- Email: [email protected]
The electrical switching and thermal behavior of bulk Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses
Journal of Non-Crystalline Solids 358 (2012) 224–228
Contents lists available at SciVerse ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
The electrical switching and thermal behavior of bulk Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses Chandasree Das a, G. Mohan Rao a, S. Asokan b,⁎ a b
Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore, India Applied Photonics Initiative, Indian Institute of Science, Bangalore, India
a r t i c l e
i n f o
Article history: Received 22 July 2011 Received in revised form 15 September 2011 Available online 12 October 2011 Keywords: Chalcogenide glasses; Electrical switching; ADSC
a b s t r a c t Bulk Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses, are found to exhibit memory type electrical switching. The switching voltages (Vt) and thermal stability of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses are found to decrease with Sn content. The composition dependence of Vt has been understood on the basis of the decrease in the OFF state resistance and thermal stability of these glasses with tin addition. X-ray diffraction studies reveal that no elemental Sn or Sn compounds with Te or Ge are present in thermally crystallized Ge–Te–Sn samples. This indicates that Sn atoms do not interact with the host matrix and form a phase separated network of its own, which remains in the parent glass matrix as an inclusion. Consequently, there is no enhancement of network connectivity and rigidity. The thickness dependence of switching voltages of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses is found to be linear, in agreement with the memory switching behavior shown by these glasses. © 2011 Elsevier B.V. All rights reserved.
1. Introduction “Electrical switching” refers to an electric-field induced transition exhibited by amorphous/glassy chalcogenides from a semiconducting OFF state to a conducting ON state [1], which can be of two types, namely memory or threshold switching. Memory switching materials retain their ON state even after removal of the field; on the other hand, threshold switching samples revert back to the initial OFF state after removal of the field. The electrical switching is fundamentally an electronic process [2] and is initiated when the field excited charge carriers fill the charged defect states and the carriers transit the sample with an enhanced mobility. Memory switching occurs in glasses which devitrify easily and is due to an irreversible amorphous-crystalline transition (phase change) induced by Joule heating in the electrode region after the initiation of switching. The structure of chalcogenide glasses exhibiting memory switching usually consists of long Te-chains in which atomic rearrangements occur more easily [3]; also certain Te based samples become vitreous easily by quenching, which is a requisite for Random Access Memory applications [4]. Some of the binary and ternary Te-based glassy systems which exhibit memory switching behavior are, Ge– Te, Si–Te, As–Te, Al–Te, As–Se–Te, Ge–As–Te, Ge–Te–Cu, Ge–Te–Ag, Ge–Te–Si [5–14] etc.
⁎ Corresponding author. Tel.: + 91 80 22932271; fax: + 91 80 23608686. E-mail address: [email protected] (S. Asokan). 0022-3093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2011.09.021
Recently, the realization on Non-Volatile Random Access Memories based on the phenomenon of memory type electrical switching, known as Phase Change Memories (PCMs), has become a reality. PCMs are considered to be more advantageous compared to conventional DRAMs or flash memories. Studies on the electrical switching behavior of chalcogenide glasses help us in identifying newer glasses which could be used for phase change memory applications [15]. In particular, studies on composition dependence of thermal properties and electrical switching parameters are necessary for the selection of proper compositions in a glassy system having easy crystallizability, good glass forming ability, good thermal diffusivity, lower switching voltages, etc., required for a good memory material. In this work, thermal and electrical switching investigations have been carried out on bulk Ge15Te85 − xSnx (1 ≤x ≤6) and Ge17Te83 − xSnx (1 ≤x ≤5) glasses. Earlier investigations on bi-layers of Ge and Snchalcogenides have revealed the possibility of obtaining multi-state behavior with enhanced thermal stability and phase change response at lower voltages [16]. The motivation behind the present study is to understand the composition dependence of switching voltages and the influence of thermal parameters on the switching voltages. 2. Experimental procedure Bulk Ge15Te85 − xSnx (1 ≤ x ≤ 6) and Ge17Te83 − xSnx (1 ≤ x ≤ 5) glasses are synthesized by the melt quenching technique. The high purity (99.999%) constituent elements in desired proportions are weighed with an accuracy of ±0.1 mg and sealed in flattened quartz ampoules, under a vacuum of 10 −5 Torr. The sealed ampoules are
C. Das et al. / Journal of Non-Crystalline Solids 358 (2012) 224–228
heated in a horizontal rotary furnace up to a temperature of 1000 °C, at the rate of about 100 °C/h. The ampoules are rotated continuously at 10 rpm for about 36 h to ensure the homogeneity of the melt and are subsequently quenched in NaOH + ice–water mixture to obtain bulk glasses. The amorphous nature of the as-prepared samples, is confirmed by X-ray diffraction. The samples are polished to a thickness of 0.3 mm and placed between a point contact top electrode and flat-plate bottom electrode, using a spring loading mechanism. The current–voltage characteristics and the electrical switching behavior have been investigated using a programmable DC source-meter (Keithley 2410 c). A constant current is passed through the sample and the voltage developed across the sample is recorded. The measurement on the I–V characteristics has been repeated at least 5 times for each sample and the switching voltages have been found to be repeatable within ±2 V. The thermal parameters, such as glass transition and crystallization temperatures of the samples are obtained by Alternating Differential Scanning Calorimetry (ADSC), using a Mettler Toledo instrument (model DSC 822 e). While a conventional Differential Scanning Calorimetry (DSC) uses a linear temperature profile, the ADSC employs a composite temperature profile in which a sinusoidal variation is superimposed on a linear ramp [17–19]. Samples in the weight range of 10–15 mg, encapsulated in Al pans are heated in argon atmosphere (flow rate of 75 ml/min). A temperature range of 50–340 °C, with a heating rate of 3 °C/min and a modulation rate of 1 °C/min, has been used. The temperature calibration is done using high purity indium. The glass transition temperature (Tg) and crystallization temperature (Tc) are measured from the reversing and nonreversing heat flow curves respectively. Typical error in the measurement of Tg and Tc is within ±2 °C. Errors are estimated using standard deviation method and error bars are included in the figures. To identify the thermally devitrified phases, two representative samples from the Ge15Te85 − xSnx and Ge17Te83 − xSnx series are sealed under a vacuum of 10 −5 Torr in a quartz ampoule and annealed at their respective crystallization temperatures for about 1 h. The annealed samples are analyzed by X-ray diffraction using a Bruker diffractometer (AXS D8 Advance).
225
known as the threshold or switching voltage (Vt), a negative resistance behavior is seen and the samples switch to a high conducting ON state. Fig. 2(a) and (b) show the composition dependence of switching voltages of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses respectively, indicating that Vt of these glasses decreases with the increase in Sn content. The total heat flow curve of one representative glassy sample, Ge17Te80Sn3, obtained from ADSC is shown in Fig. 3. Fig. 4 shows the variation of crystallization temperatures (Tc) with composition, of Ge15Te85 − xSnx (1 ≤ x ≤ 5) and Ge17Te83 − xSnx (1 ≤ x ≤ 4) glasses indicating that Tc decreases with increase in Sn content. Fig. 5 shows the variation of (ΔT = Tc − Tg), which is a measure of thermal stability, with composition for Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses. The X-ray diffraction patterns of a representative asquenched Ge17Te80Sn3 sample is shown in Fig. 6(a), confirming its amorphous nature. Fig. 6(b) and (c) show the diffraction patterns of Ge15Te82Sn3 and Ge17Te80Sn3 samples respectively, after thermal annealing. The variation of switching voltages Vt with thickness is shown in Fig. 7, which is consistent with the memory switching behavior of the samples.
3. Results The I–V characteristics of glassy samples representing the Ge15Te85 − xSnx (1 ≤ x ≤ 6) and Ge17Te83 − xSnx (1 ≤ x ≤ 5) composition tie-lines are shown in Fig. 1, which indicates that these samples exhibit an Ohmic behavior initially (OFF state). At a critical voltage
Fig. 1. I–V characteristics of Ge15Te84Sn1 and Ge17Te82Sn1 glasses representing Ge15Te85 − xSnx and Ge17Te83 − xSnx series.
Fig. 2. The variation with composition of switching voltages (Vt) of (a) Ge15Te85 − xSnx and (b) Ge17Te83 − xSnx glasses. The insets show the composition dependence of starting electrical resistance of the samples.
226
C. Das et al. / Journal of Non-Crystalline Solids 358 (2012) 224–228
Fig. 5. The variation of (Tc − Tg) of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses with Sn content. Fig. 3. The total heat flow curve of Ge17Te80Sn3 glass sample, obtained using ADSC.
4.2. Composition dependence of switching voltages 4. Discussion
The present results indicate that Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses exhibit a current controlled negative resistance behavior and memory switching. The electrical switching in both Ge15Te85 − xSnx and Ge17Te83 − xSnx samples has been found to be smooth without any fluctuations in the negative resistance zone (Fig. 1). It is well known that poor structural cross-linking, weaker bonds and more lone pair interactions favor memory switching in chalcogenide glasses [20]. The earlier investigations indicate that chalcogenide glasses with an abundance of divalent elements and having a low network connectivity/rigidity are more susceptible for local structural changes due to poor bond strength and flexibility [21]. These floppy glasses [22–25], which also have lesser thermal stability [26], lower activation energy for crystallization, etc. can permit easy creation of nucleation sites for an extended structural phase transition of the type required for memory switching [21].
It is seen from Fig. 2(a and b) that the switching voltages of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses are found to decrease with the increase in Sn content. A similar decrease in threshold voltage with metallic additives has also been observed in other Ge–Te based chalcogenide systems such as Ge–Te–Cu, Ge–Te–Ag, etc. [12]. The inset in Fig. 2(a) and (b) show the variation of initial electrical resistance with composition, indicating that the resistance in the OFF state of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses decrease with Sn content. It is well known that there is a direct empirical relationship between the switching voltages and resistance of the chalcogenide glasses [27] and the present Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses also follow this rule. Earlier studies [7,22,24,28–32] reveal that the composition dependence of switching voltage of chalcogenide glasses is determined by factors such as the resistivity of the additive element, the network connectivity, rigidity percolation etc. Normally, the switching voltages are found to decrease with the addition of more metallic additives. Such a behavior is seen in many systems, including Ge–Se–Tl,
Fig. 4. The composition dependence of crystallization temperature of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses.
Fig. 6. X-Ray Diffraction patterns of (a) as-quenched Ge17Te80Sn3 glass (b) Ge15Te82Sn3 and (c) Ge17Te80Sn3 samples annealed for 1 h at their respective crystallization temperatures.
4.1. Memory switching behavior of Ge–Te–Sn glasses
C. Das et al. / Journal of Non-Crystalline Solids 358 (2012) 224–228
Fig. 7. Thickness dependence of Vt of representative Ge15Te82Sn3 and Ge17Te80Sn3 glasses.
Ge–Se–Sb, As–Te–Tl, As–Te–Cu, etc. [33–36]. In Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses also, the addition of more metallic Sn at the expense of Te, leads to the decrease in switching voltages as the resistivity of tin is much lower than that of Te (ρSn = 11.5 μΩ cm and ρTe = 10 4 μΩ cm). The network connectivity and rigidity also play an important role in the composition dependence of switching voltages of chalcogenide glasses. The addition of higher coordinated elements increases the network connectivity and rigidity, leading to an increase in switching voltages. In general, metallic elements are considered to enter the chalcogen glassy network samples, with a four-fold or higher coordination, increasing the network connectivity [37–39]. The earlier work suggests that Sn atoms are either four-fold or six-fold coordinated in a similar Ge–Se(S)–Sn glassy system [40]. It can be therefore be assumed that Sn is four-fold or higher coordinated in Ge–Te–Sn system; the addition of higher coordinated Sn (at the expense of Te) therefore is expected to increase the network connectivity and consequently the switching voltages in the Ge–Te–Sn glassy system. However, the present results show a decrease in Vt with Sn content. Based on this, it can be concluded that the metallicity of the dopant and the resistivity factor contribute more to the composition dependence of Vt of Ge–Te–Sn samples in comparison with network connectivity. 4.3. Correlation between electrical switching and thermal properties The present ADSC studies reveal that Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses show one endothermic glass transition reaction and one exothermic crystallization reaction at Tg and Tc respectively. Further, it is seen that the crystallization temperatures (Tc) of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses decrease with the addition of Sn atoms (Fig. 4). Also, the thermal stability of these samples (Fig. 5) shows a decrease with composition which indicates that the Ge–Te glasses become more easily de-vitrifiable with the addition of Sn. The observed decrease in thermal stability also contributes for the observed decrease in the switching voltages of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses with Sn content.
227
elemental Sn or Sn compounds with Te or Ge have been found in Ge15Te82 Sn3 and Ge17Te80Sn3 glasses. When a dopant atom is added to a binary chalcogenide glass, it can form its own structural units in the system. The glass formation is enhanced, if the newly formed structural units interact with the parent glass matrix and increase the network connectivity [41]. However, if the added impurity does not interact with the host matrix, it forms a phase separated network of its own, which can remain in the parent glass matrix as a micro-inclusion. Based on the bond energy considerations [42], the possible bonds formed in this glassy system are Ge–Te, Ge–Sn, Te–Te, Te–Sn and Sn– Sn; their bonding energies (D, kJ/mol) are in the order, D (Ge–Te)= 396.7±3.3N D (Te–Sn)=338.1±6.3N D(Te–Te)=257.6±4.1N D (Ge– Sn)=230.1±13N D (Sn–Sn)=187.1±0.3. The formation of the structural network in chalcogenide glasses can be explained by the chemical bond approach as suggested by Bicerano and Ovshinsky [43]. Accordingly, in a glassy network, bonds are formed in the sequence of decreasing bond energies until all the available valencies are saturated. Also, atoms combine more favorably with atoms of different kind than with the same kind, assuming the maximum amount of chemical ordering possible. In both Ge15Te85 and Ge17Te83 base glass compositions, all the four-fold coordinated Ge atoms bond with two-fold coordinated Te atoms as the Ge–Te bond energy is highest and the glassy network is primarily constituted by the Ge–Te linkages. The Te atoms remaining after the formation of Ge–Te bonds form a network among themselves. The addition of higher coordinated Sn atoms to the Ge15Te85 and the Ge17Te83 networks, at the cost of Te atoms, can be expected to modify the networks, as Sn atoms can bond with Te atoms as well as the Ge–Te back-bone. However, in the X-ray diffraction studies on thermally crystallized Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses indicate that the interaction of Sn atoms with the Ge–Te network is not significant and they do not take part actively to enhance the network connectivity. Another possibility is that the Sn atoms randomly replace Ge atoms in the Ge–Te network, as tin can also be four-fold coordinated [44] and Ge bonds with four fold co-ordination [45]. Further, the electronegativity of Ge and Sn are 2.01 and 1.96 respectively, which are fairly closer. It is possible that the similar co-ordination and electronegativity of Ge and Sn in Ge15Te85 − xSnx and Ge17Te83 − xSnx samples lead to a random replacement of Ge by Sn, and hence there is no net increase in the overall network connectivity with the addition of Sn. The random replacement of Ge by Sn also limits the glass formation in Ge–Te–Sn system to less than 6 at.% of Sn. In the absence of the influence of network connectivity, the switching voltages of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses decrease with Sn content, as determined by the resistivity of the additive element and the decrease in thermal stability. 4.5. Variation of threshold voltage with thickness In general, the switching voltages of chalcogenide glasses vary with sample thickness (t) as t, t 1/2 or t 2, depending on whether the mechanism responsible for switching is electronic, thermal or based on carrier injection [46]; Vt is found to be proportional to t or t 1/2 in samples exhibiting memory switching with thermal origin [47]. Memory switching samples like Ge–Te–Al [48], As–Se [49], Ge–Se– Tl [50] etc. are found to show a linear variation of switching voltages with thickness, whereas in memory samples like Ge–As–Te [51], Ge– Te [5] threshold voltage varies as t 1/2. In the present Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses also, it is observed that the switching voltages vary linearly with thickness.
4.4. Thermal crystallization studies 5. Conclusions It is interesting to note from X-ray diffraction studies that the diffraction patterns of thermally crystallized Ge–Te–Sn samples can be fully indexed with hexagonal Te and hexagonal Ge–Te phases. No
Bulk Ge15Te85 − xSnx (1 ≤ x ≤ 6) and Ge17Te83 − xSnx (1 ≤ x ≤ 5) glasses exhibit memory type electrical switching. The switching
228
C. Das et al. / Journal of Non-Crystalline Solids 358 (2012) 224–228
voltages of both the series of glasses are found to decrease with Sn content. In addition, the thermal stability and OFF state resistance of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses have been found to decrease with Sn concentration, which is in agreement with the observed decrease in switching voltages with composition. Further, no elemental Sn or Sn compounds with Te or Ge are found in thermally crystallized Ge15Te82Sn3 and Ge17Te80Sn3 samples, which indicates that Sn atoms do not interact with the host matrix and form a phase separated network which remains in the parent glass matrix as a micro-inclusion. Consequently there is no enhancement of network connectivity and rigidity and no increase in switching voltages with Sn addition. Thickness dependence of switching voltages of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses is found to be linear, in agreement with the memory type of switching behavior shown by these glasses. References [1] S.R. Ovshinsky, Phys. Rev. Lett. 21 (1968) 1450. [2] D. Adler, M.S. Shur, M. Silver, S.R. Ovshinsky, J. Appl. Phys. 51 (1980) 3289. [3] S.R. Ovshinsky, K. Sapru, in: W.E. Spear (Ed.), Proceedings of the Seventh International Conference on Amorphous and Liquid Semiconductors, Institute of Physics, Bristol, 1977. [4] S.J. Yang, K. Shin, J.I. Park, K.N. Lee, H.B. Chung, Trans. EEM 4 (2003) 24. [5] E. Babenskas, S. Balevicius, A. Cesnys, A. Poskus, N. Siktorov, J. Non-Cryst. Solids 90 (1987) 601. [6] S. Balyavichyus, A. Deksins, A. Poshkus, N. Shiktorov, Fiz.Tekh. Poluprovodn. 1513 (1984) 18; Sov. Phys. Semicond. 18 (1984) 947. [7] S.S.K. Titus, R. Chatterjee, S. Asokan, A. Kumar, Phys. Rev. B 48 (1993) 14650. [8] S. Prakash, S. Asokan, D.B. Ghare, Semicond. Sci. Technol. 9 (1994) 1484. [9] R. Chatterjee, S. Asokan, S.S.K. Titus, J. Phys. D 27 (1994) 2624. [10] R. Uttecht, H. Stevenson, C.H. Sie, J.D. Griener, K.S. Raghavan, J. Non-Cryst. Solids 2 (1970) 358. [11] K. Tanaka, Y. Okada, M. Sugi, S. Iizima, M. Kikuchi, J. Non-Cryst. Solids 12 (1973) 100. [12] K. Ramesh, S. Asokan, K.S. Sangunni, E.S.R. Gopal, Appl. Phys. A 69 (1999) 421. [13] K. Ramesh, S. Asokan, K.S. Sangunni, E.S.R. Gopal, J. Phys. Chem. Solids 61 (2000) 95. [14] M. Anbarasu, S. Asokan, J. Phys. D. Appl. Phys. 40 (2007) 7515.
[15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51]
M. Wuttig, Nat. Mater. 4 (2005) 265. K.A. Campbell, C.M. Anderson, J. Microelectron. 38 (2007) 52. J.C.W. Folmer, Franzen Stefan, J. Chem. Educ. 80 (2003) 813. P. Boolchand, D.G. Georgiev, B. Goodman, J. Optoelectron. Adv. Matter 3 (2001) 703. Sindee L. Simon, Thermochim. Acta 374 (2001) 55. S.R. Ovshinsky, Phys. Rev. Lett. 36 (1976) 1469. J. Bicerano, S.R. Ovshinsky, J. Non-Cryst. Solids 74 (1985) 75. J.C. Phillips, J. Non-Cryst. Solids 34 (1979) 153. J.C. Phillips, J. Non-Cryst. Solids 43 (1981) 37. M.F. Thorpe, J. Non-Cryst. Solids 57 (1983) 355. J.C. Phillips, Phys. Rev. B 54 (1996) R6807. D. Adler, Sci. Am. 236 (1977) 36. A. Alegria, A. Arruabarrena, F. Sanz, J. Non-Cryst. Solids 58 (1983) 17. R. Aravinda Narayanan, PhD Thesis, Indian Institute of Science, Bangalore (2000). C.N. Murthy, V. Ganesan, S. Asokan, Appl. Phys. A 81 (2005) 939. S. Murugavel, S. Asokan, J. Non-Cryst. Solids 249 (1999) 145. S. Murugavel, S. Asokan, J. Mater. Res. 13 (1998) 2982. R. Aravinda Narayanan, S. Asokan, A. Kumar, Phys. Rev. B 54 (1996) 4413. B.J. Madhu, H.S. Jayanna, S. Asokan, J. Non-Cryst. Solids 355 (2009) 459. B.J. Madhu, H.S. Jayanna, S. Asokan, J. Non-Cryst. Solids 355 (2009) 2630. B.H. Sharmila, S. Asokan, Appl. Phys. A 82 (2006) 92. A.S. Soltan, A.H. Moharram, Physica B 349 (2004) 92. B.H. Sharmila, J.T. Devaraju, S. Asokan, J. Non-Cryst. Solids 326–327 (2003) 154. J.T. Devaraju, B.H. Sharmila, S. Asokan, K.V. Acharya, Phil. Mag. B 81 (2001) 583. S. Murugavel, Ph. D Thesis, Indian Institute of Science, Bangalore (1998). Steevns Mark, J. Grothaus, P. Boolchand, Solid State Commun. 47 (1983) 199. Z.U. Borisova, Glassy Semiconductors, Plenum Press, New York, 1985. R. David, Lide, CRC Handbook of Chemistry and Physics 90 Internet Version, CRC Press/Taylor and Francis, Boca Raton, FL, 2010. J. Bicerano, S.R. Ovshinsky, Proceedings of the Noble Laureates Symposium on applied quantum chemistry, D. Reidel Publishing Co., Honolulu, Hawaii, 1984. T. Fukunaga, Y. Tanaka, K. Murase, Solid State Commun. 42 (1982) 513. I. Kaban, Th. Halm, W. Hoyer, P. Jovari, J. Neuefeind, J. Non-Cryst. Solids 326&327 (2003) 120. G. Jones, R.A. Collins, Phys. Stat. Sol. (a) 53 (1979) 339. J.J. Odwyer, The Theory of Electrical Conduction and Breakdown in Solid Dielectrics, Clarendon Press, Oxford, 1973. J.R. Bosnell, C.B. Thomas, Solid-State Electron. 15 (1972) 1261. A. Giridhar, K.J. Rao, J. Non-Cryst. Solids 33 (1979) 177. M.F. Kotkata, M.A. Afifi, H.H. Labib, N.A. Hegab, M.M. Abdel-Aziz, Thin Solid Films 240 (1979) 143. H.J. Stocker, C.A. Barlow, D.F. Weirauch, J. Non-Cryst. Solids 4 (1970) 523.
Contents lists available at SciVerse ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
The electrical switching and thermal behavior of bulk Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses Chandasree Das a, G. Mohan Rao a, S. Asokan b,⁎ a b
Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore, India Applied Photonics Initiative, Indian Institute of Science, Bangalore, India
a r t i c l e
i n f o
Article history: Received 22 July 2011 Received in revised form 15 September 2011 Available online 12 October 2011 Keywords: Chalcogenide glasses; Electrical switching; ADSC
a b s t r a c t Bulk Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses, are found to exhibit memory type electrical switching. The switching voltages (Vt) and thermal stability of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses are found to decrease with Sn content. The composition dependence of Vt has been understood on the basis of the decrease in the OFF state resistance and thermal stability of these glasses with tin addition. X-ray diffraction studies reveal that no elemental Sn or Sn compounds with Te or Ge are present in thermally crystallized Ge–Te–Sn samples. This indicates that Sn atoms do not interact with the host matrix and form a phase separated network of its own, which remains in the parent glass matrix as an inclusion. Consequently, there is no enhancement of network connectivity and rigidity. The thickness dependence of switching voltages of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses is found to be linear, in agreement with the memory switching behavior shown by these glasses. © 2011 Elsevier B.V. All rights reserved.
1. Introduction “Electrical switching” refers to an electric-field induced transition exhibited by amorphous/glassy chalcogenides from a semiconducting OFF state to a conducting ON state [1], which can be of two types, namely memory or threshold switching. Memory switching materials retain their ON state even after removal of the field; on the other hand, threshold switching samples revert back to the initial OFF state after removal of the field. The electrical switching is fundamentally an electronic process [2] and is initiated when the field excited charge carriers fill the charged defect states and the carriers transit the sample with an enhanced mobility. Memory switching occurs in glasses which devitrify easily and is due to an irreversible amorphous-crystalline transition (phase change) induced by Joule heating in the electrode region after the initiation of switching. The structure of chalcogenide glasses exhibiting memory switching usually consists of long Te-chains in which atomic rearrangements occur more easily [3]; also certain Te based samples become vitreous easily by quenching, which is a requisite for Random Access Memory applications [4]. Some of the binary and ternary Te-based glassy systems which exhibit memory switching behavior are, Ge– Te, Si–Te, As–Te, Al–Te, As–Se–Te, Ge–As–Te, Ge–Te–Cu, Ge–Te–Ag, Ge–Te–Si [5–14] etc.
⁎ Corresponding author. Tel.: + 91 80 22932271; fax: + 91 80 23608686. E-mail address: [email protected] (S. Asokan). 0022-3093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2011.09.021
Recently, the realization on Non-Volatile Random Access Memories based on the phenomenon of memory type electrical switching, known as Phase Change Memories (PCMs), has become a reality. PCMs are considered to be more advantageous compared to conventional DRAMs or flash memories. Studies on the electrical switching behavior of chalcogenide glasses help us in identifying newer glasses which could be used for phase change memory applications [15]. In particular, studies on composition dependence of thermal properties and electrical switching parameters are necessary for the selection of proper compositions in a glassy system having easy crystallizability, good glass forming ability, good thermal diffusivity, lower switching voltages, etc., required for a good memory material. In this work, thermal and electrical switching investigations have been carried out on bulk Ge15Te85 − xSnx (1 ≤x ≤6) and Ge17Te83 − xSnx (1 ≤x ≤5) glasses. Earlier investigations on bi-layers of Ge and Snchalcogenides have revealed the possibility of obtaining multi-state behavior with enhanced thermal stability and phase change response at lower voltages [16]. The motivation behind the present study is to understand the composition dependence of switching voltages and the influence of thermal parameters on the switching voltages. 2. Experimental procedure Bulk Ge15Te85 − xSnx (1 ≤ x ≤ 6) and Ge17Te83 − xSnx (1 ≤ x ≤ 5) glasses are synthesized by the melt quenching technique. The high purity (99.999%) constituent elements in desired proportions are weighed with an accuracy of ±0.1 mg and sealed in flattened quartz ampoules, under a vacuum of 10 −5 Torr. The sealed ampoules are
C. Das et al. / Journal of Non-Crystalline Solids 358 (2012) 224–228
heated in a horizontal rotary furnace up to a temperature of 1000 °C, at the rate of about 100 °C/h. The ampoules are rotated continuously at 10 rpm for about 36 h to ensure the homogeneity of the melt and are subsequently quenched in NaOH + ice–water mixture to obtain bulk glasses. The amorphous nature of the as-prepared samples, is confirmed by X-ray diffraction. The samples are polished to a thickness of 0.3 mm and placed between a point contact top electrode and flat-plate bottom electrode, using a spring loading mechanism. The current–voltage characteristics and the electrical switching behavior have been investigated using a programmable DC source-meter (Keithley 2410 c). A constant current is passed through the sample and the voltage developed across the sample is recorded. The measurement on the I–V characteristics has been repeated at least 5 times for each sample and the switching voltages have been found to be repeatable within ±2 V. The thermal parameters, such as glass transition and crystallization temperatures of the samples are obtained by Alternating Differential Scanning Calorimetry (ADSC), using a Mettler Toledo instrument (model DSC 822 e). While a conventional Differential Scanning Calorimetry (DSC) uses a linear temperature profile, the ADSC employs a composite temperature profile in which a sinusoidal variation is superimposed on a linear ramp [17–19]. Samples in the weight range of 10–15 mg, encapsulated in Al pans are heated in argon atmosphere (flow rate of 75 ml/min). A temperature range of 50–340 °C, with a heating rate of 3 °C/min and a modulation rate of 1 °C/min, has been used. The temperature calibration is done using high purity indium. The glass transition temperature (Tg) and crystallization temperature (Tc) are measured from the reversing and nonreversing heat flow curves respectively. Typical error in the measurement of Tg and Tc is within ±2 °C. Errors are estimated using standard deviation method and error bars are included in the figures. To identify the thermally devitrified phases, two representative samples from the Ge15Te85 − xSnx and Ge17Te83 − xSnx series are sealed under a vacuum of 10 −5 Torr in a quartz ampoule and annealed at their respective crystallization temperatures for about 1 h. The annealed samples are analyzed by X-ray diffraction using a Bruker diffractometer (AXS D8 Advance).
225
known as the threshold or switching voltage (Vt), a negative resistance behavior is seen and the samples switch to a high conducting ON state. Fig. 2(a) and (b) show the composition dependence of switching voltages of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses respectively, indicating that Vt of these glasses decreases with the increase in Sn content. The total heat flow curve of one representative glassy sample, Ge17Te80Sn3, obtained from ADSC is shown in Fig. 3. Fig. 4 shows the variation of crystallization temperatures (Tc) with composition, of Ge15Te85 − xSnx (1 ≤ x ≤ 5) and Ge17Te83 − xSnx (1 ≤ x ≤ 4) glasses indicating that Tc decreases with increase in Sn content. Fig. 5 shows the variation of (ΔT = Tc − Tg), which is a measure of thermal stability, with composition for Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses. The X-ray diffraction patterns of a representative asquenched Ge17Te80Sn3 sample is shown in Fig. 6(a), confirming its amorphous nature. Fig. 6(b) and (c) show the diffraction patterns of Ge15Te82Sn3 and Ge17Te80Sn3 samples respectively, after thermal annealing. The variation of switching voltages Vt with thickness is shown in Fig. 7, which is consistent with the memory switching behavior of the samples.
3. Results The I–V characteristics of glassy samples representing the Ge15Te85 − xSnx (1 ≤ x ≤ 6) and Ge17Te83 − xSnx (1 ≤ x ≤ 5) composition tie-lines are shown in Fig. 1, which indicates that these samples exhibit an Ohmic behavior initially (OFF state). At a critical voltage
Fig. 1. I–V characteristics of Ge15Te84Sn1 and Ge17Te82Sn1 glasses representing Ge15Te85 − xSnx and Ge17Te83 − xSnx series.
Fig. 2. The variation with composition of switching voltages (Vt) of (a) Ge15Te85 − xSnx and (b) Ge17Te83 − xSnx glasses. The insets show the composition dependence of starting electrical resistance of the samples.
226
C. Das et al. / Journal of Non-Crystalline Solids 358 (2012) 224–228
Fig. 5. The variation of (Tc − Tg) of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses with Sn content. Fig. 3. The total heat flow curve of Ge17Te80Sn3 glass sample, obtained using ADSC.
4.2. Composition dependence of switching voltages 4. Discussion
The present results indicate that Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses exhibit a current controlled negative resistance behavior and memory switching. The electrical switching in both Ge15Te85 − xSnx and Ge17Te83 − xSnx samples has been found to be smooth without any fluctuations in the negative resistance zone (Fig. 1). It is well known that poor structural cross-linking, weaker bonds and more lone pair interactions favor memory switching in chalcogenide glasses [20]. The earlier investigations indicate that chalcogenide glasses with an abundance of divalent elements and having a low network connectivity/rigidity are more susceptible for local structural changes due to poor bond strength and flexibility [21]. These floppy glasses [22–25], which also have lesser thermal stability [26], lower activation energy for crystallization, etc. can permit easy creation of nucleation sites for an extended structural phase transition of the type required for memory switching [21].
It is seen from Fig. 2(a and b) that the switching voltages of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses are found to decrease with the increase in Sn content. A similar decrease in threshold voltage with metallic additives has also been observed in other Ge–Te based chalcogenide systems such as Ge–Te–Cu, Ge–Te–Ag, etc. [12]. The inset in Fig. 2(a) and (b) show the variation of initial electrical resistance with composition, indicating that the resistance in the OFF state of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses decrease with Sn content. It is well known that there is a direct empirical relationship between the switching voltages and resistance of the chalcogenide glasses [27] and the present Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses also follow this rule. Earlier studies [7,22,24,28–32] reveal that the composition dependence of switching voltage of chalcogenide glasses is determined by factors such as the resistivity of the additive element, the network connectivity, rigidity percolation etc. Normally, the switching voltages are found to decrease with the addition of more metallic additives. Such a behavior is seen in many systems, including Ge–Se–Tl,
Fig. 4. The composition dependence of crystallization temperature of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses.
Fig. 6. X-Ray Diffraction patterns of (a) as-quenched Ge17Te80Sn3 glass (b) Ge15Te82Sn3 and (c) Ge17Te80Sn3 samples annealed for 1 h at their respective crystallization temperatures.
4.1. Memory switching behavior of Ge–Te–Sn glasses
C. Das et al. / Journal of Non-Crystalline Solids 358 (2012) 224–228
Fig. 7. Thickness dependence of Vt of representative Ge15Te82Sn3 and Ge17Te80Sn3 glasses.
Ge–Se–Sb, As–Te–Tl, As–Te–Cu, etc. [33–36]. In Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses also, the addition of more metallic Sn at the expense of Te, leads to the decrease in switching voltages as the resistivity of tin is much lower than that of Te (ρSn = 11.5 μΩ cm and ρTe = 10 4 μΩ cm). The network connectivity and rigidity also play an important role in the composition dependence of switching voltages of chalcogenide glasses. The addition of higher coordinated elements increases the network connectivity and rigidity, leading to an increase in switching voltages. In general, metallic elements are considered to enter the chalcogen glassy network samples, with a four-fold or higher coordination, increasing the network connectivity [37–39]. The earlier work suggests that Sn atoms are either four-fold or six-fold coordinated in a similar Ge–Se(S)–Sn glassy system [40]. It can be therefore be assumed that Sn is four-fold or higher coordinated in Ge–Te–Sn system; the addition of higher coordinated Sn (at the expense of Te) therefore is expected to increase the network connectivity and consequently the switching voltages in the Ge–Te–Sn glassy system. However, the present results show a decrease in Vt with Sn content. Based on this, it can be concluded that the metallicity of the dopant and the resistivity factor contribute more to the composition dependence of Vt of Ge–Te–Sn samples in comparison with network connectivity. 4.3. Correlation between electrical switching and thermal properties The present ADSC studies reveal that Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses show one endothermic glass transition reaction and one exothermic crystallization reaction at Tg and Tc respectively. Further, it is seen that the crystallization temperatures (Tc) of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses decrease with the addition of Sn atoms (Fig. 4). Also, the thermal stability of these samples (Fig. 5) shows a decrease with composition which indicates that the Ge–Te glasses become more easily de-vitrifiable with the addition of Sn. The observed decrease in thermal stability also contributes for the observed decrease in the switching voltages of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses with Sn content.
227
elemental Sn or Sn compounds with Te or Ge have been found in Ge15Te82 Sn3 and Ge17Te80Sn3 glasses. When a dopant atom is added to a binary chalcogenide glass, it can form its own structural units in the system. The glass formation is enhanced, if the newly formed structural units interact with the parent glass matrix and increase the network connectivity [41]. However, if the added impurity does not interact with the host matrix, it forms a phase separated network of its own, which can remain in the parent glass matrix as a micro-inclusion. Based on the bond energy considerations [42], the possible bonds formed in this glassy system are Ge–Te, Ge–Sn, Te–Te, Te–Sn and Sn– Sn; their bonding energies (D, kJ/mol) are in the order, D (Ge–Te)= 396.7±3.3N D (Te–Sn)=338.1±6.3N D(Te–Te)=257.6±4.1N D (Ge– Sn)=230.1±13N D (Sn–Sn)=187.1±0.3. The formation of the structural network in chalcogenide glasses can be explained by the chemical bond approach as suggested by Bicerano and Ovshinsky [43]. Accordingly, in a glassy network, bonds are formed in the sequence of decreasing bond energies until all the available valencies are saturated. Also, atoms combine more favorably with atoms of different kind than with the same kind, assuming the maximum amount of chemical ordering possible. In both Ge15Te85 and Ge17Te83 base glass compositions, all the four-fold coordinated Ge atoms bond with two-fold coordinated Te atoms as the Ge–Te bond energy is highest and the glassy network is primarily constituted by the Ge–Te linkages. The Te atoms remaining after the formation of Ge–Te bonds form a network among themselves. The addition of higher coordinated Sn atoms to the Ge15Te85 and the Ge17Te83 networks, at the cost of Te atoms, can be expected to modify the networks, as Sn atoms can bond with Te atoms as well as the Ge–Te back-bone. However, in the X-ray diffraction studies on thermally crystallized Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses indicate that the interaction of Sn atoms with the Ge–Te network is not significant and they do not take part actively to enhance the network connectivity. Another possibility is that the Sn atoms randomly replace Ge atoms in the Ge–Te network, as tin can also be four-fold coordinated [44] and Ge bonds with four fold co-ordination [45]. Further, the electronegativity of Ge and Sn are 2.01 and 1.96 respectively, which are fairly closer. It is possible that the similar co-ordination and electronegativity of Ge and Sn in Ge15Te85 − xSnx and Ge17Te83 − xSnx samples lead to a random replacement of Ge by Sn, and hence there is no net increase in the overall network connectivity with the addition of Sn. The random replacement of Ge by Sn also limits the glass formation in Ge–Te–Sn system to less than 6 at.% of Sn. In the absence of the influence of network connectivity, the switching voltages of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses decrease with Sn content, as determined by the resistivity of the additive element and the decrease in thermal stability. 4.5. Variation of threshold voltage with thickness In general, the switching voltages of chalcogenide glasses vary with sample thickness (t) as t, t 1/2 or t 2, depending on whether the mechanism responsible for switching is electronic, thermal or based on carrier injection [46]; Vt is found to be proportional to t or t 1/2 in samples exhibiting memory switching with thermal origin [47]. Memory switching samples like Ge–Te–Al [48], As–Se [49], Ge–Se– Tl [50] etc. are found to show a linear variation of switching voltages with thickness, whereas in memory samples like Ge–As–Te [51], Ge– Te [5] threshold voltage varies as t 1/2. In the present Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses also, it is observed that the switching voltages vary linearly with thickness.
4.4. Thermal crystallization studies 5. Conclusions It is interesting to note from X-ray diffraction studies that the diffraction patterns of thermally crystallized Ge–Te–Sn samples can be fully indexed with hexagonal Te and hexagonal Ge–Te phases. No
Bulk Ge15Te85 − xSnx (1 ≤ x ≤ 6) and Ge17Te83 − xSnx (1 ≤ x ≤ 5) glasses exhibit memory type electrical switching. The switching
228
C. Das et al. / Journal of Non-Crystalline Solids 358 (2012) 224–228
voltages of both the series of glasses are found to decrease with Sn content. In addition, the thermal stability and OFF state resistance of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses have been found to decrease with Sn concentration, which is in agreement with the observed decrease in switching voltages with composition. Further, no elemental Sn or Sn compounds with Te or Ge are found in thermally crystallized Ge15Te82Sn3 and Ge17Te80Sn3 samples, which indicates that Sn atoms do not interact with the host matrix and form a phase separated network which remains in the parent glass matrix as a micro-inclusion. Consequently there is no enhancement of network connectivity and rigidity and no increase in switching voltages with Sn addition. Thickness dependence of switching voltages of Ge15Te85 − xSnx and Ge17Te83 − xSnx glasses is found to be linear, in agreement with the memory type of switching behavior shown by these glasses. References [1] S.R. Ovshinsky, Phys. Rev. Lett. 21 (1968) 1450. [2] D. Adler, M.S. Shur, M. Silver, S.R. Ovshinsky, J. Appl. Phys. 51 (1980) 3289. [3] S.R. Ovshinsky, K. Sapru, in: W.E. Spear (Ed.), Proceedings of the Seventh International Conference on Amorphous and Liquid Semiconductors, Institute of Physics, Bristol, 1977. [4] S.J. Yang, K. Shin, J.I. Park, K.N. Lee, H.B. Chung, Trans. EEM 4 (2003) 24. [5] E. Babenskas, S. Balevicius, A. Cesnys, A. Poskus, N. Siktorov, J. Non-Cryst. Solids 90 (1987) 601. [6] S. Balyavichyus, A. Deksins, A. Poshkus, N. Shiktorov, Fiz.Tekh. Poluprovodn. 1513 (1984) 18; Sov. Phys. Semicond. 18 (1984) 947. [7] S.S.K. Titus, R. Chatterjee, S. Asokan, A. Kumar, Phys. Rev. B 48 (1993) 14650. [8] S. Prakash, S. Asokan, D.B. Ghare, Semicond. Sci. Technol. 9 (1994) 1484. [9] R. Chatterjee, S. Asokan, S.S.K. Titus, J. Phys. D 27 (1994) 2624. [10] R. Uttecht, H. Stevenson, C.H. Sie, J.D. Griener, K.S. Raghavan, J. Non-Cryst. Solids 2 (1970) 358. [11] K. Tanaka, Y. Okada, M. Sugi, S. Iizima, M. Kikuchi, J. Non-Cryst. Solids 12 (1973) 100. [12] K. Ramesh, S. Asokan, K.S. Sangunni, E.S.R. Gopal, Appl. Phys. A 69 (1999) 421. [13] K. Ramesh, S. Asokan, K.S. Sangunni, E.S.R. Gopal, J. Phys. Chem. Solids 61 (2000) 95. [14] M. Anbarasu, S. Asokan, J. Phys. D. Appl. Phys. 40 (2007) 7515.
[15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51]
M. Wuttig, Nat. Mater. 4 (2005) 265. K.A. Campbell, C.M. Anderson, J. Microelectron. 38 (2007) 52. J.C.W. Folmer, Franzen Stefan, J. Chem. Educ. 80 (2003) 813. P. Boolchand, D.G. Georgiev, B. Goodman, J. Optoelectron. Adv. Matter 3 (2001) 703. Sindee L. Simon, Thermochim. Acta 374 (2001) 55. S.R. Ovshinsky, Phys. Rev. Lett. 36 (1976) 1469. J. Bicerano, S.R. Ovshinsky, J. Non-Cryst. Solids 74 (1985) 75. J.C. Phillips, J. Non-Cryst. Solids 34 (1979) 153. J.C. Phillips, J. Non-Cryst. Solids 43 (1981) 37. M.F. Thorpe, J. Non-Cryst. Solids 57 (1983) 355. J.C. Phillips, Phys. Rev. B 54 (1996) R6807. D. Adler, Sci. Am. 236 (1977) 36. A. Alegria, A. Arruabarrena, F. Sanz, J. Non-Cryst. Solids 58 (1983) 17. R. Aravinda Narayanan, PhD Thesis, Indian Institute of Science, Bangalore (2000). C.N. Murthy, V. Ganesan, S. Asokan, Appl. Phys. A 81 (2005) 939. S. Murugavel, S. Asokan, J. Non-Cryst. Solids 249 (1999) 145. S. Murugavel, S. Asokan, J. Mater. Res. 13 (1998) 2982. R. Aravinda Narayanan, S. Asokan, A. Kumar, Phys. Rev. B 54 (1996) 4413. B.J. Madhu, H.S. Jayanna, S. Asokan, J. Non-Cryst. Solids 355 (2009) 459. B.J. Madhu, H.S. Jayanna, S. Asokan, J. Non-Cryst. Solids 355 (2009) 2630. B.H. Sharmila, S. Asokan, Appl. Phys. A 82 (2006) 92. A.S. Soltan, A.H. Moharram, Physica B 349 (2004) 92. B.H. Sharmila, J.T. Devaraju, S. Asokan, J. Non-Cryst. Solids 326–327 (2003) 154. J.T. Devaraju, B.H. Sharmila, S. Asokan, K.V. Acharya, Phil. Mag. B 81 (2001) 583. S. Murugavel, Ph. D Thesis, Indian Institute of Science, Bangalore (1998). Steevns Mark, J. Grothaus, P. Boolchand, Solid State Commun. 47 (1983) 199. Z.U. Borisova, Glassy Semiconductors, Plenum Press, New York, 1985. R. David, Lide, CRC Handbook of Chemistry and Physics 90 Internet Version, CRC Press/Taylor and Francis, Boca Raton, FL, 2010. J. Bicerano, S.R. Ovshinsky, Proceedings of the Noble Laureates Symposium on applied quantum chemistry, D. Reidel Publishing Co., Honolulu, Hawaii, 1984. T. Fukunaga, Y. Tanaka, K. Murase, Solid State Commun. 42 (1982) 513. I. Kaban, Th. Halm, W. Hoyer, P. Jovari, J. Neuefeind, J. Non-Cryst. Solids 326&327 (2003) 120. G. Jones, R.A. Collins, Phys. Stat. Sol. (a) 53 (1979) 339. J.J. Odwyer, The Theory of Electrical Conduction and Breakdown in Solid Dielectrics, Clarendon Press, Oxford, 1973. J.R. Bosnell, C.B. Thomas, Solid-State Electron. 15 (1972) 1261. A. Giridhar, K.J. Rao, J. Non-Cryst. Solids 33 (1979) 177. M.F. Kotkata, M.A. Afifi, H.H. Labib, N.A. Hegab, M.M. Abdel-Aziz, Thin Solid Films 240 (1979) 143. H.J. Stocker, C.A. Barlow, D.F. Weirauch, J. Non-Cryst. Solids 4 (1970) 523.