Metal-semiconductor interfaces

12

Surface

metal-semiconductor

Science 251/252

(1991) 12-21 North-Holland

interfaces

R.H. Williams Department of Physics. Universi@ of Wales College oJ Cardrff. PO Bou 913. CurdtJJ CFI 3TH. UK Received

1 October

1990; accepted

for publication

22 November

1990

When a metal is deposited on a semiconductor surface electrical barriers may be formed. In recent years the surface science approach has been extensively used to explore the evolution of these Schottky barriers and the detailed origin of the associated interface states. In addition, theoretical estimates of such states have been successful in describing the experimental data for low and high metal coverages. The present situation is reviewed and in particular the status of the various models of electrical barrier formation. Recent new approaches are also highlighted. in particular the possibility of measuring and probing Schottky barrier heights. with high lateral resolution. by ballistic electron emission microscopy.

1. In~~uction For a solid state electronic device to perform a useful function it is necessary for electrical signals to flow into and out of it. Almost invariably such signals communicate with the device via electrical contacts. Not surprisingly, therefore, the role of contacts is central to the whole field of solid state electronics. and as the size of individual components is reduced the problem of making satisfactory contacts with stable and known characteristics becomes progressively more acute. Indeed progress in the further minuturisation of many devices is now hindered by problems associated with contacts and interconnects. In this article we will deal largely with the physics of one type of contact, namely the Schottky barrier. Consider an n-type semiconductor with electron affinity xs making contact with a metal of work function (p,. In the simplest model [l] it is assumed that, in this situation, an electrical barrier is formed at the interface and the height of the barrier is simply #,, = #, - x,. This model is, of course, a gross oversimplification since the surface dipole contributions to $J,,, and x, change in an unknown way when contact is made and this is not taken into account. Furthermore, the model neglects the existence of surface and interface 0039~6028/91/$03.50

t? 1991 - Elsevier Science Publishers

states the influence of which can be drastic and which, in the extreme limit [Z]. can render +,, completely independent of &,. In understanding the basic science of Schottky barriers the challenge has been to derive simple models which account for the nature and origin of interface states at metal-semiconductor contacts. It is in this arena that the surface science approach has played a most important role. It is well known that an interface state density, D,, of around lOI cm-’ eV’ has a pronounced effect on barrier formation if these states have energies corresponding to the fundamental band gap of the semiconductor. In the high density limit &, may be independent of (p, (or the electronegativity xm ) and the Fermi level at the interface is then said to be pinned by interface states. There have been many attempts to account for the origin, density and distribution of the interface states in a simple way applicable to all metal-semiconductor combinations. Unfortunately however, despite some outstanding efforts, a “unified” theory of such states still eludes us. The metal-semiconductor boundary is a complex region where chemical reactions, interdiffusion, disorder and defects often prevail and these and many other factors must be taken into account in models which fully describe the interfaces [3]. The surface science approach

B.V. (North-Holland)

R.H. WiNiam / Metal-semiconductor

has been particularly important in elucidating the importance of these factors and the way they depend on the particular metal-semiconductor ~mbination and on parameters such as temperature. Practically all definitive investigations of the nature of interface states have involved the deposition of ultra thin layers of the metal onto the atomically clean semiconductor with simultaneous probing of the interface structure, chemistry and electron charge redistribution. The most common substrates have been the cleaved Si(ll1) and GaAs(ll0) surfaces. The latter, in particular, is a most useful surface since, for high quality cleavages, the empty and full surface states lie outside the band gap, on account of the surface relaxation. Thus, the appearance of gap states upon deposition of a metal can be readily monitored and much of this article will address recent work on these interfaces.

2. Probing electrical barriers The Schottky barrier heights relevant to the operation of electronic devices are those measured for relatively thick metal layers. ~onvention~ly, these barriers are probed by techniques such as current-voltage (I-V), capacitance-voltage (C-

interfaces

13

V) and photoresponse (PR) which are all well described in the literature [3]. By and large (though not always) these methods yield consistent results and for a wide range of metal-se~conductor combinations it is found that the sum of the electrical barriers for a given metal on n and p-type crystals of the same semiconductor is equal to the band gap of the semiconductor. It is really the physics associated with these “thick layer” contacts that we wish ultimately to understand. The euolution of the electrical barriers when a metal is deposited on the semiconductor has been widely investigated by surface science techniques, in particular by photoelectron spectroscopy (SXPS). Here, considerable progress has been made over the past ten years or so and examples will be considered in later sections. However, there are also pitfalls associated with this approach and some of these are mentioned in this section. To illustrate the surface science approach we consider the case of indium layers deposited on clean cleaved GaAs(ll0) surfaces. From detailed observations of the binding energies and chemical shifts associated with photoemission from the Ga 3d, As 3d and In 4d core levels it is possible to monitor how the overlayer grows (for example whether it forms islands), whether or not there are chemical reactions at the interface, and how the Fermi level E, shifts at the surface as the Schott-

In Coverage

(ML)

Fig. 1. The position of the Fermi level at the GaAs(ll0) surface when thin indium layers are deposited. RT and LT refer to the substrate being at room and low temperature, respectively. I-V refers to the barrier height measured by transport techniques for thick In contacts. After ref. [4].

R. H. Williams

14

/ Metal-semiconductor

[8]. These reactions complicate any attempts to understand the dependence of interface states on bonding and relaxation, for example, and clearly are best avoided in basic studies. In order to avoid the inherent problems due to interface chemical reactions there are at least two paths open. One can use metals which do not react, and examples of this will be considered later. An alternative approach which has been attempted is to deposit the metal and carry out the measurements with the substrate held at low temperature. It is believed that problems associated with reactions and with surface diffusion and clustering can be suppressed to some extent [9]. It is clear in fig. 1 that the behaviour of E, with coverage is quite different for the low temperature situation. The form of this behaviour will be considered in more detail in the next section, but here it is relevant to consider the shifts of E, for coverages in excess of a few monolayers. It may be seen that E, reaches the same energy position for both n and p material for the low temperature case but not for the room temperature situation. The saturation value of E, seen at low temperature is often assumed to correspond to the “thick

ky barrier evolves, The variation of E, with coverage is shown in fig. 1 for the situations where the substrate is at room temperature and at a lower temperature of approximately 100 K (41. This figure is representative of a wide body of similar investigations and it illustrates a number of important points. First of all it may be seen from fig. 1 that the shift of E, is quite different for room and low temperatures. Detailed analysis of the room temperature situation indicates that the adlayer atoms readily diffuse along the surface and form clusters. Diffusion paths and activation energies have been investigated theoretically {for Al on GaAs) and the basis of the process is reasonably well understood (51. For room temperature substrates strong chemical reactions between the metal and the semiconductor are also very often observed. These reactions may lead to new phases at the interface, and to disorder and defects which in turn may lead to interface states in the band gap. By and large the thermodynamic basis of these reactions is also well understood following the work of several groups, in particular McGilp [6], McGilp and McGovern [7], and Williams and coworkers

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to by

RH.

Williams / Metal-semiconductor

layer” Schottky barrier height and in many cases the barrier is fully developed for a coverage of a few ML. However it is not true to say that the barrier is fully formed for a few ML in all situations. This is illustrated in fig. 2 for the case of Sb on n and p-type InP(llO) cleaved surfaces [lo]; it may be seen that E, is rapidly changing position relative to the band edges even for thicknesses approaching 100 ML. These measurements, by Richter and his group [lo], were performed using, Raman spectroscopy, which has the great advantage in that it can follow Schottky barrier development for coverages of many hundreds of monolayers, in contrast to SXPS which is limited to tens of ML. A second pitfall associated with the application of SXPS has been highlighted by Hecht [ll] and by Alonso et al. [12] and is concerned with the generation of a surface photovoltage by the incident photon beam used to excite carriers out of the solid. This effect can significantly influence the apparent shift of E, with coverage particularly when the substrate is at low temperature and for semiconductors with reasonably large band gaps. This distortion is clearly seen for GaP, at room temperature, as illustrated in fig. 3. Alonso et al. [12] monitored shifts of E, for Ag on GaP(llO) cleaved surfaces and corrected the core level shifts to take into account the surface photovoltage. The indication of the way the Schottky barrier evolves is clearly entirely different depending on whether or not the photovoltage correction is taken into account. This difficulty has been evident in much of the recently published work for metals deposited onto low temperature III-V semiconductors.

3. Metal-induced-gap

states

When a metal makes contact with a semiconductor it is possible for the wavefunctions from the metal to penetrate very slightly into the semiconductor [13]. Additionally any localised states, such as surface states, will change into broadened resonances. The net effect is to generate interface states commonly referred to as metal-inducedgap-states (MIGS) [14-181 or virtual-gap-states

interfaces

15

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Fig. 3. Surface Fermi level position as a function of coverage for Ag on GaP(llO) cleaved surfaces. The full circles and triangles have been corrected for the effect of surface photovoltage. After Alonso et al. [12].

(VIGS) [19]. These states are associated with the metallic nature of the overlayer and are anticipated to appear once the adlayer atoms are close enough together for the layer to be a true metal. In addition, new states can appear in the gap, due to the formation of adlayer-surface atom chemical bonds, and these adsorbate-induced-states may be observed for adlayer coverages well below that corresponding to metallic behaviour. The existence of metal-induced-gap-states has been the subject of some debate for the past fifteen years and it is difficult to devise experiments to detect them. However, there is very strong evidence from recent work that they do exist and play a major role in the formation of electrical barriers. Consider first adsorbate-induced-gap-states, and again we refer to the case of In on GaAs(ll0) shown in fig. 1. It will be seen that the Fermi level at the surface for the p-type material first shifts away from the valence band edge and then reaches a plateau for coverages of around 0.1 ML. This region is shown in more detail in fig. 4, where data for other metals are also included [20]. This plateau may be interpreted in terms of a donor

R. H. Willmm

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/ Metal-semiconductor

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been made towards identifying them and understanding their systematic behaviour. For coverages in excess of a few monolayers the adlayer in general displays metallic behaviour and the Fermi level often stabilises at the same energy for n and p-material. Often, also, this yields values of Schottky barrier height which compare well with those determined for thick layers (though not always, as already pointed out). The really important question relates to the origin of the interface states which govern these stabilisation levels in general, and here the concept of the surface charge neutrality level @(, first considered by Yndurain [14] and Tejedor and Flores [15]. and subsequently by Tersoff [18] and others is central. Tersoff, in particular. calculated the values of Q. for a wide range of semiconductors. Following Tejedor and Flores [15] it was assumed that @, corresponds to a weighted mid-gap where the complex band structure changes from valence-like to conduction-like, and is thus simply a property of the semiconductor. It was shown that the electrical barrier heights for gold on a range of p-type semiconductors showed a remarkably good correlation with the calculated values of Q0 and this could also be extended to account for heterojunction band offsets. These arguments require the existence of metal-induced-gap-states and are indeed persuasive. Recently, support for the existence of MIGS has been obtained from STM experiments where electron states were probed around the peripheries of small iron particles on GaAs(ll0) surfaces [23]. Support has also emerged from SXPS investigations of Cs adlayers on GaAs(ll0) cleaved surfaces [24]. Deposition of Cs onto GaAs surfaces maintained at low temperature led to a shift of E,: similar to that shown in fig. 1. The Cs layer reached metallic behaviour for a coverage of 2 ML leading to a stabilization of E, at the same energy for n and p-crystals, as expected. However, exposure to oxygen led to a release of the Fermi level. The oxygen interacts to form a wide gap Cs oxide and at the same time the gap states disappear. Further deposition of Cs led to large Schottky barriers which could again be removed by exposure to oxygen. These experimental data are most easily explained in terms of metal induced gap states.

__.___ 1 100

in monolayers

Fig. 4. Position of the Fermi level with respect to the valence band edge for several metals deposited on clean cleaved GaAs( 110) surfaces. After refs. [19,20].

level situated close to the middle of the band gap. Both Month [19] and Lefebvre et al. [21] have shown, using a simple surface molecule approach. that this donor level could be associated with the adlayer-gallium bonds. Indeed for the case of Ag on GaAs Lefebvre et al. calculated that the donor level associated with the Ag-As bonding electrons will overlap the valence band whereas the antibonding states will lie above the conduction band minimum. Thus, for these low coverages no acceptor states lie in the gap and no band bending appears for n-type crystals. This kind of behaviour is also observed for Cs on GaAs(ll0). Month [19] has shown that the variation in the energy of the donor level for the various metals can also be understood in terms of their electronegativity, again using the surface molecule approach. Also, the elegant STM investigations of Feenstra [22] identified Au atoms bound to Ga leading to band gap states at the Au-GaAs(ll0) interface. However in these investigations the Au-Ga donor states were reported to overlap the valence band with an acceptor state. also associated with the Au-Ga bond, being formed in the band gap. These investigations, therefore, are not entirely consistent with the data leading to figs. 1 and 4 where no acceptor level is observed (not shown in fig. 4). The influence of ignoring the surface photovoltage correction may therefore be relevant for the SXPS data for n-type material. Despite this. however, the evidence for adsorbate-induced-gapstates is convincing and excellent progress has

mierfaces

R.H. Williams

/ Metal-semiconductor

The charge neutrality level in the Tersoff model is a function of the semiconductor only and yet it is known that Schottky barrier heights for most semiconductors do show a significant dependence on the particular metal. Unfortunately, for thick layer contacts this dependence does not generally scale in a systematic way with parameters such as work function or electronegativity. Whereas the model gives a useful estimate of barrier heights for a number of systems it is clearly necessary to extend it to take into account details of bonding, interface structure and imperfections. Of particular importance is the recent work of Ortega and Flores [25,26] which suggests that the energy associated with the charge neutrality level !I’,-,may be dependent on exactly how the adatoms bond to the semiconductor. They consider an “intrinsic” @+,, which is that calculated by Tersoff, and an “extrinsic” equivalent which is sensitive to the nature of the interface. This concept of “extrinsic” charge neutrality level is a most important one which may go part of the way towards accounting for the variation of barrier heights for different metal-semiconductor combinations. This calls for detailed calculations for a range of such combinations. Hopefully these will be carried out during the next few years.

interfaces

17

ference in relaxation at type A and B interfaces. Rees and Matthai [29] have shown that such a difference in relaxation would be expected to lead to substantial differences in &,, but their calculated difference is of the opposite sign to that measured experimentally. Recently another combination, namely Pb on Si(ll1) has been reported to show a large dependence of Schottky barrier height on interface structure [31]. It is possible to form two structures when Pb is deposited on the Si(ll1) surface. In one situation the first Pb layer forms a 7 x 7 structure and when a thick Pb layer is deposited on this, a barrier height of 0.70 eV was measured for n-type crystals using 1-I’ and C-T/ techniques. The second interface structure has a (fi x fi)R30“ symmetry and leads to a barrier height of 0.93 eV for a thick Pb layer on this reconstruction. This system is of particular interest since, in contrast to Nisi, on Si, it is an unreactive one. However, the reasons for the large differences in barrier height are not yet understood but are likely to be similar to those associated with Nisi,-Si. It is certain that many more investigations, both experimental and theoretical, will be carried out on these systems and efforts will be made to identify more precisely the role of interface crystallography for a wider range of combinations.

4. Interface structure 5. Interface defects As pointed out in the previous section until recently theoretical treatment of metal-inducedgap-states had not addressed the question of whether the metal-semiconductor interface electrical barriers are influenced by the bonding configuration at the interface. Indeed there has been much discussion regarding the importance of interface crystallography. Following the pioneering work of Tung [27] it is now known that barrier heights for Nisi, contacts to Si(ll1) surfaces are dependent on the interface crystallography. Two structures, type A and type B, which are mirror images of one another yield barrier heights differing by 0.15 eV. There have been several attempts to account for this difference theoretically [28,29] though without a great deal of success. X-ray standing wave experiments [30] demonstrate a dif-

It is exceedingly difficult to form metal-semiconductor interfaces which are highly perfect and few investigations have been reported for systems which approach the ideal. Most investigations have been carried out on contacts where the order and degree of epitaxy are not known and where the metal may even be in a polycrystalline form. Clearly, therefore, it is essential to consider the role of defects, disorder and imperfections at the interface. A high density of defects which form gap states and which are not screened by the metal will inevitably influence the electrical barrier and the transport of charge across it, as pointed out by Zur et al. [32]. The so called “defect model” advocated by Spicer and coworkers [33] is based on the possibility of Fermi

18

R. H. Williams / Metal-semrconductor

level pinning by defect states, and in the model the role of vacancies and anti-site defects was considered in some detail, for III-V semiconductors in particular. An example of these considerations is given for the case of the room temperature GaAs substrates in fig. 1. It is assumed that defects may be formed when In is deposited at room temperature and the Fermi levels for n and p-GaAs becomes stabilised close to an acceptor and a donor defect levels respectively (labelled DL in fig. 1). It is certain that such defects can significantly influence the evolution of the Schottky barrier but it is still not clear what the precise role of defects is in the formation of “thick layer” contacts. In fact it is not always easy to distinguish between pinning by anti-site defects and by MIGS. Flores and Tejedor [34] have pointed out that the energy associated with a III-V antisite defect will follow closely the energy of the mid-point between the cation and anion dangling bond energies and this mid-point energy corresponds to the charge neutrality level in the MIGS model. Any systematic trends might therefore be expected to be similar for both defect and MIGS models and there is evidence that this is the case. as outlined by Rhoderick and Williams [3]. The role of interface imperfections has also been emphasised by Woodall and Freeouf [35]. As pointed out earlier it is clear that chemical reactions often occur and that new phases can appear at the interface as a result. Woodall and Freeouf discuss, in particular, the role of excess anions for III-V and II-VI semiconductors since it is commonly observed that the cations react with the metal overlayer or diffuse into it. It is certain that smaI1 regions of excess anions at the interface could significantly affect the electrical barriers and strong evidence for this has been presented by Dharmadasa et al. [36]. These authors investigated Au on CdTe surfaces and demonstrated that the effective Schottky barrier height appeared around 0.2 eV lower for surfaces which were slightly anion rich. Earlier work by Kuech (371 for Au/Cd contacts to n-CdTe were interpreted in the same way. It was observed that Au and Cd yielded relatively small barriers but Au/Cd alloy gave large barriers of around 0.9 eV. This work highlighted the fact that small differences in the interface stoichiome-

interfnces

try can significantly influence the electrical barrier. The role of interface inhomogeneity is particularly important for the transport properties across a Schottky barrier. Suppose there are small regions where the barrier height is lower than for other parts of the interface. Because of the exponential dependence of the current on the barrier height it is evident that the transport can be dominated by these regions, even though they represent only a small fraction of the total contact area. It is vitally important that we gain a better understanding of the effects of such interface inhomogeneities but until recently techniques to do this have not been available. Recently, however, this situation has changed and this forms the subject of the next section.

6. Microscopic probing of eledricai

barriers

It may be clearly seen from the previous sections that many aspects of Schottky barrier formation at metal-semiconductor contacts need to be probed on a microscopic scale. The role of steps, dislocations, and anion rich regions, for example need to be considered in detail. Conventional I- Y and C-V techniques as well as SXPS are all large area ones which do not yield the lateral resolution required. Recently a technique which overcomes these limitations has been developed by Kaiser et al. [38,39], and by Fowell et al. [40]. This method is called ballistic electron emission microscopy (BEEM) and appears to have the capability of probing barriers with a lateral resolution of lo-20 A. The method is based on the scanning tunneliing microscope. A metal overlayer, about 100 A thick, is deposited on the semiconductor. A potential applied between the tip of the STM and the metal overlayer generates a tunnelling current. The electrons tunnelling into the metal can only cross the barrier to enter the semiconductor if they have energy in excess of the barrier height #Ph, and there is thus a critical tip-overlayer bias above which a current will be measured in the semiconductor. The bias at threshold gives the local value of +,, and considerations of energy and parallel momentum conservation indicates that a lateral

R. H. Williams / Metal-semiconductor

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interfaces

19

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Fig. 7. Map of BEEM current for a fixed tip-metal bias for Au on CdTe (after ref. [4O]). The region shown is 400 AX 400 A in size. I 1.2

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Fig. 5. Plot of BEEM-current against voltage for Au-CdTe three tunnel currents, A, B, C (after ref. [4O]).

for

resolution of around 10 A may be achievable in favourable circumstances. Fig. 5 shows a typical I-I/ plot for Au-CdTe [40]. The experimental points are well accounted for by the relationship I a (V - &,)' expected from theoretical consideration of electron transmission across the interface into parabolic energy bands. Fig. 6 shows values of &, determined by BEEM, at various points on the surface, separated by 100 A. It is immediately obvious that considerable anisotropies exist at this interface with the barrier locally varying by more than 0.3 eV. Large

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area techniques such as C-V or SXPS would tend to see an average of these whereas values of &, measured by normal 1-V techniques would be heavily weighted towards the smaller values because of the exponential dependence of the current on the barrier height. It is also possible with BEEM to map out the spatial variation of the collector current for a fixed tip-overlayer bias and such a plot is shown in fig. 7. Here the gold layer was deposited on a CdTe surface which had been chemically treated and the dark regions in the fig. 7 correspond to areas where the collector current is large. The anisotropy of the transport properties of the interface is very clearly seen here, emphasising the need for techniques which can probe barrier heights with high spatial resolution. Careful XPS analysis of the CdTe surface following chemical treatment suggests that it is slightly rich in tellurium, and the dark regions in fig. 7 are believed to be associated with these anion rich regions. These findings support the model of Woodall and Freeouf [35] in this instance. Similar investigations have also been carried out for MBE grown GaAs metallised by gold in ultra-high-vacuum. In contrast to Au-CdTe these interfaces were found to be of quite remarkable uniformity. It is quite clear, therefore, that BEEM offers the opportunity of probing microscopic interactions at metalsemiconductor interfaces with unprecedented spatial resolution and its application will certainly lead to improved understanding of the role played

by defects at metal-semiconductor junctions. The studies reported to date also clearly demonstrate the need to gain a full understanding of the role of microscopic processes in the establishment of electrical barriers at metal-semiconductor interfaces.

Acknowledgements The author wishes to thank all his research assistants, research students and collaborators for their continued support. He also wishes to acknowledge the support of the SERC. EEC, MOD and the US Services.

7. Conclusions References The problem of understanding Schottky barrier fornlation at metal-se~conductor interfaces has been with us for a long time; the ultimate aim is to understand in detail how the electrical barriers originate and those factors which govern their magnitude and form. It seems certain that a number of processes are of importance, these include chemical reactions, metal-induced-gap-states, defects. interface bonding and crystallography, and interdiffusion. Surface science experimental techin particular SXPS, have allowed reniques. searchers to explore the evolution of the barrier when an ultra-thin metal layer is deposited on an atomically clean surface, also enabling the formation of interface states to be investigated. In parallel, theoretical investigations of the effects of MIGS and defects have enabled donor and acceptor states formed at the interface to be identified. The evidence in support of metal-induced-gapstates is, by now, very persuasive and their existence appear to be of primary importance in Schottky barrier formation. Defect states can also play a major role and more and more evidence is emerging underlining the importance of the interface crystallography. New techniques such as BEEM, and the application of optical methods such as Raman spectroscopy, are certain to provide new highlights in the next few years and theoretical estimates of intrinsic and extrinsic MIGS are likely to open new directions for experimentalists. Though it is unfair to claim that the Schottky barrier problem is now completely understood it is certainly true that outstanding progress has been made in the last few years, at least for intimate metal-semiconductor interfaces, This progress is likely to continue unabated during the next few years.

]I] W. Schottky. Z. Phys. 113 (1939) 367. [2] J. Bardeen, Phys. Rev. 71 (1947) 717. [3] E.H. Rhoderick and R.H. Williams. Metal~Semiconductor Contacts (Oxford Science Publications. Oxford, 1988). [4] W.E. Spicer. R. Cao, K. Miyano, C. McCants. T.T. Chiang. C.J. Spindt. N. Newman, ‘T. Kendelewicz. 1. Lindau, E. Weber and 2. Liliental-Weher. Metallisation and MetalSemiconductor Interfaces. Plenum NATO ASI Series, Vol. 195, Ed. I.P. Batra (Plenum, New York. 1989) p. 139. [S] J. Ihm and J.D. J~~annopoul(~s, Phys. Rev. Len. 47 (1981) 679. [6] J. McGilp. J. Phys. C 17 ( 1984) 2249. [7] J. McGilp and I.T. McGovern. J. Vat. Sci. Technol. B 3 (1985) 1641. [X] J.H. Pugh and R.S. Williams. J. Mater. Res. 1 (1986) 343. [9] K. Stiles and A. Kahn, Phys. Rev. Lett. 60 (1986) 343. [IO] R.H. Williams, D.R.T. Zahn. N. Esser and W. Richter. J. Vat. Sci. Tech. B7 (1989) 997. [II] M. Hecht. J. Vat. Sci. Tech. 88 (1990) 1018. [12] M. Alonso, R. Cimino and K. Horn. Phys. Rev. Lett. 64 (1990) 1947. [13] V. Heine. Phys. Rev. A 138 (1965) 1689. [14] F. Yndurain. J. Phys. C 4 (1971) 2849. [15] C. Teiedor. F. Flares and E. Louis. J. Phvs. C IO (1977) 2163: 1161S.G. Louie and M.L. Cohen, Phys. Rev. Lett. 35 (1975) 866. ]I71 S.G. Lottie and M.L. Cohen. Phys. Rev. Lett. Bli (1976) 4172. U81 J. Tersoff, Phys. Rev. Lett. 52 (1984) 465. iI91 W. Month. J. Vat. Sci. Technnl. B 6 (1988) 1270. 1. Lindau and W.E. PO1 R. Cao. K. Miyano. T. Kendelewicz, Spicer. J. Vat. Sci. Technol. B 5 (1987) 99X. PII I. Lefebvre, M. Lanoo and G. Allan, to be published. v-1 R. Feenstra. Phys. Rev. Lett. 63 (1989) 1412. D.T. Pierce and v31 P.N. First, J.A. Sroscio, R.A. Dragoset. R.J. Celotta. Phys. Rev. Lett. 63 (1989) 1416. and G. Kaindl, 1241 M. Prietsch. M. Domke, C. Laubschat Phys. Rev. Lett. 60 (1988) 436. PI 3. Ortega and F. Flares, ref. 141, p. 439. VI J. Ortega and F. Flares. Phys. Rev. Lett. 63 (1989) 2500. ~71 R.T. Tung. Phys. Rev. Lett. 52 (1984) 561. [2810. Bisi and S. Ossicini, Surf. Sci. 189/190 (1987) 285.

R. H. Williams / Meial-semiconductor [29] N.V. Rees and C. Matthai,

[30] [31] [32] [33] [34]

Semicond. Sci. Technol. 4 (1989) 412. E. Vlieg, A.E.M.J. Fischer, J.F. van der Veen, B.N. Dev and G. Materik, Surf. Sci. 178 (1986) 36. D.R. Heshnga, H.H. Weitering, D.P. van der Werf, T.M. Klapwijk and T. Hibma, Phys. Rev. Lett. 64 (1990) 1589. A. Zur, T. McGill and D.L. Smith, Phys. Rev. B 28 (1983) 2060. W.E. Spicer, I. Lindau, P. Skeath, C.Y. Su and P.W. Chye, Phys. Rev. Lett. 44 (1980) 420. F. Flores and C. Tejedor, J. Phys. C 20 (1987) 145.

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[35] J.M. Woodall and J.L. Freeouf, J. Vat. Sci. Tcchnol. 21 (1982) 574. [36] I.M. Dharmadasa, J.H. Thornton and R.H. Williams, Appl. Phys. Lett. 54 (1989) 137. (371 T.F. Kuech, J. Appl. Phys. 52 (1981) 4874. (381 W.J. Kaiser and L.D. Bell, Phys. Rev. Lett. 60 (1988) 1406. [39] W.J. Kaiser, L.D. Bell, M.H. Hecht and F.J. Grunthaner, J. Vat. Sci. Tcchnol. B 7 (1989) 945. [40] A.E. Fowell, R.H. Williams, B.E. Richardson and T.-H. Shen, Semicond. Sci. Technol. 5 (1990) 348.