Tg increases with pressure and then levels off with increasing pressure.

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In fig. 6, Tg for As2S 3 is shown as a function of pressure at a heating and cooling rate of 2°C/min. Again, Tg increases with pressure and then levels off with increasing pressure. Tg's determined on the cooling curves are less reliable than those reported for TelSGe2As 3 because of temperature control problems. This probably leads to the difference in behavior between the Tg's determined on the heating and on the cooling curve. The Tg data of Kirkinskii and Yakushev [8] are considerably different They heated the glass to about 50°C above the expected Tg and then took their data on the cooling curve at 150-200°C/min. Their atmospheric pressure value of Tg is ~25°C higher than the value obtained here, but that is expected because of I

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Fig. 6. Tg as a function o f pressure for As2S 3. ~ heating, A cooling, ~ DTA, 200°C/min cooling [81.

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their much faster cooling rates. It is uncertain whether the lack of agreement between their data and the present work should be attributed to differences in thermal and pressure history, or to differences in rates of thermal cycling, or to a combination of both. Certainly the density of the glass in their measurement was greater at each pressure than in this work owing to the higher temperatures reached above the glass transition. The density of As2S 3 is shown in fig. 7 at room temperature and atmospheric pressure as a function of the pressure under which it has been cooled from about 25°C above Tg. As expected, the density of the glass is greater than a glass formed under atmospheric pressure. Tg was also measured as a function of pressure for Cd6Ge3ASll at heating and

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Fig. 8, T g o f Cd6Ge3As 1t as a function o f pressure. Heating cycle for four pieces ~, A, o, m. Cooling cycle (not shown) exhibits similar behavior.

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cooling rates of 2°C/min; for clarity, only the data from the heating curve are shown in fig. 8. Tg initially increases with pressure in much the same fashion as for the other glasses. But at a relatively low pressure of 1.5 kbar, Tg begins to decrease with pressure. The same behavior was noted both for heating and cooling curve data. Data were taken on four pieces of this glass taken from two separate batches made some months apart. All four pieces exhibit the same behavior. The spread in the data may be an indication that the error bars are somewhat optimistic. However, there also may be minor differences of a few percent in compositions of the four pieces [9]. De Neufville et al. [10] reported only a single glass transition temperature for Cd6Ge3ASll from DTA data, so extensive phase separation is not likely.

4. Discussion

A relationship has been noted by de Neufville and Rockstad, Kastner and others between the electronic band gap and the glass transition temperature. Specifically, de Neufville and Rockstad [1] used the "connectedness" C to group various semiconducting glasses. The connectedness C was defined by C = 8 - N where/V is the average number of valence electrons. Hence C is an average coordination number for covalently bonded neighbors. For a group of semiconducting glasses with the same value of C, the band gap and Tg appear to be linearly related [ 1]. The relationship between Tg and the band gap can be understood in terms of chemical bonding arguments introduced by Kastner [2]. For instance, in Ge (C = 4) the bonding and antibonding molecular states are broadened into the valence and conduction bands in the solid. An electron excited from the valence band to the conduction band corresponds to an electron excited from a bonding state to an antibonding state. Hence, as the temperature is increased, the bonding states are fractionally depopulated; the structure of the glass is weakened; and the glass transition occurs. Thus, one would expect that factors which would change the band gap would correspondingly change Tg. The relationship is not so clear cut in the case of materials such as As2S3(C = 2.4). The structure of As2S 3 consists of covalently bonded puckered layers with van der Waals bonds between layers. Most of the necessary mobility at the glass transition is due to the weakening of the van der Waals bonds allowing mobility of segments of the layers. Based on NMR data on As2Se 3 [11 ], some covalent bonds within the layers continue to exist well above Tg. The relationships between the band gap, the lone pair states [2] and the covalent bonding states have not been completely elucidated. In As2S3, the valence band corresponds to the lone pair state of S. Hence, the process of exciting electrons from the valence band to the conduction band in As2S 3 does not directly affect the covalent bonding as it would in Ge. Yet, the lone pair electrons are no doubt

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involved in the van der Waals bonding between layers. While one would not expect a strong dependence of Tg on the band gap as in a C = 4 material, one would still expect a weak dependence of Tg on the band gap. By the above arguments, Tg would be expected to decrease if the band gap narrows under pressure. In view of the measurements of Fagen et al. [12] on the optical band gap of an alloy very similar to TelSGe2As3, its optical band gap should narrow under pressure as does As2S 3 [4]. Hence, Tg would be expected to decrease with pressure. Howe~er, in contradiction to this prediction, the glass transition is observed to increase with pressure. Perhaps, for Cd6Ge3ASll, the downward trend of Tg as a function of pressure above 1.5 kbar is a result of the band gap narrowing under pressure. However, a slight opening of the optical gap is observed as a function of pressure at room temperature in some preliminary measurements by Trotter [13]. It is not unreasonable to suggest that the band gap might be narrowing under pressure near the glass transition when the density is about 1% greater. Such a reversal is not unknown. For instance, the optical absorption edge of crystalline Ge exhibits a widening of the band gap and then at higher pressures a narrowing of the band gap with increasing pressure [14]. In considering the behavior of Cd6Ge3ASll, it should be noted that Bailey [15] measured a low value for the pressure coefficient of the bulk modulus which Anderson [16] has associated (for ionic or covalent crystals) with pressure-induced

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Fig. 9. Normalized Tg as a function of pressure. O phenol-formaldehyde resin, ® Se, • phenolphthalein, V B203, - - - - LiOAc • 10H20, - - - TelsGe2As3, - • - Cd6Ge3Asl 1, - . . . . . . As2S3.

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phase transitions. Perhaps some sort of partial phase transition is involved in the behavior of Tg. It is more instructive to compare Tg measurements with the standard theories of the glass transition. Using free volume theory, Sanchez [17] has predicted that Tg will increase and then level off with increasing pressure. Indeed, As2S 3 and TelsGe2As 3 exhibit this behavior. Unfortunately, heat capacity data and thermal expansion data are not available to allow quantitative comparison of the measurements with either the free volume theory or the configurational entropy theory of Gibbs [18]. To facilitate comparison of the pressure dependence of Tg of various glasses, consider fig. 9 which shows glass transition data for a wide variety of glasses (phenol-formaldehyde resin, B203, phenolphthalein and Se) taken from the review paper by Eisenberg [19], along with data of Williams and Angell [20] on LiOAc • 10H20. For clarity, the data of As2S3, TelsGe2As 3 and Cd6Ge3ASll from the present work are presented as lines showing the approximate behavior. The normalized slope of Tg as a function of pressure for As2S 3 and the initial slope for Cd6Ge3ASll are very much like that of a variety of other glasses, both organic and inorganic. While the initial slope of TelSGe2As 3 is considerably different, it can hardly be considered remarkable in light of Weir's [21] data on some sulfur-vulcanized rubbers which exhibit no change whatsoever in Tg with pressure up to 10 kbar. What is remarkable is that so many glasses of widely different structure, Tg, etc. have the slope of their normalized Tg's so similar. Apparently, the increase of Tg with pressure can be ascribed to the reduction in free volume due to the application of pressure. For instance on cooling, when the free volume has decreased to the point that the molecules or atoms composing the glass are unable to rearrange themselves within the time scale of the experiment, the glass transition occurs. The application of pressure reduces the free volume, thus requiring a correspondingly higher temperature to increase the free volume to the value characteristic of the glass transition at that pressure. Hence, as Sanchez [ 17] has predicted, Tg will increase with pressure. Sanchez has also predicted that at higher pressures Tg will cease to increase. One sees then that the behavior of Tg of As2S 3 and TelSGe2As 3 as a function of pressure is that expected of most glasses on the basis of free volume theory. The behavior of Tg with pressure for Cd6Ge3As 11 is unusual and unexpected and most probably is related to the specific bonding forces of that glass.

5. Conclusion

Tg was measured as a function of pressure for the semiconducting glasses As2S3, TelSGe2As 3 and Cd6Ge3ASll and compared to predictions of Sanchez from a free volume theory. For As2S 3 and Tel5Ge2As3, Tg first increased and then levelled off with increasing pressure, as predicted by Sanchez. The semiconducting glass Cd6Ge3ASll exhibited anomalous behavior: the glass

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transition temperature first increased with pressure, but at the relatively low pressure of 1.5 kbar Tg began to decrease with increasing pressure. The traditional theories of the glass transition are unable to explain this behavior. Perhaps the behavior of Tg for this material may be due to the correlation between its band gap and its Tg. However, we have not observed the clear dependence o f Tg on band gap reported by de Neufville and Rockstad where composition was the implicit parameter controlling the band gap rather than pressure as in the present work.

Acknowledgement This research was supported in part by the Advanced Projects Agency of the Department of Defense and was monitored by the US Army Research Office under Grant No. D.A. -ARO-D-31-124-73-G81, and by the Robert A. Welch Foundation, Houston, Texas.

References [1] J.P. de Neufville and H.F. Rockstad, in: Amorphous and liquid semiconductors, eds. J. Stuke and W. Brenig (Taylor and Francis, London, 1974), p. 419. [2] M. Kastner, Phys. Rev. Letters 28 (1972) 355. [3] M. Kastner, Phys. Rev. B6 (1972) 2273. [4] M. Kastner, Phys. Rev. B7 (1973) 5237. [5] R. Truell, C. Elbaum and B.B. Chick, Ultrasonic methods in solid state physics (Academic Press, New York, 1969). [6] T.A. Litovitz and T. Lyon, J. Acoust. Soc. Am. 30 (1958) 856. [7] G.O. Jones, Glass (Chapman and Hall, London, 1971). [8] V.A. Kirkinskii and V.G. Yakushev, in: Esperimental 'nye Isseldovaniia po Mineralogii, eds. A.A. Godovikov and V.S. Sobolev (Novosibirsk 1969-1970), p. 60. [9] N.S. Boltovets and S.G. Konnikov, Elek. Tekh. Nauch. - Tek. Sb. Mater. 1 (1972) 98-100 (abstract in Chem. Abstr. 79, abstract 117865h). [ 10] J.P. De Neufville, Final Technical Report (Advanced Research Projects Agency, 1973), prepared by Energy Conversion Devices, Inc., Contract DAHC 15-70-C-0187. [11] S.G. Bishop and P.C. Taylor, Solid State Commun. 11 (1972) 1323. [12] E.A. Fagen, S.H. Holmberg, R.W. Seguin, J.C. Thompson and H. Fritzsche, in: Proceedings of the 10th International Conference on the Physics of Semiconductors, eds. S.P. Keller, J.C. Hensel and F. Stern. (US Atomic Energy Commission. National Technical Information Service CONF-700801, Springfield, Virginia, 1970) p. 672. [13] D. Trotter, private communication (1975). [14] W. Paul and D.M. Warschauer, in: Solids under pressure, eds. W. Paul and D.M. Warschauer (McGraw-Hill, New York 1963), p. 179. [15] K.E. Bailey, Private communication (1975). [16] O.L. Anderson, J. Geophys. Res. 75 (1970) 2719. [17] I.C. Sanchez, J. Appl. Phys. 45 (1974) 4204. [18] M. Goldstein, J. Phys. Chem. 77 (1973) 667. [19] A. Eisenberg, J. Phys. Chem. 67 (1963) 1333. [20] E. Williams and C.A. Angell, J. Polym. Sei. B11 (1973) 383. [21] C.E. Weir, J. Res. Nat. Bur. Stand. (US) 50 (1953) 311.