Mechanisms of Schottky barrier formation in metal-semiconductor contacts
LaboratoriumfurFestk6rperphysikandSonderfor5chungsbereith254. Universitdt Duisbur, D-4100 Duisburg, Federal Republic of Germany (Received 3 February 1988; accepted 26 April 1988) During the formation of metal-semiconductor contacts two principally different types of electronic states are effective in determining the surface position of the Fermi level within the semiconductor band gap. These are, first, adatom-related surface states of donor character and, second, the continuum of adsorbate-induced interface states which result from the tailing of the metal wave functions into the virtual gap states of the semiconductor band structure. The first type of state is observed at submonolayer coverages cither after depositions at low temperatures or even at room temperature when a cation exchange occurs. Each metal adatom contributes one of those surface donors and their energy levels are linearly correlated with the first ionization energies of the metal atoms. The second type of state exists at interfaces under metallic islands and continuous metallic films. The charge transferred across the interface by these tails of the metal wave functions is explained by the difference in electronegativities of metal and semiconductor in analogy to the concept of the partial ionic character of covalent bonds. leads to the formation of depletion layers on substrates doped I. INTRODUCTION 1 both n and p type until the Fermi level finally stabilizes at its In 1938. Schottky explained the rectifying behavior observed 2 final position in the gap. The approach to that "pinning with metal-semiconductor contacts by the presence of a position of the Fermi level" as a function of metal coverage depletion layer on the semiconductor side of the interface. The drastically varies with the substrate temperature during metal transport of current across such junctions is determined by their evaporation. This is shown schematically in barrier heights which measure the energy difference from the Fermi level to the edge of the conduction or of the valence band Fig. 1. in samples doped n and p type, respectively. Two basically With the substrate held at room temperature the position of different approaches have been used for determining barrier the Fermi level within the band gap initially varies heights in such Schottky contacts experimentally. logarithmically as a function of nominal metal coverage. Since, Initially, barrier heights in metal-semiconductor contacts were as will be discussed later, island growth generally occurs even evaluated from current-voltage (I/V), capacitance-voltage (C/V), in the submonolayer range the experimental numbers of metal and spectral response curves of devices, i.e., Schottky diodes, atoms deposited on the sample only give nominal coverages. or device-like structures. With the development of experimental The Fermi-level position was found to stabilize after the techniques such as photoemission spectroscopy, which are evaporation of —1 monolayer (ML) of Ga,6 Cs,7-9 Mn, Ni, 10 Pd, surface sensitive, it became possible to study the formation of Ti and V and up to 10ML of Cu14 and Y.15 This is illustrated by metal-semiconductor contacts by following the variations of the diagram shown in Fig.1(a). Even with 30 ML of Al, Ga, In 17-19 electronic surface properties as a function of the amount of and Ag deposited the positions of the Fermi level within the metals deposited on initially clean surfaces and to determine band gap differ on substrates doped p and n type although barrier heights by using such methods. with For junctions exhibiting ideal or almost ideal // ^characteristics, which is described by an ideality factor n close to unity/ the barrier heights ФBn and ФBp measured with the same metal and substrates doped n and p type, respectively, are always 45 found to add up to the band-gap energy. ' Under thick and continuous metal overlayers the interface position of the Fermi level within the band gap is thus independent of the type of doping in the semiconductor. This conclusion was not always reached in the experiments employing surface-sensitive techniques. Clean and well-cleaved (110) surfaces of III-V compound semiconductors—with the exception of GaP—exhibit no surface states in the bulk band gap, and the bands are thus flat up to to surface. The deposition of metal atoms.
FIG L Position of the Fermi level within the band gap of a semiconductor doped n or p type as a function of nominal coverage after deposition at room (a) or low temperature (b) (schematically)
Al/GaAs - as well as Ag/GaAs Schottky diodes the barker heights ФBn and ФBp were found to add up to the band-gap energy. The buildup of Schottky barriers on cleaved GaAs surfaces held at - 100 K during the condensation of Al, In, Ag, Au and Sn was 17 18 recently studied by Kahn and Spicer and their co-workers. Their findings are schematically shown in hg 1(b). While at room temperature the surface band ending almost symmetrically develops on p and n type doped samples, at low deposition temperature a pronounced asymmetric" behavior was observed. At submonolayer coverages the bands were found to remain flat on n-GaAs while strong band bending, which already saturates at coverages between 0.01 to 0.03 of a monolayer, was observed with samples doped p type. After approximately one-half to a full monolayer were deposited, depletion layers also began to form on n-GaAs while the band bending simultaneously decreased at the surfaces of p-GaAs samples. Finally, the same stable position WFf of the Fermi level was assumed within the band gap for both types of substrate doping after 1 to 10 ML of metal were nominally deposited. The initial pinning position WFf, of the Fermi level on the samples doped p type becomes more expressed as the substrate temperatures during metal condensation are lowered. However, even after dcpoMtions at room icmpcriUUrc slight "overshooting of the Fermi level with respect to its final 19 6 position under thick metal overlayers was detected for Ag, Ca, 9 2 Cs, Cu, ^ Mn, Ti, V. and Y on p-GaAs(110). The nucleation and growth kinetics of metals evaporated on 21 solid surfaces has been widely investigated for a long time and they have been found to depend strongly on the temperature of the substrate during metal deposition and on the arrival rate of the metal atoms. Therefore, the development of surface band bending as a function of metal cover-age, at least until the final barrier height is reached under a thick metal film, should correlate with the different growth modes during depositions at low or at room temperature. For this reason, results of studies on the growth kinetics of metals on cleaved surfaces of III-V compound semiconductors will be summarized in Sec. II. In Sec. Ill two basically different mechanisms, which are determining the position of . the Fermi level within the band gap at submonolayer coverages and under metallic overlayers will be discussed. These mechanisms are surface states of donor type related to isolated metal atoms and the continuum of metal-induced gap states, respectively. Furthermore, their correlation with specific growth conditions will be analyzed. That section as well as Sec. IV also deals with chemical trends of the barrier heights and the S parameter of Schottky contacts. II. GROWTH KINETICS OF METALS ON (110) SURFACES OF III-V COMPOUNDS The growth mode of metals condensed on cleaved surfaces of III-V compound semiconductors has been studied by using. for example. Auger electron spectroscopy (AES), photoemission spectroscopy (PES) from core levels as well as the valence bands, low- as well as high-energy electron diffraction (LEED. RHEED). low-energy electron energy*loss spectroscopy (EELS), scanning electron microscopy
(SEM), and a Kelvin probe. The group III metals Al, Ga. and In as well as the noble metals Cu, Ag, and Au exhibit basically similar behavior. The surface mobility of arriving atoms may be described by a hopping frequency which can be expressed as u exp( -dH/kT). 12 -1 The frequency factor v typically amounts to 10 s and the activation energy for migration dHm has been estimated as 0.3 22 23 to 0.6 eV for Al on GaAs (110 ). - An isolated Al atom is thus 4 expected to make in the order of some 10 jumps per s at room 5 temperature but only one jump in some 10 days at 100 K. The Al atoms, and the same seems to hole} for the other metals mentioned in the preceding paragraph, are thus very mobile at room but almost immobile at low temperature, Theoretical 22123 calculations have also revealed all Al adsorption sites to be unstable against the formation of Al-Al bonds. The single bond as well as the cohesive energies of the group III and the noble metals are comparable to each other and, therefore, it is quite plausible that all those metals were found to form clusters and islands after deposition at room temperature and even at nominal submonolayer coverages. Some of the experimental results will now be discussed.
A. Room-temperature depositions
Dy using RHEUD. three-dimensional In islands were dc-. tectcd after a deposition of nominally two tenths of a mono24 layer on GaAs( 110) at room temperature. With Ag evaporated on GaAs( 110) surfaces a well-developed Fermi edge 19 was observed after a nominal coverage of 0.25 ML. The three-dimensional islands formed at such low coverages arc thus metallic. With increasing amount of metal deposited, the islands are growing in size but the area in between them remains free of any adatoms. For Al. In, and Cu on GaAs( 23 27 110) this was revealed by LEED and EELS. - The LEED I/V spectra of the clean surface as well as the 20 eV energy loss, which results from excitonic transitions from Ga( 3d) core levels to empty surface states at clean surfaces, were found to persist up to nominal coverages of 4 to 8 ML of those metals. Cs, Ge. Sb, and Se adsorbed on GaAs(llO) surfaces, on the other hand, show a distinctly different be--havior: The 20 eV energy loss vanishes after the deposition between a half to a 9 26 28 full monolayer. ' * In the latter examples, the adatoms are thus forming a two-dimensional layer rather than islands. The formation of metallic islands is preceded by nonmetallic clusters. This becomes evident from the observation that in photoemission spectra of the valence bands the typical Ag(4</) and Au(5rf) bands only gradually develop from initially narrower doublet structures, which are exhibiting an atomiclike 29 31 spin-orbit splitting, as a function of nominal coverage. " Continuous metal films are generally observed only after 24 nominal metal doses of some tens up to more than 100 A of 32 metal. In this respect the deposition rate plays an important role. Low arrival rates of, for example* Oa on InAs(llO) surfaces arc delaying the formation of continuous Ga films to 32 larger nominal coverages. In addition to the transition from nonmetallic clusters over metallic three-dimensional islands to continuous metal
films cation exchange reactions (see. for example, Refs. 10 and 12) as well as intermixing33 may occur. At room temperature the thermal concentration of surface vacancies is extremely low and three surface bonds have to be broken in order to effect, for example, a cation exchange. Although the formation of the new compound is thermodynamically favored. an activation barrier has to be overcome. The exothermic association of evaporated single atoms with already existing metal clusters or islands has been proposed to provide the necessary energy.23 However, at room temperature the cation exchange reaction was found to be rather limited for Al deposited on GaAs, GaP, and InP( 110) surfaces.34-36
B. Low-temperature depositions
FIG. 2 Fermi-level position as a function of In, Al. Ag» and Au coverage after low-temperature deposition on GaAs(110) samples doped p type (Rcf. 18) The continuous lines were calculated for surface states of donor type at 0.87.0.76.0.68. and 0.49 eV above the valence-band top and a bulk acceptor density of I X 1019 cm"3. (•) In. (0) Al. (Q) Ag. and (•) Au.
The reduced mobility of metal atoms on (110) surfaces of 1IIV compound semiconductors at low temperature causes a growth behavior of the evaporated films which is distinctly different from the one observed at room temperature. On GaAs(ll0) surfaces held at 190 K, three-dimensional In islands were detected after a deposition of nominally 0.8 ML compared to only 0.2 ML at room temperature. 24 In LEED //Fas well as in electron energy-loss spectra none of the features typical for clean GaAs (ll0) surfaces were found after the deposition of 2 or 4 ML of Al and In, respectively, at 100 K.26--*7 With Ag as well as with Au evaporated on GaAs( 110) surfaces held at 100 K, the evolution of features characteristic for metal d bands were only observed at nominal coverages above 0.8 to 1 ML by using PES.31 III. MECHANISMS OF BARRIER FORMATION A. Adsorbate-related surface donors The buildup of surface band bending onp- and the lack of itonn-GaAs(llO) in the submonolayer coverage range [see Fig. 1 (b) ] indicates the formation ofadsorbate-related surface states of donor type during metal depositions at low temperatures. The initial pinning position of the Fermi level within the gap then is close to the energy level of those donors. The surface band bending e^ V, may be calculated as a function of the density N^ of surface states from the charge-neutrality condition
W WF Qss e0 N ss exp ss kT 1
With the assumption of discrete donor states at energy Wss the charge Qss in these surface states is given by
experimental data for In, Al, Ag, and Au deposited on p-GaAs at low temperatures. The curves shown in Fig. 2 were computed by solving Eqs. (1) to (3) for adsorbate-induced donor levels at 0.87, 0.76, 0.68, and 0.49 eV above the valence-band top W^ at the surface and the assumption that each metal atom deposited creates one surface state, i.e., N^ = (y\\QO, The coverage 6 in monolayers (ML) is measured in units of the total density 110== 8.85 l014 cm"2 of atoms in GaAs(110) planes. The experimental data are excellently described by the calculated curves up to coverages of 0.25 ML. Above that coverage another mechanism obviously comes into play which will be discussed in Sec. Ill C. In the coverage range up to 10~2 ML the experimental data points are above the calculated curve. This behavior is indicative of an initial band bending at the clean surface which results from of a low density of cleavage-induced surface states of donor character. Table I shows the energies of the adsorbate-induced donor states just evaluated from the data reported by Cao et ol and the first stabilization or pinning positions of the Fermi r level above the top of the valence band as determined from the experimental data by Stiles et a/.17 Obviously, the Fenni level is found to be pinned closer to the bottom of the con* duction band in the studies by Cao et at. than in those by
TABLE I. Initial pinning positions W^ of the Fenni level above the valence-band top W^ after metal deposition at low temperature* on /^OaA»( 110) xurfaces. (in eV) Metal Cao et.al. (Rcf. 18) In Al A» Au Sn 0.87 0.76 0.68 0.49 *** Stiles et.al.. (Ref. 17) 0.77 0.59 0.56 0.5 0.59
At low temperatures the space charge density in a depletion layer may be approximated by38*39
where NA is the acceptor density of a p-type doped semiconductor and e, is its static dielectric constant* By using photoemission spectroscopy from core levels, Cao and Stiles es al.17,31,40 have studied the initial stages of band bending at cleaved GaAs( 110) surfaces as a function of metal coverage. Here, the data communicated by Cao et al shall be discussed in detail since they achieved metal coverages as low as 10-3 ML. Figure 2 displays their
Stiles et ai This difference might be caused by an increased surface temperature during the experiments by Stiles et al since Cao et at. demonstrated the effective pinning position of the Fermi level to move towards the conduction-band bottom with decreasing deposition temperature. This explanation is also supported by the following experimental results. At the lowest substrate temperatures used during metal evaporation Cao et al. found that on samples doped n type the bands remain flat up to 0.25 ML while the data of Stiles et al, exhibit a gradual buildup of a slight surface band bending. The formation of surface band bending on n-GaAs(ll0) and the reduction of the Fermi-level overshoot as a function of submonolayer metal coverages are obviously related. They are both caused by the formation of metal clusters and islands at temperatures where the evaporated metal atoms become more mobile. This will be discussed in Sec. III C. An initial overshoot of the Fermi level over its final gap position, which is the same for GaAs samples doped;? and n t)pe, has also been observed for Ca,6 Cs,9 Cu20 and the transition metals Ti, V, Mn, and Y10,20 after deposition at room temperature on substrates doped p type. With coverages as low as 0.01 ML of Ti, V, Mn, and Y, Ludeke et al observed a shifted Ga( 3d) component which they attributed to elemental gallium. They concluded that the transition metals have replaced surface gallium atoms. Such exchange reactions thus yield isolated metal atoms at room temperature. Therefore the overshoot energies of the Fermi level as observed with Cs, Ca, Cu, Ti, V, Mn, and Y evaporated on p~ GaAs(110) at room temperature will be tentatively included in the following discussion. Experiments after deposition of those metal at low temperatures are highly desirable. B. Chemical trends of adsorbate-related surfacedonor energies Till now, the energy levels of metal atoms adsorbed on semiconductor surfaces have not been calculated and models developed for the adsorption on metals cannot be simply transferred. Therefore, chemical trends shall be looked for in correlating the energy of the metal-induced donor level on GaAs( 110) with atomic properties such as, for example, the _ electronegativities and the ionization energies. No correspondence was found by using the electronegativities. Figure 3, however, where the first stabilization energies of the Fermi level at p-GaAs( 110) surfaces after deposition of Ag. Al, Au, In, and Sn17'18 at low and of Ca,6 Cs,9 Cu,20 and the transition metals Ti. V. Mn, and Y10,12 at room temperature are plotted versus the ionization energies ly of the respective metal atoms41 reveals a pronounced chemical trend. A least-square fit to either the low-temperature data only or the whole set shown in Fig. 3 yields the linear correlation WFi - W,, == - 0.077 Ia +1.21 eV. ' (4) The plot presented in Fig. 3 shows that the adsorbate-related donor levels of the metals investigated are all located above the charge-neutrality level W0 — Wvs = 0.5 eV42 of the virtual gap states (ViGS) of the complex.band structure of GaAs; thus, they are in that part of the band gap where the ViGS exhibit acceptor character. All the data displayed in Fig. 3 and described by Eq. (4)
Atomic ionization energy FIG. 3. Energy of adsorbate-induced donor levels and initial pinning positions of the Fermi level above the valence-band top for metals deposited at low and at room temperature, respectively, on GaAs (110) samples doped p type as a function of the atomic ionization energies. A data from Rets. 18 and 20,0 data from Rcf. 17,0 data from Refs. 6,10 and 12,0 data from Ref 9. /
were obtained with isolated adatoms on GaAs(llO) surfaces. Therefore, the initial "overshoot" positions of the Fermi level observed with the room-temperature deposits can most probably also be identified as the energy positions of the respective adsorbate-related donor levels. This data set then calls for a theoretical model. Results of a tight-binding approach, which will be published elsewhere, are reproducing the chemical trend observed with these adatom-related donor levels. C. Adsorbate-induced gap states and metallic behavior As shown in Figs. 1 and 2, the Fermi level "moves" from its flat-band condition on p type and from its initial pinning position on n-type GaAs, when the nominal coverage of the metals deposited at low temperature exceeds —0.25 ML. With increasing coverage the Fermi level eventually reaches its final pinning position which is the same for both types of doping. This process is caused by the formation of islands which become metallic, when their diameter goes beyond approximately 20 A43 and finally ends, when the lateral spacecharge layers under the metallic islands overlap. The development of the metallic character of the metal deposited may be most simply followed by monitoring the evolution of the broad d bands from the narrow-spaced atomic d levels in photoemission spectra as a function of, for example, Ag or Au coverage at low temperatures on GaAs(ll0) surfaces. This was done by Stiles et at31 and they found that as a function of nominal coverage the Ag(4rf) peak initially showed a constant width of 2 eV which increases at the onset of the "Fermi-level movement" from its stabilized positions, i.e., above —0.5 ML, and finally saturates at 3.2 eV. This value, which is reached at a nominal coverage of 4 A, is characteristic for bulk Ag. The broadening of the atomiclike Ag(4d) peak is caused by the 4d~5s hybridization in metallic silver. The final pinning position of the Fermi level and the full width of the d bands arc
corresponding to increasing/?-type (upward) band bending. A deposition of only 2 A is sufficient to produce a second Ga !d peak feature due to dissociated Al in both surface- and bulksensitive spectra. This feature continues to grow with increasing Al coverage and the splitting between dissociated and undissociated peaks increases. At coverages of 10-20 A Al, the bulk-sensitive Ga 3d spectra still provides distinct energies for the substrate Ga while the surface-sensitive Ga 3</spectra reflect almost entirely the dissociated component. By considering only the undissociated Ga 3d component in the bulk-sensitive spectra, one obtains a 0.27 eV total bnnd bending. A similar shift is apparent for the corresponding As 3d core level shown. Since the starting Ef position was Ev + 0.53 eV, Ef moves to 0.80 eV above EVBM. We followed similar procedures in analyzing spectra for all other metals and GaAs surfaces reported here. Figure 2 illustrates the Ef movements induced by deposition of Au, Al, Cu, and In on both n-type and p-type GaAs surfaces. The Ef behavior is strikingly different from that reported consistently for UHV-cleaved GaAs(ll0) surfaces. First, this set of common metals produce a range of E f stabilization energies extending over 0.7 eV from Ey + 0.18 eV to Ev + 0.92 eV. This is in contrast to the narrow 0.2-0.25 eV range reported for 10 11 12 GaAs (110) * and GaAs (100) . Second, the Ef stabilization energies are the same for both n-type and p-type GaAs with the same metal. This is in contrast to the 0.2 eV separation 10»1 u3 seen for many adsorbates on UHV-cleaved GaAs (110)* Third, the Ef stabilization occurs over 5-20 A in all cases, and not within the sub-monolayer coverages reported for GaAs 10 11 (110). ' The GaAs specimens exhibit a range of 0.35 eV in Ey energies for their initial clean surfaces. The variation in starting
energies may be related to differences in Ga:As st0ichiometry, 30 31 which is known to produce changes in Ef position. - These variations correspond to reconstructions from (4x2) through (2X4). However, significant differences in starting energies produce little or no differences in final stabilization energies, as evidenced by the Au and Al curves. For Au deposition on three fl-type and one^-type surfaces, Fig. 2 shows an Ef stabilization range of 0.3 eV but a final Ef spread of only 0.05 eV after 20-A deposition. Likewise, for Al deposition on one n-type and two/Mypc surfaces. Fig. 2 displays a 0.2 eV initial Ef range but a final Ef spread of only 0.12 eV. Thus the metal interaction rather than the starting surface appears to be dominant in determining final stabilization energies. This does not preclude compositional Ef effects caused by variations in Ga:As outdiffusion and resultant interfacial stoichiometry. Of primary significance. Fig. 2 demonstrates that metals on GaAs produce a wide range of Ef movements which is not constrained to a narrow window of mid-gap energies. ^ IV. DISCUSSION Figure 3 illustrates the contrast between the band bending induced by metal deposition on clean MBE-grown GaAs(lOO) versus melt-grown GaAs(110) surfaces. Plotted versus metal work function ФМ are barrier heights ФВ (left ordinate) and Ef positions below the vacuum level (equal to barrier height ФВ plus electron affinity Xsc) (right ordinate). Comparison of absolute valence band energies for UHV-cleaved (110) and thermally decapped (100) surfaces under identical conditions reveals the same binding
FIG 2. Fermi level shifts within the GaAs band gap for deposition of Au, Al, In and Cu on both n-and p-type GaAs (100) surfaces. The Ef shifts extend over 0.7 eV. are the same within experimental error ( ± 0.05 eV) for n' and p-type. and evolve over 5-20 A coverages, depending bn the metal* The initial Ef portions for clean, ordered GaAs are located in a O.35 eV window near mid-gap. \
FIG. 3. GaAs barrier heights ФВ and Ef positions below the vacuum level (ФВ + electron affinity Xsc) plotted vs metal work function. Meltgrown GaAs (110) surfaces exhibit a 0.2-0.25 eV range near mid-gap for a wide variety of metals. Only four metals on MBE-grown GaAs (100) surfaces exhibit a 0.7 eV range which overlaps the melt-grown band and which extend to within 0.2 eV of the valence band. Ideal Schottky behavior appears in the upper ten-hand inset and corresponds to the diagonal line.
simultaneously reached as a function of nominal coverage. 24 Independent RHEED studies revealed that in the same nominal coverage range the edge reparation of the inlands tm decreased to zero, i,c., the metal now forms a continuous film 37 but not necessarily a flat film of uniform thickness. The approach of the Fermi level from its position in the initial isolated-adatom coverage range to its final position under a continuous metal film might be simulated by using model 44 calculations by Tang and Freeouf They have computed measured, i.e., probe averaged, surface potentials for a variety of distributions of sites at which the Fermi level is pinned. Such simulations might be repeated and compared with the more recent low-temperature data.
D. ViGS-model of the barrier heights In Schottky contacts
Chemical bonds in diatomic molecules, in which the constituent atoms are different, are partially ionic in character. Following 45 Pauling both the sign and the approximate amount of charge transferred can be determined from the atomic electronegativities of the atoms involved: The bonding charge is shifted towards the more electronegative atom and the lonicity of the bond is given by the difference of their electronegativities. It has been proposed that the same concepts can be applied to adatoms at semiconductor surfaces as well as to semiconductor 46 51 interfaces. " The surface, states of the semiconductor, which are involved in this charge transfer, have been identified as the virtual gap states (ViGS) of the complex band structure of the semiconductor which are then forming the tails Of the wave 52 function of the adatoms into the semiconductor. For metalsemiconductor contacts considered here, this then leads to the following simple model. The tails of the metal wave functions into the semiconductor are described by the ViGS of the semiconductor, which are now called adsorbate-induced gap states 46 53 (AIGS), metal-induced gap states (MIGS), or induced density of 54 interface states (IDIS). Consequently, the amount of charge in these AIGS should be determined by the difference of the 55 electronegativities of the semiconductor and the metal. The ViGS predominantly possess acceptor character closer to the conduction and donor character clos- ^ er to the valence-band edge. The final pinning position of the Fermi level under a continuous metal film should thus be found above, at or below the charge-neutrality level (CNL) or branch point of the semiconductor ViGS when the metal exhibits a smaller, the same or a larger 55 electronegativity than the semiconductor. ^ Following this model, the final saturation or pinning positions (WFf — Wvs) of the Fermi level are plotted in Fig. 4 over the electronegativity difference (Xad — XGaAs) of the metal and the 56 GaAs substrate. All the data shown were determined by using photoemission spectroscopy, i.e., the / nominal metal thickness never exceeded some tens of angstroms. The metals considered exhibit the same pinning positions for substrates doped n and p50 type. The straight line in Fig. 4 was earlier concluded from the 7 0 data points for Cs and Cl^ and the CNL calculated for the ViGS 42 of GaAs. All the experimental results arc following the trend predicted by that line and they are, therefore, confirming the ViGS
Electronegativity difference Xad – XGaAs,
FIG. 4. Final pinning positions of the Fermi level above the valenceband top vs the electronegativity (Ref. 58) for various adsorbates on GaAs(110) surfaces as determined by using photoemission spectroscopy. Unfilled and partly filled symbols for substrates doped p type and p as well as n type, respectively A data from Rets. 7, 8 J 1, 13, 14, 16 J 8, and 20, D data from Rets. 6.10.12,15.57. and 58, V data from Ref. 17, > data from Ref. 59.0 data from Rets 9, 50, and 60 and charge-neutrality level (CNL) of the ViGS from Ref. 42, straight line (ViGS line) from Ref. 50. . -'
model ofadsorbatc- or metal-induced gap states at semiconductor interfaces. Some of the data points are above the ViGS line but none are below it. The same observation was made when the barrier heights evaluated from I/V characteristics of Si and GaAs Schottky diodes were plotted vs the metal electro49151 negativities. The deviations of experimental barrier heights to lower values than predicted by the ViGS line were attributed to defects of donor type created during the formation of the diodes. This explanation is favored by recent aifnealing experiments. In Fig. 4 the partly filled and the unfilled data points for V:GaAs( 110) were obtained immediately after the deposition of 1 A of V at room temperature and after a 57 subsequent heat treatment at 300 °C, respectively. The data point evaluated after the annealing treatment is on the ViGS line. This finding supports the presence of defects in the unannealed samples since excess defects are generally eliminated by thermal annealing. Similar observations were also reported for LaB6 : GaAs(100) Schottky diodes where the barrier height was increased and brought closer to the ViGS 61 line by heat treatments. As was already discussed in the Introduction, even after the deposition of up to more than 10 A of Ag, Al, and In at low temperature no common final pinning position of the Fermi level was observed with GaAs substrates doped p and n type 17 18 when PES was used - although the barrier heights 4>^ and 4 ^sp measured with Ag-GaAs as well as Al-GaAs Schottky diodes are adding up to the band-gap energy. It is, however, generally observed that on samples doped;? type the Fermi level assumes its final pinning position, which is characteristic for a continuous metal layer, at much lower coverages than on substrates doped n type. With low-temperature metal deposits one reason for that behavior certainly is that the effect of adsorbatc-related surface donors, which are determining the initial stabilization of the Fermi
Ievel in the low-submonolayer coverage range, is easily compensated by the AIGS under even a small density of metallic islands. Therefore, Fig. 4 also includes data points for Ag, Al and 16 18 16 In, - as well as Ga deposited on GaAs(110).samples doped p type. These data points are also excellently following the chemical trend predicted by the ViGS model of the interface states on metal-semiconductor contacts. IV. CHEMICAL TRENDS OF THE S PARAMETER OF METAL-SEMICONDUCTOR CONTACTS Already in 1965 Cowley and Szc showed that for a continuum of interface states at metal-semiconductor interfaces the slope S== dФВт/dФmet where Фmet is the metal work function, is
2 e0 S 1 Dis eff 0
and thus only depends on the product of the density of states Dis of interface states, which was assumed to be constant in the range of Fermi-level positions considered, and the effective width eff of the dipole layer at the interface, which is a 63 consequence of the presence of interface states. The Schottky65 Mott rule^
Fro. 5. Slopes S =dФВ/dФmet plotted vs the electronic contribution , to the dielectric constant of the semiconductor.
ФВn = Фmet - s
Or, what is equivalent, S == 1 would be only obtained with no interface states present at all. In Eq. (6) s, is the electron . affinity of the semiconductor The band structures of all semiconductors, however, 'contain solutions for complex wave vectors in energy gaps and, therefore S == 1 should not be observed experimentally. The density of the virtual gap states decreases with increasing width of the respective energy gap and, indeed, S == 0.85 was recently reported for metal-xenon 66 67 contacts. The band gap of xenon amounts to 9.3 eV. 55 A more detailed analysis of the arguments given above shows that the product D^S^ is a function of the average width of the semiconductor band gap which, on the other hand, is proportional to the inverse of the.square root of ( — 1) in a simple two-band model. Here is the electronic part of the dielectric constant. From Eq. (5) it then follows: (7) The experimental slope parameters S determined with 20 different semiconductors and insulators were shown to follow 55 such a power law. In Fig. 5 the recently reported data point for metal-xenon contacts is included and it obeys the chemical trend predicted from the ViGS model adsorbate-or metal-induced gap states.
(1/S)-1 ( -1) .
The surface-science approach towards an understanding of the electronic properties of metal-semiconductor contacts has identified two principally different types of states in the semiconductor band gap which are adatom-related surface states of donor character and the continuum of metal-induced gap states which result from the tailing of the metal wave functions into the virtual-gap states of the complex
semiconductor band structure. Each metal adatom contributes one of those surface donors and their energy levels are linearly correlated with the first ionization energies of the metal atoms. This chemical trend is reproduced by tight-binding calculations 68 which are assuming covalent adatom-substrate bonds. The identification of those two basically different mechanisms at submonolayer coverages and under continuous overlayers is in excellent agreement with results of self-consistent electronicstructure calculations of Al deposited on Ge( 100) by Batra and Ciraei. By increasing the Al coverage from one-half a monolayer to a full monolayer they found that the initially directional and covalent Al-Ge bonds begin to be replaced by more delocalized metallic-type interactions. - Depositions of highly mobile metal atoms at room temperature result in a complex behavior of the Fermi-level position within the semiconductor band gap as a function of metal coverage since under such experimental conditions metallic islands are forming even at nominal submonolayer coverages and part of the surface area is then left bare up to much larger nominal coverages. Generally the surface band-bending changes almost logarithmically as a function of nominal coverage with a slope of O.1 eV per decade. With Ti and Pd on GaAs( 110) the slope is larger by a factor of 2.5. For this growth 70 mode a model proposed by Doniach et a/. might be applicable but it should be tested with metals simultaneously deposited on samples doped p and n type. This growth mode is also responsible for occasional observations of different pinning position^ of the Fermi level on samples doped;? or n type even for very large nominal thickness of the evaporated metals. With respect to the adatom-related surface donors and the adsorbate-induced interface states discussed above, theoreti-
cal as well as further experimental studies are urgently needed. The ionization energies of adatoms on semiconductor surfaces as well as the charge transfer across metal-semiconductor interfaces into the ViGS of the complex semiconduc-. tor band structure should be calculated for metals other than just Al on Ge. GaAs, ZnSe, and ZnTe. Additional experiments should investigate the change of the electronic proper-tics of semiconductor surfaces as a function of metal deposition at low temperatures.
ACKNOWLEDGMENTS Part of the woric reported here, was done at the IBM Research Center in Yorktown Heights during an extended summer visit. I should like to thank IBM Corporation for the kind hospitality and Dr. R. Ludeke for many stimulating and challenging discussions. Furthermore, discussions with Professor A. Kahn. Professor J. Pollmann, L. Koenders, and H.U. Baier as well as the help with a computer program by Dr. H. J. Clemens are gratefully acknowledged.