Non-crystalline materials

Non-crystalline materials E. A. Davis Non-crystalline materials have recently made an impact on solid state physics that threatens to relegate the role of the single crystal from its venerable position in this field to that of a particular, and not very common, example of condensed matter. The discovery that glassesneed not necessarily be insulators, but can be semiconductors and even metals, has opened up a whole new field of fundamental investigation,.in addition to promising a host of possible uses. In this article, some of the properties of non-crystalline materials will be described, with emphasis on current and potential applications. Most text books on the physics of solids restrict their coverage to a particular class of materials-single crystals-in which the atoms are situated in an ordered periodic arrangement. Knowledge of the configuration of a few atoms in a ‘unit cell’ of a crystalline material is sufficient to specify the whole structure, since the units repeat and stack perfectly throughout the solid. This translational periodicity considerably simplifies theoretical treatments of such structures and is one of the reasons why most emphasis has been placed on them in the past, although the use of single crystals in certain devices, such as the transistor, is another. Single crystals, however, do not pervade our environment. Apart from the occasional diamond on an item of jewellery or a silicon crystal as the ‘brain’ in a pocket calculator, we have to look rather hard to find examples outside the laboratory. Most metallic objects are polycrystalline; that is, they consist of small crystals fairly randomly stacked together. The majority of other materials around us, for example paper, wood, glass, and plastic, are not crystalline at all. The arrangement of atoms in these materials is not periodic, although, as figure 1 illustrates, complete randomness does not exist (as for the atoms of a gas) and often the immediate environment of a given atom is rather similar to that of every other atom of the same kind. This shortrange order is of more importance in determining properties than has hitherto been realised. Glasses

It is fairly common knowledge that glass is a supercooled or frozen liquid and this not only describes the way that most vitreous (glassy) materials are made but also gives a fair picture of its structure. It is a metastable state of condensed matter and all glasses are in process ofcrystallising; that is approaching a lower energy, more ordered state, albeit often on a geological time scale. Glass that is thousands of years old has been found in all parts of the world (and even on the moon) and it would be rather upsetting to find some of our fine stained glass windows crystallising before our eyes. The composition of glasses used in windows and for receptacles is in fact chosen to produce a complex structure which has extreme difficulty in rearranging to the crystalline state. Some glasses, however, crystallise fairly readily on a time scale of days or even minutes and some have to be maintained at a low temperature to avoid this devitrification process. Other commonly accepted attributes of glass should be abandoned. These are optical transparency, brittleness, and poor electrical conductivity. An important and recently discovered class of materials, known as ‘metallic glasses’, are quite opaque to visible light; have a strength approaching the ultimate attainable; and are excellent conductors of electricity. These substances are prepared by very rapid quenching of the molten state using various ingenious methods. Their structure and some applications will be discussed later.

E.A.

Davis,

BSc.,

Ph.D.,

M.A..

M.lnst.

P.

Graduated from the Universities of Birmingham and Reading, and is currently a lecturer in the Physics Department at the University of Cambridge and Fellow of Fitzwilliam College. His research work, principally on semiconductors. has been carried out at the Universitv of Illinois and the Xerox Corporation in the U.S.A., and at the Cavendish Laboratory, Cambridge. He is co-author with Professor Sir Nevill Mott of ‘Electronic Processes in Non-Crystalline Materials’ (Oxford University Press, 197 1). the second edition of which is in press. EXD

1

3:4

(

Semiconductors

Semiconductors are best known for their use in transistors and other electronic devices such as photocells, light-emitting diodes, and solar cells, for which applications they are almost always used in a crystalline state. Although some can be prepared in a non-crystalline form by quenching from the melt, others require deposition in thin film form by condensation from the vapouras in vacuum evaporation or sputtering. Prepared in this way, they are normally called ‘amorphus’, although this term is often used synonymously with glassy, vitreous, or disordered, and no universally accepted description has yet been adopted. Whether crystalline or amorphous, semiconductors are materials with an electrical conductivity lying between that of metals and insulators. This is not, however, their most important property. Their usefulness lies in the sensitivity of their conductivity to heat, light, and other external influences, in addition to the ease with which their properties can be changed by the addition of small amounts of impurities. The latter technique is known as ‘doping’ and is a vital step in the fabrication of most semiconductor devices. Figure 2(a) shows a schematic twodimensional representation of the structure of crystalline germanium in which one of the atoms has been replaced by an atom of the ‘dopant’, in this case arsenic. Each of the chemical bonds between atoms (represented by lines) contains two electrons, resulting in strong ‘covalent binding’. The number of electrons in the outer shells of each germanium atom is just sufficient to provide four bonds and the material is said to be ‘tetrahedrally co-ordinated’. The arsenic atom, on the other hand, has an extra electron additional to that required to form four covalent bonds and, except at very low temperatures, this is free to wander through the material and contribute to electrical conductivity. Similar doping by, say, boron, which has a deficiency of one electron under that required for tetrahedral bonding, results in the creating of a ‘hole’ or a positively charged carrier that can be just as mobile in the structure as the electron in the case of arsenic doping. The two types of doping lead to n-type or p-type germanium according as to whether the excess carriers introduced have a negative (electrons) or positive (holes) charge. For many applications, for example diodes, solar cells, etc., junctions are made between n- and p-type material and, for transistors, n-p-n orp-n-p structures have to be fabricated. Current technology allows hundreds of such electronic components to be incorporated on to a single 1 mm square ‘wafer’ or ‘chip’ of crystalline germanium (or more commonly silicon), complete with the necessary interconnections, to produce the complex circuits used in radios, computers, and a multitude of other applications. W. von Braun, the rocket engineer, has been quoted as saying that, without the great savings in weight, size, and power consumption provided by this technology, man could never have reached the moon. For some applications of semiconductors, however, for example photocopying, visual displays, and solar energy conversion-it is necessary to have fairly large areas of active material and it is for these that amorphous films have a decided advantage. The production of large single crystals is difficult as well as expensive and, for many purposes, quite impracticable. On the other hand, several techniques for thin film deposition are ideally suited for the production of large, uniform areas of materials (figure 3). The photocopying process used in the Xerox and similar machines employs a large-area photoreceptor in the form of a thin amorphous film of selenium which has been 103

’

Models of the structure of a crystal (left) and the same material in an amorphous or glassy state (right). There are two different kinds Figure 1 of atoms, A and 6 (dark and light balls) and each is four-fold co-ordinated (apart from those on the surface of these limited-size models). In the crystal, the atoms are arranged in a repeatable structure (the ‘zinc-blend lattice’) and the symmetry is evident. Every A atom is surrounded by four B atoms and every 6 atom byfourA atoms, i.e. there are no A-A or A-B bonds. In addition every bond angle is 109“ 28’; all bonds are in a staggered configuration (i.e. the dihedral angle-the angle between next-nearest bonds when projected on to a plane perpendicular to the intermediate bond -is 600); and all atoms lie on rings containing six atoms (3 of each kind). In the glass, the bond angles are distorted by about & 1 OO; the dihedral angle is not fixed at a particular value; and the network contains 5-as well as 6-membered rings, Furthermore ‘wrong bonds’ between like atoms occur. All bonds have the same length in both structures. The structure on the right is called a ‘continuous random network.

depositedon to a cylindrical drum by vacuum evaporation(figure 3(a). Photocopying is probably the largest current application of an amorphous semiconductor (figure 4). Until very recently, however, it appeared that amorphous semiconductors suffered from a disadvantage that threatened to jeopardise their wide-scale use for many electronic applications, namely the difficulty experiencedin trying to dope them. One of the reasons for this can be understood by considering the twodimensional representation of amorphous germanium in figure

b.

a.

Ydangling

ree electron 0

germanium

bonds

@ arsenic

Figure 2 Two-dimensional representations of the structure of (a) crystalline germanium and (b) amorphousgermanium (Ge) both containing one arsenic (As) atom. In the crystal, every atom, including the As atom, is at a lattice site and is surrounded by four atoms: the extra electron contributed by the As atom is not required for covalent bonding and is free to conduct electricity. In the amorphous structure, the As atom is surrounded by three Ge atoms and there are no free electrons. Also shown in (b) are two ‘dangling bonds’. Note that these representations of three-dimensional structures are incorrect in one respect: in the crystal (which has the diamond structure) the Ge atoms are actually connected together on 6membered rings, not 4-; in the amorphous state the atoms lie mainly on 5 and B-membered rings-see figure 1. 104

2(b). The added arsenic atom in this network is surrounded by three germanium atoms. Of the five electrons in the outer shellsof the arsenic atom, three are in directional p-like orbitals and contribute to the bonds, while the remaining two are in symmetrical s-like orbitals and remain paired at the arsenic site. The arsenic is electrically neutral and no free electrons are available for conduction. In the crystalline lattice (figure 2(a)) the dopant atom was forced into a tetrahedral configuration but, in the amorphous network, the absenceof stearic hindrances allows the strong chemical bonding forces to have the upper hand and the normal co-ordination is three. A few arsenic atoms might be four-fold co-ordinated, in which caseone might expect somefree electrons, but the overall effect of doping would be of lower efficiency than in a crystal. It appearsthat there is another reasonfor the virtual absenceof doping effectsin amorphous germanium or silicon when they are prepared in conventional ways. This is that an amorphous

argon e

a.

b.

C.

Figure 3 Techniques of thin-film deposition. (a) Evaporation in vacuum from an electrically-heated boat. (b) Sputtering in an argon atmosphere. A radio frequency signal is applied between the plates. Argon ions are driven into the source (on the boom plate) thereby ejecting atoms of the desired material which travel to the substrate (attached to the upper plate). (c) Glow-discharge decomposition of, say, silane gas (SiH,) in a radiofrequency induced plasma. Amorphous silicon is deposited on the pedestal. Doping can be achieved by including small amounts of phosphine (PH,) ordiborane (B,H,) in the gaseous mixture.

(3) Clraq$ng

0))

silicon would reduce the cost of production, firstly becausethe technology associated with fabrication would be cheaper and secondly becausethinner films could be used, the absorption of solar radiation by amorphous silicon being approximately twice as great as that of a single crystal. In addition the wavelength response better matches that of the solar spectrum and is therefore more suitable for the process of conversion. The efficiency of solar cells fabricated from amorphous silicon is at present 6 per cent, which may seemlow, but an increaseto 8-10 per cent would in fact, herald an economic breakthrough.

Exposure Chalcogenides

(c) Ihcharge

(d) lkrrloplllcllt

(e) ‘I’rar1sfw

is Figure 4 The xerographic process. (a) The photoconductingfilm charged positively by a corona discharge induced from a wire, held at a high potential, which is moved parallel to the topsurface. (b) the document to be copied is imaged on to the film. Electron-hole pairs are created in the film by strongly absorbed photons reflected from light areas on the document. (c) Under the action of the electric field, the holes drift towards the metal substrate; the electrons move in the opposite direction to neutralise the positive surface charge. (d) Negatively charged ‘toner’ particles (carbon black dispersed in a low-melting plastic) are cascaded on to the surface, adhering to those areas of the film that have not been discharged. (e) The toner is transferred to paper with the aid of a second corona discharge. The paper is removed and the image made permanent by heating.

network contains ‘dangling bonds’, that is, orbitals each containing only one electron (figure 2(b)). Such dangling bonds could arise from the presence of the three-fold co-ordinated germanium atoms or small voids. Any extra electrons introduced by doping soon find these defects, become trapped, and are thereby lost for conduction. A method for the production of amorphous germanium or silicon, that appearsto avoid the unwanted presenceof dangling bonds or other defects and allows doping, has recently been discovered. The technique is to deposit the silicon (say) by glowdischarge decomposition of gaseoussilicon hydride (figure 3(c)). The resulting films appear to contain far fewer defects,owing in part to the nature of the deposition process (the atoms arrive at the substrate with rather low velocities) but probably more importantly to the incorporation of hydrogen which attaches itself to unsatisfied orbitals. By including small amounts of arsenic hydride or boron hydride in the gaseousmixture, n- andptype material can be deposited. This breakthrough in successful doping of amorphous semiconductors offers considerable promise for their future commercial exploitation. One of the applications likely to be realised fairly soon is in the field of solar energy conversion. Solar cells, fabricated from crystalline silicon, have beendevelopedand used extensively in space vehicles for the direct conversion of solar radiation into electricity. However, a major obstacleto their widespread terrestrial use is their high cost of production: at present the cost of generating electricity via solar cells is nearly 100times that of producing it from fossil fuels. Use of amorphous

The use of amorphous selenium in photocopying has already been mentioned, although its much longer use in silicon rectifiers should not be overlooked. Selenium has a normal bonding configuration in which each atom is covalently bonded to two other atoms. In two crystalline forms, trigonal and monoclinic, the atoms lie along chains and in close rings respectively. In the amorphous state both of these species probably exist, the molecular-like units being randomly mixed but with the shortrange two-fold co-ordination being retained. Selenium is one of three similar elements, tellurium and sulphur being the others, that are called ‘chalcogens’. They are frequently used to form more complex materials, called ‘chalcogenides’, by combining them with silicon, germanium, arsenic and other elements of different valency. Freedom to depart from stoichiometric proportions is one of the most useful features of amorphous semiconductors, allowing fine control over certain properties. In multi-component alloys, the normal tendency is for each atom to adopt an environment in which the valency of each atom is satisfied by covalent bonding. Thus a chalcogen atom-is bonded to two other atoms, germanium to four, arsenic to three, etc. This is not to say that defectsin the structure are not present. Indeed it is now known that under- and over-co-ordinated sites normally occur, leading in themselvesto useful properties which are also of considerable fundamental interest. A deeper understanding of active defect sites in amorphous chalcogenideswill undoubtedly lead to a knowledge of how to eliminate, neutralise or even to use the defectsto commercial advantage. Some of the current applications of amorphous chalcogenides may be mentioned here. They include use in miniature imagepick-up tubes (television cameras) having high sensitivity and colour response,fast electrical switches, computer memories,and display devices. Two types of electrical switch have been developed. They both consist of a thin wafer or film of a multicomponent amorphous chalcogenide equipped with two electrodes:in the off-state they have a low electrical conductance. In the threshold switch, application of a low voltage (say 20 V) causesthe conductance to rise by about a million in a time that can be short as one billionth of a second(lo* set). This on-state is maintained if the voltage is maintained above a few volts but below this value the device reverts back to the low conductance state. Such switches were at one time unjustifiably criticised as being unreliable, eventhough many can withstand more than 1014 cycles without failure. The mechanism is not completely understood but the latest evidence is that it is a fundamentally electronic processwith the current in the on-state being carried in a narrow filament. Memory switches, fabricated out of similar material but generally having compositions such that they are fairly easily crystallised, have characteristics similar to threshold switches with the main difference being that the on-state is maintained even when the applied voltage is reduced to zero. The current in these is again carried in a thin filament between the electrodes but in this case the filament is material that has crystallised. The off-state can be restored by applying a suitable pulse of current which melts the filament and allows it to re-form in a non-crystalline state. An array of 256 memory switches packed on to an area a few millimetres square is available commercially and has filled a gap in computer technology as a read-mostly memory (RMM). Since switching can also be initiated optically, there are potential applications in information storage and retrieval. A laser beam, focused down to a spot of 105

Y

6-r

metolllc /

b

0.

glass ribbon

d

Figure 5 Techniques offast quenching. In (a), the melt, contained in a sealed quartz tube, is quickly immersed into a cold liquid. In (b), a pressure-driven gun forces molten drops to strike a cold surface at high velocity. In (c), a molten jet is squirted between cooled, counter-rotating drums producing a thin ribbdn of glass that can emerge at a rate as high as 2000 metres per minute. In (cl, a similar jet is allbwed to impinge on to the surface of a single rotating drum.

diameter lessthan a micro-metre, can be used to write, read, and eraseinformation on a massmemory with a capacity of lOI bits per squaremetre and on time scalesof the order of a billionth of a second. The ‘read’ facility arises becauseof the different optical properties of the material in its non-crystalline and crystalline states.Even greater capacity and flexibility could be achieved by the use of electron-beam writing, since electrons can be more easily focused and directed.’ A further interesting property of chalcogenide glasses is ‘photodarkening’. Excitation with light near the fundamental absorption band has been found to produce a decreasein the optical transparency at a different wavelength, a process which, dependingon the material and conditions, can be reversible in the sensethat heating removesthe photodarkening, or it can be made irreversible. These effects, not completely understood at the present time, probably involve subtle structural transformations. Several applications of these effects spring to mind, for example light modulation devices, storage of holograms, and use in photolithography, an important step in the fabrication of integrated circuits. Metallic

glasses

The bonds betweenthe atoms in a metal are not covalent as in the semi-conductors discussedso far. The high concentration of free electrons, responsible for a metal’s good electrical conductivity, exists as a sort of sea in which the atoms (ions) are embedded, thereby providing overall cohesion. The inter-atomic forces are therefore non-directional and rather unsuitable for glass formation. The barrier separating the crystalline and noncrystalline stateis small and simple cooling of metallic melts does not produce a glass.To freezein the disorder characteristic offhe liquid state, requires employment of ultra-fast quendhing techniques (figure 5). Early methods relied on propelling small globules at high velocity on to cold surfaces, a technique known as ‘splat-quenching’ and capable of achieving cooling rates of several million degreesper second.More recent methods involve the injection of molten material betweencooled counter-rotating drums or on to the surface of a single spinning disc. Production by the first of these two methods is advantageous from an economic point of view because it bypasses the conventional casting, rolling, and drawing processesusedin metallurgy. Metallic glassesnormally contain at least two constituents-a transition or noble metal and a smaller ‘metalloid’ element (for example, palladium-silicon) but multi-component alloys (for example, iron-phosphorus-carbon) are not uncommon. A surprisingly good approximation to the structure of a binary metallic glass is that of random close-packing. It is the arrangement that would be obtained by filling a bucket with two sizes of ball bearings-indeed many models, using spheres of diameters proportional to those of the constituent atoms and mixed in the appropriate ratios, have been built based on this principle. Such structures can also be simulated by computer modelling. Sometimes‘relaxation’ of these models, to achieve a Endeavour, (Pergamon

106

New SeriesVolume 1, No. 314.1977 Press. Printed in Great Britain)

lower energy state, provides better agreement with the local structure as determined, for example, by X-ray diffraction. Also of current interest, are microcrystalline models in which the diameter of individual crystallites are a few atomic diameters. In the glassy state, metals have some remarkable properties that promise to be exceedingly advantageous in a variety of applications. One of theseproperties is their great strength which, for certain alloys, can exceed three times that of stainless steel. Furthermore, unlike strong and hard crystalline metals,which are normally very brittle, metallic glassesexhibit a high plasticity: typically they can withstand shear strains of 50 per cent or more. One obvious application that could capitalise on theseproperties is their use, in the form of filaments, as fibre reinforcement, for example in automobile tyres. The reasons for the weakness of crystalline materials has its origin in the unavoidable presenceof dislocations (that is mismatches between rows of atoms) which are mobile under stress.It is debatable whether one can define or identify a dislocation in a non-periodic structure (one might even view the structure as being all dislocations!) but in any case it seemsclear that any misfits that may be present in the structure do not move as readily as they do in a crystal, thereby accounting for the high strength. When metallic glassesfail, they appearto do so by ‘ductile fracture’. Metallic glasses also exhibit a remarkable resistance to corrosion. The vulnerability of normal metals to attack by corrosive agents stems in large part from the presenceof grain boundaries and other defects that are chemically reactive. The absence of such inhomogeneities in glasses is presumably a strong factor in reducing their tendency to oxidise and in preventing attack by corrosive atmospheresand liquids. Another interesting property of metallic glasses, containing cobalt and iron, can also be attributed to the absenceof grain boundaries. This is their low ‘coercivity’; that is to say, they are easily magnetised and demagnetised. This property suggests applications to magnetic memory devices; for example, in computers and tape recorders, since it would allow rapid recording and erasure of information. Certain ferromagnetic glasses have exceedingly high permeability making them potentially useful for microphones and transformers. Others exhibit a very small magnetostriction (that is a change in dimensions in a magnetic field) suggesting applications in transducers. ,,’ From a fundamental point of view there is much to be learnt about tke properties of metallic glasses. Apart from their structural, mechanical, and magnetic properties, their electrical and optical behaviour merit close investigation. At low temperatures, some metallic alloys are superconducting and a search for materials having high superconducting transition temperaturesis certain to be made.The large number of possible combinations of elements, in compositions not restricted by conditions of stoichiometry, will be valuable in this pursuit. As more materials are discovered, other interesting and valuable properties are certain to be found in this rapidly developing field.

Mott, N. F. and Davis, E. A. ‘ElectronicProcesses in Non-Crystalline Materials’,Oxford Universitv Press.1971.(2nd editionto be oublished in 1978).

Le Comber, P. G. and Mort, J. (eds). ‘Electronic and Structural Propertiesof AmorphousSemiconductors’,Proceedingsof the 13th session of the Scottish Universities’ Summer School in Physics. AcademicPress,London.1973. Taut, J.‘AmorphousandLiquid Semiconductors’, Plenum.1974. Stuke, J. and Brenig, W. (eds). ‘Amorphous and Liquid Semiconductors’,Proceedingsof the 5th International Conference (Garmisch-Partenkirchen). Taylor & Francis,London.1974. Kolomiets,B. T. (ed). ‘Structure and Propertiesof Non-Cyrstalline Semiconductors’and ‘Electronic Phenomenain Non-Cyrstalline Semiconductors’.Proceedingsof the 6th International Conference (Leningrad).Nauka.1976. Cotterill,R. M. J. ‘GlassyMetals’,AmericunScientist, 64,430, 1976. Adler, D. ‘Amorphous-Semiconductor Devices’,Scientzjic American, 236,36,

1977.