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Bond type, polarisation and electron conduction in some oxide and chalcogenide glasses
JOURNALOF NON-CRYSTALLINESOLIDS4 (1970) 234--247 © North-Holland Publishing Co., Amsterdam
BOND TYPE, POLARISAT1ON AND E L E C T R O N C O N D U C T I O N IN SOME OXIDE AND CHALCOGENIDE GLASSES
C. F. DRAKE and I. F. SCANLAN Standard Telecommunication Laboratories, Harlow, Essex, England
Although it is commonly accepted that the mechanism of switching must differ in detail in the numerous systems in which it has now been reported, the close parallelism between the electrical phenomena suggests that a common and fundamental process remains to be found as the prime cause of the various effects. The systems in which bistable (memory) switching occurs, can be divided into two groups; two - or more component metal oxide system, and single or multi-component metal chalcogenide system, and in every case the systems either are glasses or are closely related to known vitreous compositions. It is reasonable to assume that the tendency of a system to form a glass and its ability to show electrical bistable behaviour are intimately related. This paper is an attempt to sketch a framework for such a correlation and to follow through some of the implications. The first part will present a view of the structure of the vitreous state which is to be used in the second part to develop a model for switching covering both oxide and chalcogenide systems, and in the third part some results on the thermoelectric properties of some copper phosphate glasses are reported and their implications considered. 1. Structure o f the vitreous state
It is necessary to define the limits of the vitreous state a n d in particular to distinguish vitreous from " a m o r p h o u s " materials. Here we shall specify the vitreous state macroscopically as that disordered state which, for a fixed composition, has a well defined e q u i l i b r i u m configuration with a u n i q u e value of such macroscopic properties as density refractive index, expansivity a n d the elastic moduli. Thus a m o r p h o u s Si, Ge etc. are excluded in that they a p p a r e n t l y have no unique disordered form. Microscopically, as a first a p p r o x i m a t i o n one can say that a m o r p h o u s materials are characterised by disorder associated with very large but variable n u m b e r s of b r o k e n bonds, the n u m b e r d e p e n d i n g on the details of preparation, whilst the vitreous state requires disorder b u t at the same time a m a i n t e n a n c e of the saturation of the chemical bonding. A similar view has been expressed earlier by Cohen, Fritzsche, a n d Ovshinsky 1). It clearly becomes necessary now to define the considerations that force a system in the vitreous state to a d o p t its u n i q u e (macroscopic) configu234
BONDTYPE~POLARISATION ANDELECTRON CONDUCTION
235
ration. It is suggested here, and a more detailed justification is in preparation, that dipolar forces are the significant considerations. The vast majority of glass systems are based on tetrahedral oxygen coordination of glass-forming atoms (silicate, germanate, phosphate etc. glasses). The tetrahedra are linked in finite or infinite arrays by sharing corners, but not edges or faces, with neighbouring tetrahedra. Taking silicate glasses as a specific example, it is well known that the angle - S i - O - S i - can adopt a range of values, and that this variation, together with the freedom of rotation about the O (consequent on the corner only sharing rule), provides the basis for the geometrical disorder in the silicate glass systems. A regular tetrahedral arrangement of the O about the Si is compatible with either pure sp a covalent bonding, or with electrovalent bonding; in fact various empirical considerations and experimental data lead to a value for the ionicity of the bond of between 40 and 60~o. It is necessary however to take into account three further second order factors that influence the detail of the first coordination shell; a) there is certainly some Si d-orbital contribution to the bond hybrid state in S i O 2 and hence some ~z-bonding to be taken into account; b) as the bonds are partially ionic and the second coordination
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236
C.F.DRAKE AND I.F.SCANLAN
(b) Fig. 1.
fl-Cristobalite.
sphere is non-regular there will be a local non-symmetrical "crystal field" at the (SiO4) site; c) in glasses other than pure SiO2 the distortions introduced by the cations and the non-bonding oxygen produce a further deformation of the local fields. Thus, the detail picture now includes distorted (SiO4) tetrahedra with overall saturation of the bonds but with a disproportionation between bond numbers, and ionicities and hence real charge, on the atoms within a given tetrahedron and between neighbouring tetrahedra. The tendency, even in the crystalline forms of SiO2 for such disproportionation to occur is shown in a particularly marked form in fl-cristobalite (fig. l) and has been noted by Voronkov 2) as characteristic of silicates. It should be noted that the double (SiO4) units in cristobalite represent dipoles that in principle are rotatable by transfer of charge from A ~ B producing an identical system rotated through 180°. A further type of rotatable dipole that has been shown by Strakna a) to exist in high concentrations in vitreous silica is shown in fig. 2. The rotation of such a dipole requires not only transfer of charge from one tetrahedron to the other but in addition displacement of the common O atom over a larger distance ( ~ 0.4 ./~) than required for the first type of dipole. The third form of dipole, already well established by the work of Charles 4), is that associated with movement of a Na + ion (and presumably other monovalent cations of no greater radius) between alternative sites in the vicinity of a non-bonding oxygen ion (fig. 3). It is now possible to present a model of the vitreous state that is compatible with the requirements of saturated valence bonds, short-range order, and long-range disorder, but includes at the same time a minimum-energy
BOND TYPE, POLARISATION AND ELECTRON CONDUCTION
237
Silicon is represented in two dimensions as three coordinated instead of four
Oxygen
"~on Fig. 2. Dipole types in glass. After Strakna3). Silicon is shown in two dimensions as three ~oordinntad instead of four
~
Oxygen
Fig. 3. Dipole types in glass. After Charles4). principle that is the vitreous state analogue of the Madelung energy contribution to a regular crystal lattice. During the cooling of a melt various configurations will occur in juxtaposition, and for some of these parallel or anti-parallel dipoles of one of the three types outlined above will be able to form by bond adjustment. Such
238
C.F.DRAKE AND I.F.SCANLAN
mutual dipole orientation does not imply a geometrically mutually regular (e.g. parallel) arrangement of the contributing tetrahedral complexes. The directional dipole field of such "nuclei" will tend to induce further growth of the domains of similarly oriented clusters and eventually, at a temperature sufficiently low that no major rearrangement requiring bond-rupture and topological rearrangement can occur, a "solid glass" will be formed. In the glass below Tg, the activation enthalpy for most dipole reorientation is very large compared with k T and structural rearrangement of the glass, even when stressed, is very slow. As far as conductive and dielectric properties are concerned the following are the essential features of such a model. A given atom, glass-former or metal cation, has initially (in the process of cooling to form the glass from a molten mix) adopted a first-order ligand arrangement close to that which it would adopt in its normal crystalline association with such a ligand, and this bonding arrangement has not been seriously disturbed on cooling. A striking example of this has been observed in phosphate glasses containing Cu I and Cun. Fig. 4 shows the apparent molar volume (AMV) of oxygen in a series of Cu ~, Cu u, phosphate glasses with the same total Cu content. The AMV is calculated from the density, assuming that oxygen atoms alone determine the volume of the material. Most glasses and metal oxides have an AMV for oxygen of ~ 12 cm3/g atom. The points represented by x in fig. 4, for Cu-containing glasses, give an AMV for oxygen well outside the ---o---
ccs/gm atom 0 assuming each Cu*ion introduces 1 0
--0--
ccs/gm atom 0 if total Cu present as Cu**(calc)
14-0 CCS per gn'L atom of O
23"85 for Cu20 iI iI
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ccs/gm, atom of Oin Cu°,CU °°glasses
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o
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Cu+/Cu ++ glasses; A M V o f oxygen.
BOND TYPE, POLARISATION AND ELECTRON CONDUCTION
239
normal range. If it is assumed however that the Cu ~ introduces one O atom per atom of Cu I and not ½0, and consequently behaves from the point of view of the AMV as if it were Cu u, then the recalculated AMV has a normal value and is independent of Cu I concentration (open circles fig. 4). It follows that the structural arrangement in the vicinity of the Cu I atom differs from that in the vicinity of the Cu" atom, and moreover, the similarity between the AMV in crystalline Cu20 and the value obtained by extrapolation of the AMV in the Cu ~glass, suggests that the Cu r coordination is similar in Cu20 and in the phosphate glasses, whilst there is considerable evidence that Cu It atoms are present in phosphate glasses in a distorted octahedral oxygen environment. The second feature of importance is the close association between a particular atom including its immediate coordination shell and the neighbouring region of the glass matrix which has become polarized (dipole oriented) to accommodate the atom in question. A change in the valence state of the atom, or in physical terms the location thereon of a charge (electron or hole), will correspond to a polaron of a special type. There exist the possibility of two types of potential well; the conventional type with electron shell polarization of the spatially unchanged environment, and a more fundamental type in which permanent dipole reorientation has occurred and the local structure has been modified to lower still further the energy of the charge system. Such considerations will be invoked later to account for switching in vitreous systems. This model also implies that doping to produce extrinsic impurity conduction is almost ruled out per se in glasses. If a glass can be formed from a given composition by cooling the melt then each of the ions will be present in a local environment appropriate to its valence state - there is no "reference structure" to define an impurity. However, in contrast with crystalline semiconductors, a difference in principle exists between doping the melt and impurity doping the solid (by low temperature diffusion, ion-implantation etc). As every local configuration has already been defined by the time the glass has been cooled below Tg there may be no sites available for a particular impurity that is introduced into the solid glass, other than those in which it will act as a donor or acceptor, and in this special case a vitreous state equivalent of impurity doping may be possible. The model also provides a mechanism for indirect interaction between high applied fields and the current carriers, which will affect the conductive properties, of a type related, but not identical to the Frenkel field-aided thermal emission. In the Frenkel 5) model, electron orbitals extending over many a.u. provide a means of acquiring sufficient energy from fields of the order of 104 V/cm to significantly increase the probability of thermal emission of the
240
C.F.DRAKEANDI.F.SCANLAN
electrons: in this present model the field can alter the emission probability by changing the polarization state of the extended polarized matrix.
2. Chalcogenide and oxide glasses A model has been presented~) for bistable switching in the system Cu l, Cu u, phosphate glass. In this section an attempt will be made to show that the same generic type of model can be developed for chalcogenide glasses, and that monostable and bistable switching may not be fundamentally different phenomena. In order to illustrate the principles involved, SbzS 3 and related compositions will be discussed. Crystalline Sb2S 3 has been shown by Gildart v) to exhibit switching behaviour, and SbSI, with which it has a close structural relationship, is a ferroelectric semiconductor. Glasses based on SbSI with some Sb replaced by Cu or Ag have been reported 9) as exhibiting switching behaviour analagous to that in the A s - T e - G e system. At the other extreme of the scale Sb2FeS4 and CuSbS2 are crystalline semimetallic conductors with structures closely related to SbzS3 and SbSI. All these compounds are based on infinite chains of
I
I
Sb - - S
I
I
S --Sb
I
I
similarly oriented with respect to each other in the different compounds. The other constituents of the compound are arranged between the chains. In SbSI, for example, the I- ions are stacked vertically in close packed columns parallel to the (SbS) chains; in CuSbS 2 the (CuS) is arranged in folded horizontal - C u - S - chains. In Sb/S3 the same (SbS) chains are present and the rest of the Sb and S are located between the chains but with a different coordination and bond-length associated with the two types of Sb atom (fig. 5). The (SbS), chains are modified in two ways. In different compounds the angle of fold of the chain is adjusted to provide the distance in the vertical (c-axis) direction necessary to accommodate the additional species present. Also, in a given compound (e.g. SbSI and probably 8b283) the chain can exist in two forms, a regular form in which the horizontal Sb-S bond is perpendicular to the c-axis, and the crystal has no polar axis, and the form in which the Sb-S bond is not normal to the c-axis and the resultant structure is ferroelectric (e.g. SbSI below 20 °C).
241
BOND TYPE, POLARISATION AND ELECTRON CONDUCTION
Compound
Formula
Stibnite
Sb2 $3
bLC
Unit replacing iodine between SbS chains
chaio j Berthierite
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a) SbSI looking down the c axis
To
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,Wolfsbergite
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B
Para-electr ic
~.~
I
o I
Ferro electric
b) Looking along xx' i n a) showing one of the vertical
chains which occur at cell centres and corners
Fig. 5. Structural relationships in some systems based on (SbS) chains.
The significant feature is the persistence of the (SbS) chain in a series of apparently very different compounds (fig. 5). It is suggested that the (SbS), structural unit is retained in glasses based on this system but is modified to produce geometrically irregular dipolar units by chain folding, bond length alterations, etc., similar to those described for oxide glasses. In the (Cu, Sb) SI glass, therefore, the glass will consist of (SbS) chains with the i and excess CuS interspersed in appropriate sites formed by the matrix. As in CuS itself the Cu atoms are assumed to be present in two valence states. The Cu ions will act as hopping sites, and in switching off-on the matrix can be polarized, and the S coordination about the Cu altered by small displacements of the atoms within the chain making the environment of the two types of Cu identical. Thus a model, formally identical to that presented for the copper phosphate glass, can be developed for switching in this glass system.
cl ain
242
C.F.DRAKE AND I.F.SCANLAN
In crystalline S b 2 S 3 two types of Sb atom are present, with different total bond numbers. Several ferroelectric phase transitions in the temperature interval - 3 0 to + 7 0 ° C have been tentatively reported s). It is tempting to suggest that the switching reported by Gildart is associated with a fieldinduced ferroelectric-like transition that makes the local environment of the two Sb atoms more nearly similar. The presentation of a suitable model in the case of complex glasses containing As, Te, Ge(Si) is not presently possible as neither the structural features of the relevant crystalline compounds are known nor the valence state of the constituent atoms. A study of the coordination and valence of the As atoms in typical glass compositions could provide a basis for an analogous model of switching in this system. One of the features of switching behaviour discussed below common to both Cu phosphate and to chalcogenide glasses, is sufficiently striking to suggest that both processes have a common cause. When the voltage and current waveform are monitored during the switching of a bistable chalcogenide glass switch it is clear that the process takes place in several stages. Almost identical characteristics have been recorded during switching of Cu phosphate glasses and are shown in figs. 6a and 6b. The switching characteristics for both types of material include the following features: an induction period (I1) with a duration z n ~ Ae-BV; a rapid drop in terminal voltage (fall in device resistance) occurring in a time r m ~< 10 - 9 sec; a quasi on-state lasting for Z~v"~10-s sec; and finally the stable on-state. The current flow during switching is also shown in the same figure. If we consider first the repetitive switching behaviour it is interesting that the quasi on-state (IV) is always associated with noise. An additional feature, which is most marked in the first switching operation on a device, is the pulse of current opposed in direction to the applied voltage that occurs during period III. The magnitude of the pulse depended on the sense in which the device was connected in the circuit. The devices on which these measurements were made were physically asymmetrical, consisting of a copper substrate, a thin glass layer, and an evaporated top electrode. The "polarity" of the device, occurring only with respect to this current pulse, may be explained by this asymmetry. These switching characteristics can be accounted for qualitatively by the switching model. The voltage-time dependence of the initial switching (II) has been described in a previous paper 6) in terms of a spread in dipole relaxation times. The fast process (III) represents the field induced production of ferroelectric-like domains in the region between the electrodes. As Shur 1°) has shown theoretically, and Sawaguchi 11) has demonstrated experimentally in SbSI, charge can be transported in ferroelectric semiconductors, on the
243
BOND TYPE, POLARISATION AND ELECTRON CONDUCTION
1
~AAppl. i Device 100~/
lOOK -
Vo (CRT) I D (CRT)
-
V appl.f
VD I 50-100msec
4°vv'- 40v/u sec
10 p see
t
t
IoI l,Tr _~j (a)
v°t
15V
v°~'I ,ov/p., TD
t
(b) Fig. 6. Switch-on measuring circuit. (a) Switch-on (forming); (b) switch-on (repetitive).
244
C.F.DRAKE AND I.F.SCANLAN
faces of polarized domains which travel from one electrode to the other. It is suggested that the noisy region IV in fact corresponds to this type of reversibly field-dependent charge transport and that the permanently onstate (V) represents the conversion of the material between the electrodes into a ferroelectric-like monodomain. In this model the difference between mono- and bi-stable switching is a quantitative not a qualitative one. If the field is removed before the transition I V ~ V , a normally bi-stable behaves in the same way as a monostable switch. The tendency of a mono-stable switch to become bi-stable after a period of switching is determined by the ease with which the reversibly polarized state can become ferroelectrically locked-in.
3. Seebeck coefficient of copper phosphate glass switches Thermoelectric measurements have been made using thin films of copper calcium phosphate glasses between Cu electrodes. A temperature gradient was produced by differential radiant heating of the two Cu leads, and the temperature difference between the two glass faces was measured by two thermocouples formed by attaching constantan wires to the tips of the main Cu electrodes. At each temperature the value of the Seebeck coefficient (S)r was derived from the slope of the straight line plot of the thermoelectric voltage against the temperature difference, (A T)7.
Seebeck coelf.~VI*C
~00
"0
0
0
0
0-"
300 200
100
I
90
I
100
I
110
I
120
I
130
I
I
1/,0 150 Temperature *C
Fig. 7. Seebeckcoefficientof copper phosphate glass in the high resistance state measured against copper, cold junction with respect to hot.
BOND TYPE, POLARIZATION AND ELECTRON CONDUCTION
245
A number of independent test specimens gave results which were qualitatively identical, but the magnitude of S in the non-conducting state varied by up to 2 to 1 between specimens. In the preparation of the specimen the glass was bonded to the Cu electrodes by melting, and some compositional changes (CuII~Cu l) occur during this process. Repeated measurements of the Seebeck coefficient on a device before and after switching through a cycle (on-off-on or vice versa) gave values which differed by not more than + 10~. Further off-state thermoelectric measurements using thin specimens of known composition with the electrodes applied by a room temperature process are being made. In the off-state the Seebeck coefficient was p-type and different samples gave values between 400 and 750/~V/°C. In the on-state S was of opposite sign, and about 25/~V/°C at room temperature. The difference in sign and magnitude between the Seebeck coefficient for the two states is compatible with any model which involves a structural change in the material of such a type that the conduction changes from hopping conduction in the off-state to semi-metallic or metallic conduction in the on-state. The magnitude of S in the on-state is not compatible with the formation of a pure Cu filament, but it is not possible to distinguish on the basis of these results between a "copper alloy" (e.g. Cu, P) filament and the "ordered" copper glass we have postulated. The striking feature of the off-state S is its temperature independence. If the carrier concentration is temperature dependent, unless the material is intrinsic with equal hole and electron mobilities, then a term
(k/q)(E/kT) must appear in S. The magnitude of E in any term in the expression for S of this form is certainly 40.1 eV, in contrast with an activation energy for conduction of ~ 0.8 eV. It is therefore not possible to include a temperature dependent carrier concentration term in the conductivity, and the artificial division of the temperature dependent part of the conductivity into carrier concentration and mobility, made use of by the author in an earlier paper6), is clearly not justified. At the same time, other evidence such as the visible absorption spectra and the very different molar volume of oxygen associated with the Cu I and CulI ions respectively, clearly indicates that the local coordination of these two ions are substantially different. The thermoelectric results, however, indicate that the number of carriers is effectively temperature independent and that only the mobility is activated.
246
C.F.DRAKE AND LF.SCANLAN
The general features of the model of switching are not affected by this revision of the detail of the conduction mechanism in the off-state, but the value of identifying the coordination of the Cu I and Cu" ions by some independent means becomes the greater. The simplest interpretation of the temperature independence of the Seebeck coefficient is the assumption that some of the Cu ~and Cu" ion sites each occupy a spread of energy levels that just overlap. A limited number of centres, corresponding to this overlap, have exchanged electrons producing holes in the Cu ~and electrons in the Cu n impurity levels available for phonon activated hopping transport. From the Seebeck coefficient it follows that the holes on the Cu I levels must have the higher mobility. The appropriate expression for S will then be that suggested by Mott zz) for iron-containing glasses. The cooperative rearrangement on switching will still involve a readjustment of the positions of the coordinating oxygen such that the Cu ~ and Cu" ion environments are made more nearly the same. In terms of the physical model the energy level of the two sets of impurity bands will tend to merge one with another, increasing the number of free carriers and of the mobility as a result of the Mott semiconductormetal transition.
4. Conclusions It is suggested that switching in both oxide and chalcogenide glasses can be explained in similar terms. In the high resistance state two centres, representing different valence states of the same element, are present in different coordination spheres. Thermoelectric results appear to require the assumption of a spread of energies of each of these states sufficient to produce some overlap of levels and conduction is then by polaron hopping in these overlap levels. Under high fields, interaction between these sites and the field is facilitated by the highly polarizable matrix, and a cooperative rearrangement of the structure, involving the shift of the appropriate coordinating anions without the rupture of any valence bands, leads to the conducting form in which the local environment of each of the centres is effectively identical. The monostable and bistable switch are considered to be extreme representatives of the same phenomena, and phase changes (melting, crystallization) when they occur are to be regarded as secondary rather than primary features.
Acknowledgement The authors wish to thank the Ministry of Technology under whose sponsorship much of this work was undertaken.
BOND TYPE, POLARISATION AND ELECTRON CONDUCTION
247
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)
M. H. Cohen, H. Fritzsche and S. R. Ovshinsky, Phys. Rev. Letters 22 (1969) 1065. M. G. Voronkov, Soviet Phys.-Dokl. 6 (1961) 367. R. E. Strakna, Phys. Rev. 123 (1961) 2020. R. J. Charles, J. Appl. Phys. 32 (1961) 1115. J. Frenkel, J. Tech. Phys. (USSR) 5 (1938) 685. C. F. Drake, I. F. Scanlan and A. Engel, Phys. Status Solidi 32 (1969) in press. Gildart, J. Appl. Phys. 36 (1965) 335. I. P. Girigas and A. S. Karpus Soviet Phys.-Solid State 9 (1968) 2265. B.P. 1,117, 211. M.S. Shut, Fiz. Tverd. Tela 10 (1968) 2652. E. Sawaguchi and T. Mori, J. Phys. Soc. Japan 21 (1960) 2077. N. F'. Mort, J. Non-Crystalline Solids 1 (1968) 1.
BOND TYPE, POLARISAT1ON AND E L E C T R O N C O N D U C T I O N IN SOME OXIDE AND CHALCOGENIDE GLASSES
C. F. DRAKE and I. F. SCANLAN Standard Telecommunication Laboratories, Harlow, Essex, England
Although it is commonly accepted that the mechanism of switching must differ in detail in the numerous systems in which it has now been reported, the close parallelism between the electrical phenomena suggests that a common and fundamental process remains to be found as the prime cause of the various effects. The systems in which bistable (memory) switching occurs, can be divided into two groups; two - or more component metal oxide system, and single or multi-component metal chalcogenide system, and in every case the systems either are glasses or are closely related to known vitreous compositions. It is reasonable to assume that the tendency of a system to form a glass and its ability to show electrical bistable behaviour are intimately related. This paper is an attempt to sketch a framework for such a correlation and to follow through some of the implications. The first part will present a view of the structure of the vitreous state which is to be used in the second part to develop a model for switching covering both oxide and chalcogenide systems, and in the third part some results on the thermoelectric properties of some copper phosphate glasses are reported and their implications considered. 1. Structure o f the vitreous state
It is necessary to define the limits of the vitreous state a n d in particular to distinguish vitreous from " a m o r p h o u s " materials. Here we shall specify the vitreous state macroscopically as that disordered state which, for a fixed composition, has a well defined e q u i l i b r i u m configuration with a u n i q u e value of such macroscopic properties as density refractive index, expansivity a n d the elastic moduli. Thus a m o r p h o u s Si, Ge etc. are excluded in that they a p p a r e n t l y have no unique disordered form. Microscopically, as a first a p p r o x i m a t i o n one can say that a m o r p h o u s materials are characterised by disorder associated with very large but variable n u m b e r s of b r o k e n bonds, the n u m b e r d e p e n d i n g on the details of preparation, whilst the vitreous state requires disorder b u t at the same time a m a i n t e n a n c e of the saturation of the chemical bonding. A similar view has been expressed earlier by Cohen, Fritzsche, a n d Ovshinsky 1). It clearly becomes necessary now to define the considerations that force a system in the vitreous state to a d o p t its u n i q u e (macroscopic) configu234
BONDTYPE~POLARISATION ANDELECTRON CONDUCTION
235
ration. It is suggested here, and a more detailed justification is in preparation, that dipolar forces are the significant considerations. The vast majority of glass systems are based on tetrahedral oxygen coordination of glass-forming atoms (silicate, germanate, phosphate etc. glasses). The tetrahedra are linked in finite or infinite arrays by sharing corners, but not edges or faces, with neighbouring tetrahedra. Taking silicate glasses as a specific example, it is well known that the angle - S i - O - S i - can adopt a range of values, and that this variation, together with the freedom of rotation about the O (consequent on the corner only sharing rule), provides the basis for the geometrical disorder in the silicate glass systems. A regular tetrahedral arrangement of the O about the Si is compatible with either pure sp a covalent bonding, or with electrovalent bonding; in fact various empirical considerations and experimental data lead to a value for the ionicity of the bond of between 40 and 60~o. It is necessary however to take into account three further second order factors that influence the detail of the first coordination shell; a) there is certainly some Si d-orbital contribution to the bond hybrid state in S i O 2 and hence some ~z-bonding to be taken into account; b) as the bonds are partially ionic and the second coordination
B 1.6643 137.2~~,,~
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BoO 1.6494
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A
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A
137.24" 1.6086 ("I
8 4 4
SIO2 per' unit cell Type A T e t ro hedr'o B (a)
236
C.F.DRAKE AND I.F.SCANLAN
(b) Fig. 1.
fl-Cristobalite.
sphere is non-regular there will be a local non-symmetrical "crystal field" at the (SiO4) site; c) in glasses other than pure SiO2 the distortions introduced by the cations and the non-bonding oxygen produce a further deformation of the local fields. Thus, the detail picture now includes distorted (SiO4) tetrahedra with overall saturation of the bonds but with a disproportionation between bond numbers, and ionicities and hence real charge, on the atoms within a given tetrahedron and between neighbouring tetrahedra. The tendency, even in the crystalline forms of SiO2 for such disproportionation to occur is shown in a particularly marked form in fl-cristobalite (fig. l) and has been noted by Voronkov 2) as characteristic of silicates. It should be noted that the double (SiO4) units in cristobalite represent dipoles that in principle are rotatable by transfer of charge from A ~ B producing an identical system rotated through 180°. A further type of rotatable dipole that has been shown by Strakna a) to exist in high concentrations in vitreous silica is shown in fig. 2. The rotation of such a dipole requires not only transfer of charge from one tetrahedron to the other but in addition displacement of the common O atom over a larger distance ( ~ 0.4 ./~) than required for the first type of dipole. The third form of dipole, already well established by the work of Charles 4), is that associated with movement of a Na + ion (and presumably other monovalent cations of no greater radius) between alternative sites in the vicinity of a non-bonding oxygen ion (fig. 3). It is now possible to present a model of the vitreous state that is compatible with the requirements of saturated valence bonds, short-range order, and long-range disorder, but includes at the same time a minimum-energy
BOND TYPE, POLARISATION AND ELECTRON CONDUCTION
237
Silicon is represented in two dimensions as three coordinated instead of four
Oxygen
"~on Fig. 2. Dipole types in glass. After Strakna3). Silicon is shown in two dimensions as three ~oordinntad instead of four
~
Oxygen
Fig. 3. Dipole types in glass. After Charles4). principle that is the vitreous state analogue of the Madelung energy contribution to a regular crystal lattice. During the cooling of a melt various configurations will occur in juxtaposition, and for some of these parallel or anti-parallel dipoles of one of the three types outlined above will be able to form by bond adjustment. Such
238
C.F.DRAKE AND I.F.SCANLAN
mutual dipole orientation does not imply a geometrically mutually regular (e.g. parallel) arrangement of the contributing tetrahedral complexes. The directional dipole field of such "nuclei" will tend to induce further growth of the domains of similarly oriented clusters and eventually, at a temperature sufficiently low that no major rearrangement requiring bond-rupture and topological rearrangement can occur, a "solid glass" will be formed. In the glass below Tg, the activation enthalpy for most dipole reorientation is very large compared with k T and structural rearrangement of the glass, even when stressed, is very slow. As far as conductive and dielectric properties are concerned the following are the essential features of such a model. A given atom, glass-former or metal cation, has initially (in the process of cooling to form the glass from a molten mix) adopted a first-order ligand arrangement close to that which it would adopt in its normal crystalline association with such a ligand, and this bonding arrangement has not been seriously disturbed on cooling. A striking example of this has been observed in phosphate glasses containing Cu I and Cun. Fig. 4 shows the apparent molar volume (AMV) of oxygen in a series of Cu ~, Cu u, phosphate glasses with the same total Cu content. The AMV is calculated from the density, assuming that oxygen atoms alone determine the volume of the material. Most glasses and metal oxides have an AMV for oxygen of ~ 12 cm3/g atom. The points represented by x in fig. 4, for Cu-containing glasses, give an AMV for oxygen well outside the ---o---
ccs/gm atom 0 assuming each Cu*ion introduces 1 0
--0--
ccs/gm atom 0 if total Cu present as Cu**(calc)
14-0 CCS per gn'L atom of O
23"85 for Cu20 iI iI
13-5 --x--
ccs/gm, atom of Oin Cu°,CU °°glasses
13.0
x
x
12-5
120 ~
~
~
o
~ o
11-5 0
o
10
20 F i g 4.
30
I
40
510 Mole'/. Cu"
Cu+/Cu ++ glasses; A M V o f oxygen.
BOND TYPE, POLARISATION AND ELECTRON CONDUCTION
239
normal range. If it is assumed however that the Cu ~ introduces one O atom per atom of Cu I and not ½0, and consequently behaves from the point of view of the AMV as if it were Cu u, then the recalculated AMV has a normal value and is independent of Cu I concentration (open circles fig. 4). It follows that the structural arrangement in the vicinity of the Cu I atom differs from that in the vicinity of the Cu" atom, and moreover, the similarity between the AMV in crystalline Cu20 and the value obtained by extrapolation of the AMV in the Cu ~glass, suggests that the Cu r coordination is similar in Cu20 and in the phosphate glasses, whilst there is considerable evidence that Cu It atoms are present in phosphate glasses in a distorted octahedral oxygen environment. The second feature of importance is the close association between a particular atom including its immediate coordination shell and the neighbouring region of the glass matrix which has become polarized (dipole oriented) to accommodate the atom in question. A change in the valence state of the atom, or in physical terms the location thereon of a charge (electron or hole), will correspond to a polaron of a special type. There exist the possibility of two types of potential well; the conventional type with electron shell polarization of the spatially unchanged environment, and a more fundamental type in which permanent dipole reorientation has occurred and the local structure has been modified to lower still further the energy of the charge system. Such considerations will be invoked later to account for switching in vitreous systems. This model also implies that doping to produce extrinsic impurity conduction is almost ruled out per se in glasses. If a glass can be formed from a given composition by cooling the melt then each of the ions will be present in a local environment appropriate to its valence state - there is no "reference structure" to define an impurity. However, in contrast with crystalline semiconductors, a difference in principle exists between doping the melt and impurity doping the solid (by low temperature diffusion, ion-implantation etc). As every local configuration has already been defined by the time the glass has been cooled below Tg there may be no sites available for a particular impurity that is introduced into the solid glass, other than those in which it will act as a donor or acceptor, and in this special case a vitreous state equivalent of impurity doping may be possible. The model also provides a mechanism for indirect interaction between high applied fields and the current carriers, which will affect the conductive properties, of a type related, but not identical to the Frenkel field-aided thermal emission. In the Frenkel 5) model, electron orbitals extending over many a.u. provide a means of acquiring sufficient energy from fields of the order of 104 V/cm to significantly increase the probability of thermal emission of the
240
C.F.DRAKEANDI.F.SCANLAN
electrons: in this present model the field can alter the emission probability by changing the polarization state of the extended polarized matrix.
2. Chalcogenide and oxide glasses A model has been presented~) for bistable switching in the system Cu l, Cu u, phosphate glass. In this section an attempt will be made to show that the same generic type of model can be developed for chalcogenide glasses, and that monostable and bistable switching may not be fundamentally different phenomena. In order to illustrate the principles involved, SbzS 3 and related compositions will be discussed. Crystalline Sb2S 3 has been shown by Gildart v) to exhibit switching behaviour, and SbSI, with which it has a close structural relationship, is a ferroelectric semiconductor. Glasses based on SbSI with some Sb replaced by Cu or Ag have been reported 9) as exhibiting switching behaviour analagous to that in the A s - T e - G e system. At the other extreme of the scale Sb2FeS4 and CuSbS2 are crystalline semimetallic conductors with structures closely related to SbzS3 and SbSI. All these compounds are based on infinite chains of
I
I
Sb - - S
I
I
S --Sb
I
I
similarly oriented with respect to each other in the different compounds. The other constituents of the compound are arranged between the chains. In SbSI, for example, the I- ions are stacked vertically in close packed columns parallel to the (SbS) chains; in CuSbS 2 the (CuS) is arranged in folded horizontal - C u - S - chains. In Sb/S3 the same (SbS) chains are present and the rest of the Sb and S are located between the chains but with a different coordination and bond-length associated with the two types of Sb atom (fig. 5). The (SbS), chains are modified in two ways. In different compounds the angle of fold of the chain is adjusted to provide the distance in the vertical (c-axis) direction necessary to accommodate the additional species present. Also, in a given compound (e.g. SbSI and probably 8b283) the chain can exist in two forms, a regular form in which the horizontal Sb-S bond is perpendicular to the c-axis, and the crystal has no polar axis, and the form in which the Sb-S bond is not normal to the c-axis and the resultant structure is ferroelectric (e.g. SbSI below 20 °C).
241
BOND TYPE, POLARISATION AND ELECTRON CONDUCTION
Compound
Formula
Stibnite
Sb2 $3
bLC
Unit replacing iodine between SbS chains
chaio j Berthierite
Sb 2 FeS 4
1,
a) SbSI looking down the c axis
To
Q
c
chain
Fe
ab plane
G
,Wolfsbergite
CuSbS 2
T ,'Wu cha n
B
Para-electr ic
~.~
I
o I
Ferro electric
b) Looking along xx' i n a) showing one of the vertical
chains which occur at cell centres and corners
Fig. 5. Structural relationships in some systems based on (SbS) chains.
The significant feature is the persistence of the (SbS) chain in a series of apparently very different compounds (fig. 5). It is suggested that the (SbS), structural unit is retained in glasses based on this system but is modified to produce geometrically irregular dipolar units by chain folding, bond length alterations, etc., similar to those described for oxide glasses. In the (Cu, Sb) SI glass, therefore, the glass will consist of (SbS) chains with the i and excess CuS interspersed in appropriate sites formed by the matrix. As in CuS itself the Cu atoms are assumed to be present in two valence states. The Cu ions will act as hopping sites, and in switching off-on the matrix can be polarized, and the S coordination about the Cu altered by small displacements of the atoms within the chain making the environment of the two types of Cu identical. Thus a model, formally identical to that presented for the copper phosphate glass, can be developed for switching in this glass system.
cl ain
242
C.F.DRAKE AND I.F.SCANLAN
In crystalline S b 2 S 3 two types of Sb atom are present, with different total bond numbers. Several ferroelectric phase transitions in the temperature interval - 3 0 to + 7 0 ° C have been tentatively reported s). It is tempting to suggest that the switching reported by Gildart is associated with a fieldinduced ferroelectric-like transition that makes the local environment of the two Sb atoms more nearly similar. The presentation of a suitable model in the case of complex glasses containing As, Te, Ge(Si) is not presently possible as neither the structural features of the relevant crystalline compounds are known nor the valence state of the constituent atoms. A study of the coordination and valence of the As atoms in typical glass compositions could provide a basis for an analogous model of switching in this system. One of the features of switching behaviour discussed below common to both Cu phosphate and to chalcogenide glasses, is sufficiently striking to suggest that both processes have a common cause. When the voltage and current waveform are monitored during the switching of a bistable chalcogenide glass switch it is clear that the process takes place in several stages. Almost identical characteristics have been recorded during switching of Cu phosphate glasses and are shown in figs. 6a and 6b. The switching characteristics for both types of material include the following features: an induction period (I1) with a duration z n ~ Ae-BV; a rapid drop in terminal voltage (fall in device resistance) occurring in a time r m ~< 10 - 9 sec; a quasi on-state lasting for Z~v"~10-s sec; and finally the stable on-state. The current flow during switching is also shown in the same figure. If we consider first the repetitive switching behaviour it is interesting that the quasi on-state (IV) is always associated with noise. An additional feature, which is most marked in the first switching operation on a device, is the pulse of current opposed in direction to the applied voltage that occurs during period III. The magnitude of the pulse depended on the sense in which the device was connected in the circuit. The devices on which these measurements were made were physically asymmetrical, consisting of a copper substrate, a thin glass layer, and an evaporated top electrode. The "polarity" of the device, occurring only with respect to this current pulse, may be explained by this asymmetry. These switching characteristics can be accounted for qualitatively by the switching model. The voltage-time dependence of the initial switching (II) has been described in a previous paper 6) in terms of a spread in dipole relaxation times. The fast process (III) represents the field induced production of ferroelectric-like domains in the region between the electrodes. As Shur 1°) has shown theoretically, and Sawaguchi 11) has demonstrated experimentally in SbSI, charge can be transported in ferroelectric semiconductors, on the
243
BOND TYPE, POLARISATION AND ELECTRON CONDUCTION
1
~AAppl. i Device 100~/
lOOK -
Vo (CRT) I D (CRT)
-
V appl.f
VD I 50-100msec
4°vv'- 40v/u sec
10 p see
t
t
IoI l,Tr _~j (a)
v°t
15V
v°~'I ,ov/p., TD
t
(b) Fig. 6. Switch-on measuring circuit. (a) Switch-on (forming); (b) switch-on (repetitive).
244
C.F.DRAKE AND I.F.SCANLAN
faces of polarized domains which travel from one electrode to the other. It is suggested that the noisy region IV in fact corresponds to this type of reversibly field-dependent charge transport and that the permanently onstate (V) represents the conversion of the material between the electrodes into a ferroelectric-like monodomain. In this model the difference between mono- and bi-stable switching is a quantitative not a qualitative one. If the field is removed before the transition I V ~ V , a normally bi-stable behaves in the same way as a monostable switch. The tendency of a mono-stable switch to become bi-stable after a period of switching is determined by the ease with which the reversibly polarized state can become ferroelectrically locked-in.
3. Seebeck coefficient of copper phosphate glass switches Thermoelectric measurements have been made using thin films of copper calcium phosphate glasses between Cu electrodes. A temperature gradient was produced by differential radiant heating of the two Cu leads, and the temperature difference between the two glass faces was measured by two thermocouples formed by attaching constantan wires to the tips of the main Cu electrodes. At each temperature the value of the Seebeck coefficient (S)r was derived from the slope of the straight line plot of the thermoelectric voltage against the temperature difference, (A T)7.
Seebeck coelf.~VI*C
~00
"0
0
0
0
0-"
300 200
100
I
90
I
100
I
110
I
120
I
130
I
I
1/,0 150 Temperature *C
Fig. 7. Seebeckcoefficientof copper phosphate glass in the high resistance state measured against copper, cold junction with respect to hot.
BOND TYPE, POLARIZATION AND ELECTRON CONDUCTION
245
A number of independent test specimens gave results which were qualitatively identical, but the magnitude of S in the non-conducting state varied by up to 2 to 1 between specimens. In the preparation of the specimen the glass was bonded to the Cu electrodes by melting, and some compositional changes (CuII~Cu l) occur during this process. Repeated measurements of the Seebeck coefficient on a device before and after switching through a cycle (on-off-on or vice versa) gave values which differed by not more than + 10~. Further off-state thermoelectric measurements using thin specimens of known composition with the electrodes applied by a room temperature process are being made. In the off-state the Seebeck coefficient was p-type and different samples gave values between 400 and 750/~V/°C. In the on-state S was of opposite sign, and about 25/~V/°C at room temperature. The difference in sign and magnitude between the Seebeck coefficient for the two states is compatible with any model which involves a structural change in the material of such a type that the conduction changes from hopping conduction in the off-state to semi-metallic or metallic conduction in the on-state. The magnitude of S in the on-state is not compatible with the formation of a pure Cu filament, but it is not possible to distinguish on the basis of these results between a "copper alloy" (e.g. Cu, P) filament and the "ordered" copper glass we have postulated. The striking feature of the off-state S is its temperature independence. If the carrier concentration is temperature dependent, unless the material is intrinsic with equal hole and electron mobilities, then a term
(k/q)(E/kT) must appear in S. The magnitude of E in any term in the expression for S of this form is certainly 40.1 eV, in contrast with an activation energy for conduction of ~ 0.8 eV. It is therefore not possible to include a temperature dependent carrier concentration term in the conductivity, and the artificial division of the temperature dependent part of the conductivity into carrier concentration and mobility, made use of by the author in an earlier paper6), is clearly not justified. At the same time, other evidence such as the visible absorption spectra and the very different molar volume of oxygen associated with the Cu I and CulI ions respectively, clearly indicates that the local coordination of these two ions are substantially different. The thermoelectric results, however, indicate that the number of carriers is effectively temperature independent and that only the mobility is activated.
246
C.F.DRAKE AND LF.SCANLAN
The general features of the model of switching are not affected by this revision of the detail of the conduction mechanism in the off-state, but the value of identifying the coordination of the Cu I and Cu" ions by some independent means becomes the greater. The simplest interpretation of the temperature independence of the Seebeck coefficient is the assumption that some of the Cu ~and Cu" ion sites each occupy a spread of energy levels that just overlap. A limited number of centres, corresponding to this overlap, have exchanged electrons producing holes in the Cu ~and electrons in the Cu n impurity levels available for phonon activated hopping transport. From the Seebeck coefficient it follows that the holes on the Cu I levels must have the higher mobility. The appropriate expression for S will then be that suggested by Mott zz) for iron-containing glasses. The cooperative rearrangement on switching will still involve a readjustment of the positions of the coordinating oxygen such that the Cu ~ and Cu" ion environments are made more nearly the same. In terms of the physical model the energy level of the two sets of impurity bands will tend to merge one with another, increasing the number of free carriers and of the mobility as a result of the Mott semiconductormetal transition.
4. Conclusions It is suggested that switching in both oxide and chalcogenide glasses can be explained in similar terms. In the high resistance state two centres, representing different valence states of the same element, are present in different coordination spheres. Thermoelectric results appear to require the assumption of a spread of energies of each of these states sufficient to produce some overlap of levels and conduction is then by polaron hopping in these overlap levels. Under high fields, interaction between these sites and the field is facilitated by the highly polarizable matrix, and a cooperative rearrangement of the structure, involving the shift of the appropriate coordinating anions without the rupture of any valence bands, leads to the conducting form in which the local environment of each of the centres is effectively identical. The monostable and bistable switch are considered to be extreme representatives of the same phenomena, and phase changes (melting, crystallization) when they occur are to be regarded as secondary rather than primary features.
Acknowledgement The authors wish to thank the Ministry of Technology under whose sponsorship much of this work was undertaken.
BOND TYPE, POLARISATION AND ELECTRON CONDUCTION
247
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)
M. H. Cohen, H. Fritzsche and S. R. Ovshinsky, Phys. Rev. Letters 22 (1969) 1065. M. G. Voronkov, Soviet Phys.-Dokl. 6 (1961) 367. R. E. Strakna, Phys. Rev. 123 (1961) 2020. R. J. Charles, J. Appl. Phys. 32 (1961) 1115. J. Frenkel, J. Tech. Phys. (USSR) 5 (1938) 685. C. F. Drake, I. F. Scanlan and A. Engel, Phys. Status Solidi 32 (1969) in press. Gildart, J. Appl. Phys. 36 (1965) 335. I. P. Girigas and A. S. Karpus Soviet Phys.-Solid State 9 (1968) 2265. B.P. 1,117, 211. M.S. Shut, Fiz. Tverd. Tela 10 (1968) 2652. E. Sawaguchi and T. Mori, J. Phys. Soc. Japan 21 (1960) 2077. N. F'. Mort, J. Non-Crystalline Solids 1 (1968) 1.