Ellipsometric and Gas-Volumetric Investigation of Adsorption Reactions on Clean Silicon and Germanium BY F. MEYER AND M. J. SPARNAAY Philips Research Laboratories N.V. Philips' Gloeilampenfabrieken Eindhoven- Net herlands Received 21st September 1970 The chemical adsorption of a few organic gases on clean silicon and germanium is discussed. The adsorption appears to depend strongly on the presence and number of dangling bonds at the surface. Structures for the adsorption complexes have been proposed based on ellipsometric and gas-volumetric data. There is evidence that the adsorption complexes for CH3Cl and CHJBr on the (1 11) face have a reversible transition at higher temperatures which regenerates dangling bonds. Thermodynamic calculations for this transition give information on the free energy of mutual compensation of these dangling bonds.Chemical adsorption of a number of gases on the clean surfaces of silicon and germanium has been investigated. We have mainly used three different techniques of surface study viz. ellipsometry Auger electron spectroscopy (A.E.S.) and gas- volumetric adsorption measurements on powders. All three methods have a sensitivity of 1-5 % of a monolayer. A combination of the results makes it possible to propose structures for the adsorption complexes. The adsorption appears to be governed by the presence and number of dangling (uncompensated) bonds of the surface atoms and is therefore similar for silicon and germanium surfaces.1 The dangling bonds have some mutual compensation which is probably the reason for the displacements of the surface atoms from their normal positions as observed by low-energy electron diffraction e.g.Si (1 11) - 7 x 7 Ge( 1 1 1) - 2 x 8 etc.2 The degree of compensation on the clean surface is not known but the reactivity of the surface atoms is such that stable molecules such as methyl chloride and methyl bromide adsorb ~hemically.~ There is evidence that the chemical adsorptions are dissociative compensating the dangling bonds with formation of adsorption complexes in which all atoms have their normal va1ency.l. This paper gives a short review of previous work and some new ellipsometric results on the adsorption of organic gases on silicon and germanium; the results are used to obtain information on the degree of mutual compensation of the dangling bonds. EXPERIMENTAL The ellipsometric apparatus has been de~cribed.~ The two angles pertaining to the ellipsometric effects could be determined reproducibly to 0.01 ".The single crystal silicon and germanium samples were cut from high ohmic crystals oriented to within 0.5" of the desired orientation and finely polished. The silicon samples were cleaned by resistive heating to 1200°C for a few minutes and the germanium samples by heating to 850°C for a few hours in a vacuum of The A.E.S. measurements could be performed in combination with elli~sometry.~ An apparatus equipped with a 127" electrostatic analyzer for the measurement of the energy Torr. 17 18 ADSORPTION REACTIONS ON SILICON AND GERMANIUM distribution of the electrons has been used. Temperature measurements on the single crystalline samples were carried out with an Ircon 300C infra-red pyrometer.The gas-volumetric adsorption and desorption experiments were performed on germanium powders only. The powder was obtained by crushing a high-ohmic single crystal in air and cleaned by heating to 650°C in a vacuum of The specific surface area was -0.1 m2/g. Pressure readings of the admitted or desorbed gases were taken with a McLeod manometer and the decomposition products were analyzed by an Atlas M86 mass-spectrometer. Torr for 15 h.'. RESULTS AND DISCUSSION COMBINATION OF ELLIPSOMETRY GAS-VOLUMETRY AND A.E.S. Gas-volumetric adsorption measurements on powders yield the amount of gas adsorbed and therefore the surface coverage since the total surface area can be deter- mined by physical adsorption of krypton at liquid nitrogen temperature interpreting the results with the B.E.T.equation.' Surface cleanliness can be checked by oxygen chemical adsorption at room temperature. The reaction appears to proceed rapidly (exposure - 1 Ton min)' to a coverage of one oxygen atom per germanium or silicon surface atom independent of the crystallographic orientations (1 1 l) (100) and (1 lo).* The further reaction at room temperature is much slower. This seems to be a common feature of the chemical adsorptions on silicon and germanium. The amounts adsorbed in the " fast " reactions seem to correspond to the compensation of the dangling bonds by &ssociation of the adsorbing molecules. The inherent difficulty of the powder measurements is the presence of more than one crystallographic orientation of the surfaces. Calculations based on bond energies predicted a 75 20 5 ratio for (1 11) (100) and (1 lo).' A detailed study of methanol adsorption and subsequent decomposition of the adsorption complex as a function of temperature suggested an 80 20 ratio for (1 11) and Ellipsometry correlates well with these measurements.Ellipsometry is a very accurate optical method whch measures the change in the state of polarization of polarized light upon reflection from a surface. Since the measurements are normally performed with a light spot of 1 mm2 one is able to investigate single crystal surfaces. Comparison with radiotracer techniques O and with gas-volumetric measurements on powders 4* l1 suggested strongly that in many cases the macroscopic theory can be extrapolated to the sub-monolayer region using an effective index of refraction and thickness for the adsorbed layer.It has been demonstrated that in good approxima- tion the Lorentz-Lorenz eqn (1) can be used to relate the macroscopic parameters index of refraction n and thickness d to the microscopic parameters polarizability a surface coverage 8 and the number of surface atoms per cm2 N The value of the atomic or molecular diameter of the adsorbate can be taken for d. It appears that the ellipsometric angle $ for layers in the thickness range 0-50A is related to the absorption coefficient of the layer and the ellipsometric angle A with the real part of the index of refraction and the thickness. The layers discussed in this paper are not strongly optically adsorbing in the visible region and the expected change in @ upon adsorption will therefore be very small.The change in A which contains two unknowns can be interpreted in terms of surface coverage if a value is chosen for the polarizability of the adsorbate. In general literature values for ct have been used. This procedure has been tested for a few physical adsorptions e.g. krypton on clean and oxidized silicon and germanium at liquid-nitrogen tempera- F. MEYER AND M. J . SPARNAAY 19 ture.'" l 2 The coverages 6 were determined independently by gas-volumetry on a powder and a value for 6A (change in A upon adsorption) was calculated using the n and d from eqn (1) in the formulae from the macroscopic theory. Excellent agreement was obtained between calculated and measured values. For chemical adsorptions however anomalous ellipsometric effects both in A and $ have been observed for the first monolayer (a monolayer in chemical adsorption is defined as the coverage where all dangling bonds have just been compensated) whereas further adsorption seemed to give normal effect^.^ There are two possible interpretations.(a) The ellipsometric effects are due to the adsorbate only. This implies that the optical constants of the first monolayer are greatly different from the next layer. Calculations give unrealistic values for the optical constants viz. n < 1 and k> 0.5 in the visible region. Phys. ads. C lean Chem. ads germanium. FIG. I .-Schematic representation of physical and chemical adsorption on clean silicon and (b) The second interpretation of the ellipsometric effects includes a possible change in the substrate optical properties.The effects 6 6 and 6$ could be divided in an adsorbate-dependent part which obeyed the macroscopic theory as for the physical adsorption and an adsorbate-independent part which is due to a change in the substrate upon adsorption. The effect on the substrate which all chemical adsorp- tions have in common is the compensation of the dangling bonds of the surface atoms. This can be described in macroscopic terms as depicted in fig. 1. The top layer of atoms on the clean surface is taken as a layer with optical constants different from the underlying bulk. This layer which we call a transition layer is 0.5 0.4 0.3 3 6Q 0.7 0. I 0.2 01 0.6 0.8 1.0 1-2 1.L t 1.6 8 6h" FIG. 2.-The @A Sl)) curves for chemical adsorption on Si(ll1) and Si(100) measured at an angle of incidence of 70.5" and 69.5" respectively.The wavelength was 0.55 pm. a CH3Cl on Si(ll1) ; A CH3Br on Si(l11) ; 0 CH3C1 on Si(100) ; A CH3Br on Si(100) ; 17 O2 on Si(100). &I represents points which were obtained by adsorbing oxygen on the partially covered surface after the CH3Br adsorption on Si( I 1 1 ). 20 ADSORPTION REACTIONS ON SILICON AND GERMANIUM unaffected by physical adsorption but chemical adsorption which compensates the dangling bonds causes the optical constants to return to their normal bulk values. Ths is optically equivalent to removing the transition layer. The effective optical constants n and k of the transition layer have been calculated from the results for a number of adsorptions where 8 had been determined gas- volumetrically. The differences between the measured ellipsometric effects and those calculated for the adsorbate only gave the values 6A and all/ for the transition layer.A value of 5 has been assumed for the thickness dt. The wave-length dependence of n and k studied in the region 0.34-1.8 pm appeared to be similar to the wave-length dependence of the optical constants of the corresponding amorphous silicon and germarZium.12 This supports this interpretation since it is expected that the amorphous lattice-like material has distorted or dangling bonds throughout its bulk similar to the danghng bonds at a clean single-crystalline surface. It appears that at certain wavelengths (0.55 pm for silicon and 0.80 pm for ger- manium) the adsorbate effect is completely described by 6A whereas the substrate effect is fully reflected in S ~ ." This is a convenient wavelength to measure the number of dangling bonds compensated per molecule adsorbed. The @A plot shows a kink at the " monolayer " coverage as demonstrated in fig. 2. These kinks give valuable information on possible structures of the adsorption complexes if the assumption is made that all atoms in the adsorption complex have their normal valency. Desorption experiments as a function of temperature from a powder surface yield decomposition products which give information on the bonding and the presence of certain units in the complex. It appeared that adsorption complexes on silicon and germanium were the same in nearly all cases. TABLE 1.-" MONOLAYER " COVERAGE ON SILICON AND GERMANIUM CALCULATED FROM ELLIPSOMETRIC DATA adsorbate BonSi(111) BonSi(100) OonGe(111) OonGe(100) CHSSH 0.15 0.55 0.14 0.42 CHsCl 0.13 0.44 0 0.40 CHjBr 0.14* 0.39 0.17 0.44 * The CH3Br adsorption on Si(ll1) does not attain " monolayer " coverage.In this table the extrapolated value is given. STRUCTURE MODELS FOR ADSORPTION COMPLEXES The ellipsometric data for methyl-mercaptide adsorption on silicon and ger- manium as given in table 1 suggested a one-to-six coverage on the (1 11) face and a one-to-two coverage on the (100) face. Gas-volumetric adsorption measurements on a germanium powder yielded an average coverage of 0.23 molecules CH3SH per surface atom in good agreement with ellipsometry if an 80 20 dlstribution for (1 11) and (100) planes was taken. Desorption at higher temperatures gave hydrogen and methane as reaction products. The methane formation depended on the presence of Hz in the system (of at least 0.1 Torr).This same behaviour has been observed for methanol decomposition and both the temperature dependence and the amount desorbed suggested strongly that this reaction takes place on the (100) pIanes. The hydrogen from the (111) planes evolved in two steps; approximately one half desorbed around 200°C and the other half at 450°C. The adsorption complex of CH3SH on a (111) face given in fig. 3 exhibits therefore two binding states; one half of the hydrogen bonded directly to the germanium surface atoms F. MEYER AND M. J . SPARNAAY 21 and one half bonded to carbon. Since hydrogen bonded directly to germanium desorbs at 200°C it is probable that the first desorption step corresponds to those hydrogen atoms in the complex.The ellipsometric data for methyl chloride and methyl bromide adsorption on Si(ll1) and Si( 100) are given in fig. 2. The ellipsometrically-determined coverages given in table 1 suggest a one-to-six coverage on the (1 11) face and a one-to-two coverage on the (100) face. The CH3Br does not attain full coverage on the (111) (-70 %); the remaining dangling bonds can be compensated by subsequent 0 adsorption as indicated in the figure. Ellipsometric and gas-volumetric measure- ments on germanium suggested also one-to-two:coverages on the (100) face and an incomplete (70-90 %) one-to-six coverage for CH,Br on the (111) face. CH3Cl did not adsorb significantly on Ge(ll1) with exposures up to 50 Torr min. CH S H \ / \ / Si Si 7 /"? J\ 'i' CH SH Si Si Si Si Si Si H CH2 H X ,*- I 'i A I I Si Si Si Si Si Si FIG.3.-Structure models of the adsorption complexes of methyl mercaptide and methyl halide (X = C1 or Br) on the (1 11) and (100) faces of silicon or germanium. The adsorption complexes on the (1 1 1) face have to involve a carbon-atom bonded to three surface atoms (using the assumption that all atoms have their normal valency in the complex). Furthermore it is likely that the adsorption complex exhibits a direct germanium or silicon halogen bond since the first adsorption step probably involves this " active " atom (e.g. CH4 does not react chemically). The structures given in fig. 3 seem therefore the most probable. It has been observed in many instances that hydrogen bonded to a germanium surface atom desorbs by heating in vacuum at temperatures of 150-200°C.Examples are H2 adsorption and desorption;13 CH30H and CH3SH decomposition; HCl H2S etc. decomposition.l If the methyl-bromide adsorption complex on germanium powder was heated in vacuum no hydrogen evolution occurred below 350°C. This could be explained by a rearrangement in the structure of the adsorp- tion complex in which the hydrogen is transferred from a germanium atom to the CH-group forming a methylene (CH,) bridge. The driving force for this transition is probably the entropy gain since the CH bridge has a low frequency vibration mode compared to the rigid CH-group. This is treated more quantitatively in the next section. The hydrogen transfer from germanium to carbon regenerates two dangling bonds which can possibly react with a gas molecule. A further adsorption of methyl bromide was indeed observed if the germanium powder was heated in the presence 22 ADSORPTION REACTIONS ON SILICON AND GERMANIUM of CH3Br at temperatures of 150-250°C.This further adsorption did not take place at room temperature after heating the adsorption complex briefly in vacuum to 250"C indicating that the hydrogen transfer is reversible. Heating the germanium powder in CH3Br to temperatures higher than 300°C gave a reaction l4 in which mixed germanes are probably formed i.e. Ge(CH,),Br,-,. The surface proved to be heavily contaminated after such a treatment and could not be cleaned again completely. temp. "C FIG. 4.-The ellipsometric effects 8A and Sl) in deg. representing the " extra " adsorption upon heating a silicon (111) sample (covered by CH3Cl at room temperature and annealed in vacuum at 300°C for 5 min) in CHSC1 to different temperatures.The ellipsometric meaurements were taken at room temperature with an angle of incidence of 71.5" and a wavelength of 0.55 pm. The reaction below 300°C has been investigated by ellipsometry the advantage being that the (111) plane can be studied separately. The ellipsometric data for the adsorption of CH3Cl on Si(ll1) as a function of temperature are given in fig. 4. The procedure was as follows. Methyl chloride was adsorbed at room temperature on the clean silicon surface to approximately " monolayer " adsorption (one-to-six coverage). The crystal with adsorbate was then heated in vacuum to 3Oo0C which gave an irreversible change in A and II/ as measured at room temperature seemingly independent of the adsorbate.This might be correlated with the change in surface structure commonly observed by LEED (compare Si( 1 1 1)-PH3-7 x 7- Si( 1 1 1 )- PH3-l x 1). Room temperature adsorption gave no significant further reaction indicating that no dangling bonds were present after the heating cycle. This was followed by heating in CH3C1 to different temperature for short periods of time (a few minutes) and the ellipsometric effects measured after cooling to room temperature, F . MEYER A N D M. J . SPARNAAY 23 indicated an extra adsorption between 100 and 300°C. The change in $ was small as expected when all dangling bonds stay compensated. The total amount adsorbed after heating in the gas is roughly between a one-to-four and a one-to-two coverage. CH3Br gave similar results.The ellipsometric measurements have also been per- formed at temperatures between 120 and 300°C. Since most data had been obtained however at room temperature we have chosen this temperature as a standard for comparison. THERMODYNAMIC CONSIDERATIONS The adsorption data of CH3CI and CH3Br (or in brief of CH3X) on Ge and Si substrates led us to believe that there is a low-temperature complex (complex (a)) and a high temperature complex ( b ) ; a reversible transition between these two complexes taking place at about 200" (Si) and 150" (Ge). The situation is schemati- cally given in fig. 3. We now consider the transition between complexes (a) and (b) from a statistical point of view and follow roughly the theory given in ref. (16). We limit ourselves to a zeroth approximation because so far we have only rough information as to the complexes (a) and (b).The total number of adsorbed molecules CH3X is assumed to be constant and is denoted as n. The number adsorbed as complex (a) is -$n(l - r ) and the number adsorbed as complex (b) is *n(l+ r ) . The partition function 2 is this system is where the term containing the factorials is the configurational part and where Z, z b are partition functions for individual complexes (a) and (b). Finally f ( r ) denotes a contribution accounting for possible interactions between two neighbouring complexes. In the zeroth approximation it is customary to write for f ( r ) (3) where E,, &ab and Ebb are the interaction energies between two neighbouring complexes (a) (a) and (b) and (b) respectively. The number of neighbours is in this approxima- tion assumed proportional to (1 - r),2 (1 - r)(l + r ) and (1 +r)'.Finally z is a coordination number. j ( r ) = +nz((l- r)2&aa + 2(1- r)(l+ r)Eab -I- (1 + r)2&bb] The procedure is as follows. The Helmholtz free energy P of the system is P = -kTInZ (4) where k is the Boltzmann constant and T the absolute temperature. Equilibrium between the complexes (a) and (b) at temperature Trequires that In the following case eqn (4) and (5) can be written as F = (n/2)kT[( 1 - r ) In (1 - r ) + (1 + r ) In (1 + r)] + (n/2)[( 1 - r)F + (1 + r)&] +f(r) (6) where F = -kTIn 2 and F b = -kTIn z b and where we applied Stirlings' approxi- mation and (aP/ar) = 0. ( 5 ) When the only temperature-dependent term is kT In [( 1 - r)/(l + r)] then a transition takes place at that temperature where r+O provided E + E ~ ~ < ~ E ~ .In that case 24 ADSORPTION REACTIONS O N SILICON AND GERMANIUM there is a high-temperature phase where r = 0 and a low temperature phase where r # 0 and this represents the usual development in the zeroth approximation. However we have a case here where we have a transition from negative to positive r and we ascribe this transition to the temperature dependence of Fa-Fb. The energies E,, Ebb and &,b may serve to " sharpen " or to weaken this transition depend- ing on their sign and magnitude but at this stage we know very little of the physical nature of these energies. In contrast we have at least a crude model of the individual complexes (a) and (b). w e now assume that t&,z&bbE8ab and discuss the difference F,-F'.Inspection of the model depicted in fig. 3 suggests that we can write (8) where is a free energy to be assigned to the mutual compensation of the silicon dangling bonds. The other contributions in eqn (8) pertain to the Si2CH2 the Si3CH and the SiH groups. The important difference between the low-temperature and the high-temperature configurations is the removal of a H-atom from a Si-atom to a C-atom. This removal has as one consequence a loosening of the position of the C-atom because it is now no longer bonded to three Si-atoms (placed in a triangle) but to only two. Consider- ing its vibrations in a plane normal to the plane of the paper (fig. 3) its frequency Vb in the high-temperature SizCHz case will be considerably lower than that in the low-temperature case where we denote this frequency as v vb 4 v a - (9) We apply to these vibrations the free energy expression of a harmonic oscillator with frequency v where h is Planck's constant and assume the classical limit (v<kT/h) for vbn This gives where Fii2C~2 contains contributions F, arising from other frequencies than v b .These contributions are less temperature dependent than the one given by v b . Inserting this equation together with eqn (8) into eqn (7) and ignoring the energies E,, Ebb and &,b one obtains Fa - Fb = FSi 3CH + FSi H - FSi.. .Si - FSi 2CH1 F = $hv + kT In [ 1 - exp (- hv/kT)] FSi2CH2 = F&zCH2 + kT1n lhvblkT (10) (1 1) 1-r kT kT ln- + kT In- = F&2CHZ+FSi...Si - l + r hVb Assuming that the right-hand side of this equation is temperature independent the rate of change of the equilibrium value of r with changing temperature is which is valid near r = 0.The value r = 0 will be defined as the transition point between the low-temperature and the high-temperature configurations. The transi- tion temperature is at about T = 470 K (complex adsorbed on Si) and at about 420 K (Ge). When Vb = 5 x 10" s-1 (a wave number of 25 cm-l) kT-20 hvb (Si case). This means that when dT = 0.1 T a change dr of $- is taking place. This is in qualitative agreement with experiment. Finally we inquire into possible values of the most interesting contribution Issi. . s i . For this purpose we write complex FSi3CHfFSiH-FSi2CH2 = AFH+FSiC Y F . MEYER AND M. J . SPARNAAY 25 where A& is the free energy change involved in the step of the H-atom from a Si-atom to a C-atom and where F i t F p l e x is the free energy connected with the third bond of this C-atom with one of the underlying Si-atoms (fig.3). This is a dangerous procedure but it allows us to make a comparison with the adsorption of CH3SH. Here no " detour " was made by the H-atom. Instead it was disconnected from the surface at about 300°C (Si substrate) whereas at about 500°C other H-atoms probably bonded to the C-atoms were freed. This leads us to believe that AFH cannot be much larger than kT where T-600 K. Therefore since at r = 0 we have Fa-& = 0 (Y = O) Fsi ... si Fsic 3 our estimate is complex This is only a first estimate. However it suggests a working programme. Thus investigations in the far infra-red or microwave region may lead to more information concerning frequencies such as the one denoted here as v,.Such experiments may also lead to a better insight into the nature of the free energy difference AF and of p o m p l e x S i c (and of CONNECTION WITH ELECTRICAL MEASUREMENTS The work described in this paper is a combination of optical and gas volumetric measurements and as such it must be considered as a continuation of previous work consisting of a combination of electrical and gas volumetric measurements. For clean Ge and Si surfaces of samples of intrinsic conductivity type most workers agree l 8 that there is a weakly p-type space charge. This has been found by surface conductance field effect and Hall measurements. For Ge the hole density in the space charge is 3-4 x loll cm-2 and for Si it is even less. The physical origin of the space charge is found in the existence of about 10I5 surface states cm-2.These surface states have both an acceptor and a donor character but the acceptor character slightly dominates and provides for a negative charge in the surface states of 3-4 x 10l1 electrons cm-2 or less (300 K). These electrons are drawn from the bulk of the crystal over a depth beneath the surface of about a Debye length. In this way the positive space charge is created. This weak double layer can probably be ignored in the interpretation of optical data. The electrical effect of the chemisorption of O2 and of the gaseous adsorbates used in this paper is two-fold. First up to a certain coverage which is 10 % of a monolayer for 0 2 1 the space charge density rises (at 300 K) to 6-7 x loll holes cm-2.(Ge) Beyond this coverage (for O2 rising beyond 10 %) there is a decrease of the density to lo1* holes cm-2 or less (Ge) depending on the nature of the chemisorbed molecule. The second effect is a continuous decrease of the surface state density upon an increasing coverage to 10I1 states cm-2 or less (300 K). In the crude " dangling bond " model the second effect is understandable ; chemisorption means a saturation of the dangling bonds and associating the dangling bonds with surface states chemisorption leads to the annihilation of the surface states. The first effect is more difficult to understand in particular the maximum observed in the space charge density. However the first effect and also the second effect lend support to the hypothesis that the change of the ellipsometric angle + observed upon chemi- sorption can be ascribed to a change of the optical constants of a surface layer of the substrate.The chemisorption of widely varying species led in all cases to quali- tatively both the same change of + and the same change of space charge density and 26 ADSORPTION REACTIONS ON SILICON AND GERMANIUM surface state density. It is more obvious to ascribe these changes to changes of properties of the substrate region than to characteristics which the various adsor- bate molecules may have in common. In this respect it would be interesting to investigate possible electrical effects due to the sophisticated chemical reactions discussed in this paper. We thank Mr. E. E. de Kluizenaar for performing most of the ellipsometric measurements . l A.H. Boonstra and J. van Ruler Surface Sci. 1966 4 141 ; A. H. Boonstra Philips Res. Reports suppl. no. 3 (1968). F. Jones I.B.M. J. Research Developt. 1965 9 375. F. Meyer and J. M. Morabito J. Phys. Chem. in press. G. A. Bootsma and F. Meyer Surface Sci. 1969,14 52. J. J. Vrakking and F. Meyer to be published. F. Meyer J. Phys. Chem. 1969,73,3844. S . Brunauer P. H. Emmett and E. Teller J. Amer. Chem. SOC. 1938,60,309. A. Liberman and M. Green J. Phys. Chem. Solids 1962,23,1407. A. J. Rosenberg J. Phys. Chem. Solids 1960,14,175. lo J. R. Miller and J. E. Berger J. Phys. Chem. 1966,70,3070. l1 G. A. Bootsma and F. Meyer Surface Sci. 1969,13,110. l2 F. Meyer E. E. de Kluizenaar and G. A. Bootsma Surface Sci. 1971 27 88. l 3 K. Tamaru J. Phys. Chem. 1957,61,647. l4 E. G. Rochow J. Amer. Chem. SOC. 1947,69,1729. l5 A. J. van Bommel and F. Meyer Surface Sci. 1967 8 381. l6 E. A. Guggenheim Mixtures (The Clarendon Press 1952). l7 A. H. Boonstra J. van Ruler and M. J. Spamaay Proc. Kon. Nederland Akad. Wetens. B 1963,6,64 70. M. J. Sparnaay A. H. Boonstra and J. van Ruler Surface Sci. 1964,2 56. l 8 see textbooks such as A. Many Y. Goldstein and N. B. Grover Semiconductor Surfaces (North-Holland Publ. Co. Amsterdam 1964) and D. R. Frankl EZectrical Properties of Semi- conductor Surfaces (Pergamon Press 1967).