- Email: [email protected]
Spectrophotometric determination of the optical properties of an adsorbed oxygen layer on gold
SURFACE
SCIENCE 28 (1971) 321-334 0 North-Holland
SPECTROPHOTOMETRIC PROPERTIES
OF AN
Publishing Co.
DETERMINATION ADSORBED
OXYGEN
OF THE LAYER
OPTICAL ON
GOLD
D. M. KOLB and J. D. E. MCINTYRE* Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey 07974, U.S.A.
Received 2 June 1971 A new differential spectrophotometric technique for determining the optical constants of very thin surface films is described. This method is of particular utility for in situ studies of surface reactions on metallic substrates by ultraviolet-visible specular reflection spectroscopy. Its application is illustrated by the determination of the optical properties of an adsorbed oxygen layer on gold.
1. Introduction Differential reflection spectroscopy has recently received increased attention as a method for investigating in situ the optical properties of surface films in the monolayer thickness rangel-lo). In the UV-visible wavelength region, this method is often comparable in sensitivity of film detection to classical ellipsometry [cf. Hayfieldii)] but has the significant advantage of much faster response (N lo-’ set), thus facilitating kinetic studies of very fast surface reactions. Owing to the influence of the substrate, however, reflection spectra often differ markedly in character from conventional transmission spectra63 ls). It is then necessary to evaluate the actual optical constants of the thin film before detailed information about its optical and electronic properties can be deduced. In the present communication, we describe a new differential spectrophotometric method for determining the optical constants of very thin surface films. The application of this method is illustrated by the determination of the spectral dependence of the optical constants of an adsorbed 0 layer formed anodically on a gold mirror electrode in acid solution.
2. Theory When
electromagnetic
* To whom correspondence
radiation
is incident
should be addressed. 321
on a multiphase
stratified
322
D.M.KOLB
AND J.D.E.MCINTYRE
system, conservation of energy requires that the sum of the energy fluxes in the reflected and transmitted beams, plus the sum of the rates of energy dissipation in any absorbing phases, be equal to the energy flux in the incident beam. For a beam of unit intensity, which is incident on a bare metallic substrate, L=R+A,+T,
(1)
where R and Tare, respectively, the reflected and transmitted beam intensities in the transparent ambient phase and A, is the rate of energy absorption by the metallic phase. If a thin film is deposited on the substrate surface 1 = R’ + A, + A:, + T’ ,
(2)
where the primed symbols denote terms analogous to those in eq. (1) and A, is the rate of energy dissipation in the surface film. For a thick strongly absorbing substrate, T=T’=O, and we have from eqs. (1) and (2) AR+A,+AA,=O.
(3)
The form of the differential reflection spectrum, AR versus /?w is thus governed by two factors - absorption in the thin surface film and the change in absorption in the bulk substrate phase caused by deposition of this film. Two limiting cases can be distinguished. (i) If the surface film is transparent, A,= 0 and AR= -AA,,,. (ii) If the substrate reflectivity is very high (i.e., Rz 1) there is very little energy dissipated in this phase and hence AA,zO. In this case, the differential reflection spectrum resembles a distorted transmission spectrum of the film material. Numerous examples of this type of behavior have been observed in infrared reflection studies of metal surfaces [cf. Poling 13)]. In intermediate cases where the film is absorbing but the substrate is only a moderately good reflector (Rx 0.5), the two effects are not readily separable. The reflectivity change produced by a weakly absorbing film may be dominated by effects due to absorption in the substrate. Such behavior is typified by the reflection spectra of surface films on noble metal substrates in the UVvisible wavelength region6). Since the absolute reflectivity of a surface enclosed in an experimental cell is very difficult to determine accurately, the normalized differential reflection spectrum, AR/R versus hw, is usually measured in practice. By measuring the ratio of two reflectivities, spurious effects from a number of common error sources can be cancelled 14*15). A number of noble metals (e.g., Cu, Ag, Au) exhibit pronounced structure in their visible-UV reflectivity spectra owing to the onset of interband transitions. Interpretation of AR/R spectra is thus further complicated by the inclusion of a factor due to the variable
background reflectivity of the substrate. In order to obtain the absorption spectrum of the thin film material per se, it is first necessary to determine the characteristic optical constants of the film. In the sections which follow, a procedure is developed for evaluating the complex dielectric constant of a surface film in the monolayer thickness range from polarized differential reflection spectra. This treatment, which is based on the linear approximation theory of McIntyre and Aspnesi2), assumes that the dielectric constants of the ambient and substrate phases are known from independent measurements. 2.1.
&NEAR
~PF~UX~M~T~~N
THEORY
When a film of thickness d is deposited on a bare substrate surface, the fractional reflectivity change is defined by
AR
R(d) - R(0)
-~~--“_=-----------__
R
R (0)
R(d) R(0)
1
’
where R(d) is the reflectivity of the stratified three-phase system (ambient, film, substrate) and R(O) is the reflectivity of the ambient-substrate interface. If the film thickness is very small relative to the vacuum wavelength 1Eof the incident light, the fractional reflectivity changes for radiation polarized perpendicular and parallel to the plane of incidence are given, to first order in C&U,byI%)
(5b)
In eqs. (.5), ‘pi is the angle of incidence of the light beam in the transparent ambient phase (1) with r-e& dielectric constant a1 and refractive index yti, and t2 and Z&are the complex dielectric constants of the absorbing thin film and substrate phases, respectively. These terms are defined in accordance with the Nebraska ~onven~on~6)~ The above relations provide a very good approximation for AR/R when d/A
324
D.M.KOLB
AND
J.D.E.MCINTYRE
(ii) Measurement of (AR/R), or (AR/R),, at two (or more) angles of incidence. These are referred to as single- and multiple-angle methods, respectively. 2.2. SINGLEANGLEOFINCIDENCE,TWO
POLARIZATIONS
With this method, values of ~AR~R)~ and (ARiR~,, are measured at a single angle of incidence, usually chosen to he between 45” and the pseudoBrewster angle of the ambient-substrate interface. Eqs. (5a) and (5b) can be inverted and solved simultaneously for the real and imaginary parts of &. Expressing the complex dielectric constant of phase j as gj = 8; - is;‘)
(6)
E; = a, - CQE;,
(7)
we find from eq. (5a)
where 1 El
-
El
&;“I --- (AWR)I
El&; - [(El - E;)' +
- E;
8nn,~l
@a)
(>jiq ’
E); a2 = ---‘-r’ Et -83 Letting u=sin2~, and v=cos2~,, third-order in E; and E; : p
WI
we obtain
from eq. (5b) an expression
’ +p
of
(9)
l&2
where fll =
VE[;
(E;’
+
E1;’
-
2X&),
p2 = ZI(E1- E;) (E;’ + f13
=
UEf&;
(EL2
+
p4 = Z&E1 ((E;2 + ____-.-I__
E;’ E1;‘)
~
E1;’
(loa) 2UErE;) +
-
-
2UQEj),
[IV
(&j2
U2Q
-
8;)’
+
+
E;‘)
-
El&;]
+
[(El -
E;)’
+
&1;‘]
[(?.tE1
U&f
EgElj
(&i2
-
-
+
(lob)
(&i2
+
y2”;2
+
y&
+
y4
=
+
&1;2
0,
(fad)
&Ij2)),
V&i)’
of &I;from eqs. (7) and (9) yields a cubic in y,g
&I;‘],
UOC)
-
Elimination
[(El
V’&:;‘]
2U&,&3
-
E;
Ooe)
:
011
where Yl = (1 + 6)
(PI -
a2Pz)T
(12a)
SPE~ROPHOTO~~IC
y2 = -
Zc+@l
34) B2 + (1 + 4) B5 9
+ a1 (1 +
Y3
=
&
-
3&M*
Y4
=
dPz
+
ad4
+ P3 - @A - 2%%& 7
+
&J
325
TECHNlQUE
*
(12b) (12cf VW
Eq. (11) has three roots. If yi, y2, y3, y4 are real, the following solutions are possible”*): (i) one real root and two conjugate imaginary roots; (ii) three real roots of which at least two are equal; (iii) three real and unequal roots. When the number of real roots of eq. (11) is greater than one, it is not always evident which is the physically meaningful value of 8;. Methods for distinguishing the pertinent value are discussed in a following section. Substitution of this value into eq. (7) then yields the corresponding value of &I;. The complex index of refraction of phase] is expressed as fij=nj-ikj,
(13)
where nj and kj are, respectively, the index of refraction coefficient of phase j. Since &j
=
AS
and extinction
) WQ
6;
~(ir
=
=
n;
-
kj” ,
2njkj,
04b)
(14c)
the equivalent set of optical constants n2, k2 of the thin-~lrn phase can be determined from the relations n2 = {J[E; i- (EL2+ E’;~)+]}*,
WW
k, = E;/2n2.
0 5b)
The optical behavior of a thin isotropic surface film is characterized by the three parameters: E;, E; and d (or n2, k2 and d). For a single angle of incidence, however, only two quantities can be measured spectrophotometrically, (AR/R), and (AR/R)/, . If the film is nonabsorbing, &;I= k2 =O, and these two measurements suffice to determine uniquely the values of E; = ~2; and d. If the film is absorbing, the value of d must be determined independently. In studies of heterogeneous electrochemical reactions, for example, d can be estimated from coulometric measurements of the charge passed during film formation or removal. In studies of adsorption on highly-reflecting metallic substrates (e.g., in the infrared), (AR/R), is very small compared to (AR/R),, since the component of the standing-wave electric field tangential to the surface has a node at the surface planel$). The single-angle method cannot be used in this case to evaluate the optical constants of the film. However, for a weakly absorbing
326
film on a highly-reflecting
D.M.KOLB
AND J.D.E.MCINTYRE
substrate,
8, %& and t3 %,~i, such that to a good
approximation
(16)
=-4sin2cp,
The quantity (djcos qpl) is the volume of film sampled by a light beam of unit cross-sectional area, while CI~is the absorption coefficient, defined by a2 = 4nkJl.
(17)
At a film-free surface (z=O) and for angles of incidence smaller than the principal angle, qDp,the value of the normal component of the mean square field strengthaa) in the standing wave in phase 1 is given by49 21)
(18) where (E1[12) is the field strength in the incident plane wave propagating in the positive z-direction. The fractional reflectivity change in this case is thus directly proportional to the energy absorbed by the film, as expressed by Poynting’s theorem. Since AR/R@ 1, it is simply related to the change in “reflection absorbance”, sic4) AA =log,,
by AR R
R (0) [R(d) 1’
= - 2.3 AA .
(19)
(20)
Eq. (16) is thus equivalent to an analagous expression for AA,, derived by Hansen4) (for ‘pr
INCIDENCE,SINGLEPOLARIZATION
Inspection of eqs. (5a) and @a) reveals that since (AR/R)I is directly proportional to the only angle-dependent term, cos ql, no evaluation of E; and sl; can be made using first-order theory and a multiple-angle technique with perpendicular polarization. Analogously, methods which involve a variation of film thickness are not applicable for either polarization.
SPECTROPHOTOMETRIC
TECHNIQUE
327
If measurements of (AR/R),, are made at two (or more) angles of incidence, E; and E; (and d) can be evaluated in principle from eq. (9), although analytical solution for these quantities does not appear feasible. This method will be insensitive when ‘pl <45”, since to a good approximation, (AR/R),, is directly proportional to (l/cos ‘p1)12). In view of the difficulties reported for multipleangle ellipsometric studies of very thin surface films22-24), we have not pursued this method further. In the UV-visible wavelength region, the single angle method discussed previously is more accurate, although an independent measurement of d is required for an absorbing film. In addition, it affords the possibility of detecting optical anisotropy in monolayer films@).
3. Experimental Polarized differential reflection spectra of adsorbed oxygen (or oxide) layers, formed anodically (Eu = 1.6 V) on vacuum-evaporated Au mirror electrodes in Ar-saturated 1.0 M HClO,, were measured in situ at vi =45” over the photon-energy range 1.6-5.5 eV. The film thickness was estimated by coulometry to be 6.0 A, assuming the composition to be Au,O, with a bulk density of ca. 6 g cmm3. Optical constants of the Au substrate were determined by a Kramers-Kronig analysis of normal incidence reflectivity data, measured in air. A detailed description of the experimental apparatus and procedures has been given previouslys).
4. Results and discussion The spectral variation of the optical constants of the vacuum-evaporated Au film substrate is shown in fig. 1. The results are in close agreement with recent measurements of Irani et al.25) and earlier data of Schulz et al.26t27). Illustrated in the inset is the normal incidence reflectivity of the Au film in air. The polarized differential reflection spectra (q)i =45”) of the 0 layer on Au are shown in fig. 2. The influence of the optical properties of the substrate is clearly evident. Using the measured optical constants of the Au film, values of R,(O) and RI, (0) were calculated as a function of photon energy for ~0, =45”, assuming n, to be constant (1.333). Fig. 3 illustrates the pronounced variation of the reciprocal reflectivity, R-l, with tto for these conditions. From the measured values of AR/R and the calculated values of R-“, the differential reflection spectra of AR versus ho were computed; these spectra are shown in fig. 4. Three main peaks are evident in these spectra near 2.35, 3.3, and 4.7 eV. On the basis of the single-angle method described in section 2.2, the dielectric constant of the 0 layer on Au was computed from the measured
328
D. M. KOLB
-24
I 1.6
I 2.4
1
AND J. D. E. MCINTYRE
I 3.2
I
hw
Fig. 1.
I 4.0
I
I 4.8
I 5.6
[ev]
Spectral dependence of the real and imaginary components of the dielectric constant of Au: 8 = E’--ie”. The normal incidence reflectivity of Au (in air) is shown in the inset.
8.0
cc 2 a N 0 7
6.0
4.0
2.0
'iw[ev] Fig. 2. Normalized differential reflection spectra, AR/R versus AU at ql= 45”, of the 0 layer formed anodically on an Au electrode at EH = 1.6 Vin 1.0 M HClOb(Ar saturated).
SPECTROPHOTOMETRIC
229
TECHNIQUE
6
0
1.0
2.0
3.0
4.0
5.0
6.0
Aw !ev) Fig. 3.
Reciprocal reflectivity spectra of Au in an aqueous electrolyte (m = 1.333) at ~1 = 45”.
I
I
I
3.0
[L 2.0 a N 0 T
1.0
0
, I.0
I
I
I
I
2.0
3.0
4.0
5.0
hw
Fig. 4.
0
(ev)
Differential reflection spectra, AR versus ftw at II= 45”, of the 0 layer on Au.
values of (AR/R),,, (AR/R),, 8, and d. As discussed previously, the firstorder theory for the single-angle method yields three solutions for each component of 6,. The frequency dependence of the three sets of roots is shown in fig. 5. At low energies, there are three pairs of real and unequal roots, but at 2.1 eV two of these sets become identical. For ku > 2.1 eV, there is only one set of real roots and this set must therefore correspond to the
D.M.ROLB
330
AND J.D.E.MClNTYRE
actual physical values of E; and 8:. Since these quantities are inherently continuous, their pertinent physical values can easily be distinguished in energy regions where more than one real solution exists. Examination of fig, 5 also reveals that the discarded sets of s; and E; are physically unrealistic
1.0
2.0
3.0
4.0
5.0
6.0
hw rev] Frequency dependence of the three possible solutions of the linear appro~~~~tion retationsl”) for the diekctric constant of the 0 layer on Au. The physicaily meaningful
Fig. 5.
set is w, I&“.
for a semiconducting oxide film and that these discarded values become identical just before turning imaginary. Several useful criteria thus exist for distinguishing the correct physical solution of the optical equations. The frequency dependence of the absorption coefficient of the 0 layer on Au is illustrated in Sg. 6. Also plotted for comparative purposes is the absorption coefkient of the Au substrate. On comparing figs. 2 and dl it becomes evident that the detailed features of the absorptjon spectrum of the
SPE~ROPHOTO,~ETRiC
331
TEC~QUE
0 layer on Au are concealed in the differential reflection spectrum; they can only be revealed by a computer analysis of the optical data. This is particularly evident for the case of the two prominent absorption bands at 4.2 and 4.9 eV. In the spectrum of AR(o), only a single broad maximum centered at 4.7 eV
8.0 -
- 1.0
\
I
I
2.0
3.0
I
I
4.0
5.0
\
6.0
hw [ev] Fig. 6.
Absorption
spectra of bulk Au and the anodic 0 layer on Au (assumed to be Au~03).
is apparent (cf. fig. 4). Similar behavior was observed in the analysis of the differential reflectivity spectra of the 0 layer on Pt mirror electrodes6). As discussed previously6) the very high magnitudes of CQindicate that charge-transfer or other fully-allowed transitions are responsible for the absorption. These processes are likely to be associated with transitions involving excitation of an electron from: (i) an oxygen ion, 02- (2p6), to vacant d levels of a nearest-neighbor gold ion, Au3+ (5d’); (ii) a 2p6 level of 02- to an unfilled 6s level of the Au3” ions; or, (iii) a filled 5d level of Au3’ to an unfilled 6p level of this ion. A more definitive assignment must await quantitative calculations that take specific ligand-field effects into account. Inspection of fig. 6 also reveals that the rapid rise in Q,, at low energies, characteristic of the free-electron behavior of metallic gold, is not duplicated by the thin-film absorption coefficient. The optical properties of the 0 layer on Au thus resemble those of a semiconductor. The results of this study provide an interesting contrast to infrared reflection studies. Fig. 7 illutrates the frequency dependence of the components of the mean square electric field strength in the ambient phase at a film-free
332
D.M.KOLB
AND J.D.E.MCINTYRE
Au surface (z=O), as computed from the exact relations of Hansen20); the maximum value of the ratio (Elf i )/( E,;:) 1z= o is 4. The boundary conditions of electromagnetic theory require that the tangential components of the displacement, D = b E, be continuous across the interface of two phases. In
3.6 3.2 28 t A
;'2.41? ,$2L)w
__
V
.
\
1.61.2cm0.4-
I
O.Ol.0
I
I 2.0
I 3.0
I 4.0
I 5.0
I 6.0
liw(eV)
Fig. 7. Spectral variation of the components of the meansquare electric field strength in the standing wave at the surface (z = 0) of a film-free Au substrate, relative to that of the incident beam, for PI= 45” and nl = 1.333.
the thin-film phase, since cfgi and the energy loss is small, the field strength is only slightly attenuated. Hence to a good approximation
= (E:z)
(E;,.J
= C&x)
E:.@;I,)
= M2
5
(214
2
@lb)
WC)
At the absorption maximum near 2.4 eV (cf. fig. 6), E; =2.3, s;‘=7.0 and hence l&l = 7.37. For an aqueous electrolyte, .si = 1.78, and hence (Eifzz) = =0.058 10,
SPECTROPHOTOMETRIC
<~~,.J/@;;,2$z=,
TECHNIQUE
= 4/k:,
333 (22)
while (~~l,Y<~~~)~,=O
= 4 sin2’p1.
(18)
Thus even for very strong infrared absorption bands (k2 w l), the energy loss is almost entirely due to interaction of the molecules in the film with Ezz, the field-component normaE to the surface. A comparison of figs. 4 and 7 also reveals that the main peaks near 2.4 eV in the differential reflectivity spectra, AR,(w) and AR,, (o), occur near the energies at which both CC,, (Ei,) and (Ei,,) exhibit maxima. A similar peak occurs in the electroreflectance spectrum of Au at this energy”s). This energy corresponds to the onset of the interband transition 5d -+ 6s (Fermi surface) in Au metal. The prominent peak at 2.4 eV in fig. 4 is thus attributable to the combined effects of absorption in the film and a change in absorption by the metal substrate. The successful application of the above spectrophotometric method for determining the optical constants of very thin surface films depends upon the accuracy with which the ratio R(~)/R(O) can be measured. Owing to the cancellation of intensity loss factors in ratio measurements, the accuracy of determination of AR/R is limited primarily by the linearity and freedom from zero-level errors and noise of the photodetector and associated electronic amplification system. In cases where AA,+ Al, AR/R is primarily determined by the real part of the refractive index of the film and the absorptive properties of the substrate12). In order to deduce the true absorption spectrum of the film per se by computer analysis, highly accurate measurements of (AR/R), and (AR/R),, are required. Since the absolute reflectivity of a surface enclosed in an experimental cell of conventional design (cf. ref. 6) cannot be measured accurately, it is not possible to determine the optical constants of the film-free substrate in situ*. The calculation of the thin film optical constants therefore depends upon an external determination of 2,. In this respect, the spe~trophotometric method suffers by comparison with classical ellipsometry which permits an internal measurement of 6,. It has recently been recognized, however, that in optical studies of metal substrates in electrolyte solutions, significant errors in measurements of the apparent optical constants of the bulk substrate may result from neglect of electroreflectance effects. The latter arise primarily from a field-induced change in the free-electron surface charge distribution, which can produce large perturbations of the dielectric constant of the metal in its surface region3r). Ultimately, a combined application of in situ ellipsometry and differential * The use of cylindrical all-quartz cells 2Q*30) may facilitate such measurements.
334
D. M. KOLB
AND
J. D. E. MCINTYRE
reflection spectroscopy may prove most effective in surface studies. The technique described in the present communication promises to be of utility for in situ spectroscopic investigations of the optical properties of monomolecular films on metal surfaces, particularly in studies of the kinetics of rapid adsorption processes and the nature of the electronic interactions of adsorbed species with catalytic substrate materials.
References 1) D. F. A. Koch, Nature 202 (1964) 387. 2) D. F. A. Koch and D. E. Scaife, J. Electrochem. Sot. 113 (1966) 302. 3) T. Takamura, K. Takamura, W. Nippe and E. Yeager, J. Electrochem. Sot. 117 (1970) 626. 4) W. N. Hansen, Disc. Faraday Sot., in press. 5) M. A. Barrett and R. Parsons, Disc. Faraday Sot., in press. 6) J. D. E. McIntyre and D. M. Kolb, Disc. Faraday Sot., in press. 7) A. Bewick and A. M. Tuxford, Disc. Faraday Sot., in press. 8) W. J. Plieth, Disc. Faraday Sot., in press. 9) R. Memming and F. Mollers, Disc. Faraday Sot., in press. 10) H. B. Mark, Jr. and E. N. Randall, Disc. Faraday Sot., in press. 11) P. C. S. Hayfield, in: Surface Phenomena of Metals (Sot. Chem. Ind. Monograph No. 28, London, 1968) p. 128. 12) J. D. E. McIntyre and D. E. Aspnes, Surface Sci. 24 (1971) 417. 13) G. W. Poling, J. Colloid Interface Sci. 34 (1970) 365. 14) D. G. Avery, Proc. Phys. Sot. (London) B 65 (1952) 425. 15) H. E. Bennett and J. M. Bennett, in: Physics of Thin Films, Vol. 4, Eds. G. Hass and R. E. Thun (Academic Press, New York, 1967) p. 1. 16) R. H. Muller, Surface Sci. 16 (1969) 14. 17) S. P. F. Humphreys-Owen, Proc. Phys. Sot. (London) 77 (1961) 949. Ed. S. M. Selby (Chemical Rubber, Cleveland, 1970) 18) Handbook of Mathematics, 4th ed., p. 129. 19) R. G. Greenler, J. Chem. Phys. 44 (1966) 310. 20) W. N. Hansen, J. Opt. Sot. Am. 58 (1968) 380. 21) S. A. Francis and A. H. Ellison, J. Opt. Sot. Am. 49 (1959) 131. 22) F. L. McCrackin and J. P. Colson, in: Ellipsometry in the Measurement of Surfaces and Thin Films, Eds. E. Passaglia, R. R. Stromberg and J. Kruger (Nat]. Bur. Std. (U.S.) Misc. Publ. 256, U.S. Govt. Printing Office, Washington, 1964) p. 61. 23) D. G. Schueler, Surface Sci. 16 (1969) 104. 24) J. A. Johnson and N. M. Bashara, J. Opt. Sot. Am. 61(1971) 457. 25) G. B. Irani, T. Huen and F. Wooten, J. Opt. Sot. Am. 61(1971) 128. 26) L. G. Schulz, J. Opt. Sot. Am. 44 (1954) 357. 27) L. G. Schulz and F. R. Tangherlini, J. Opt. Sot. Am. 44 (1954) 362. 28) J. D. E. McIntyre, Paper (Abstract No. 231) presented at the 135th National Meeting of the Electrochemical Society, New York, May 7, 1969. 29) L. Masing, J. E. Orme, and L. Young, J. Electrochem. Sot. 108 (1961) 428. 30) B. D. Cahan, private communication. 31) J. D. E. McIntyre and D. E. Aspnes, Bull. Am. Phys. Sot. 15 (1970) 366.
SCIENCE 28 (1971) 321-334 0 North-Holland
SPECTROPHOTOMETRIC PROPERTIES
OF AN
Publishing Co.
DETERMINATION ADSORBED
OXYGEN
OF THE LAYER
OPTICAL ON
GOLD
D. M. KOLB and J. D. E. MCINTYRE* Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey 07974, U.S.A.
Received 2 June 1971 A new differential spectrophotometric technique for determining the optical constants of very thin surface films is described. This method is of particular utility for in situ studies of surface reactions on metallic substrates by ultraviolet-visible specular reflection spectroscopy. Its application is illustrated by the determination of the optical properties of an adsorbed oxygen layer on gold.
1. Introduction Differential reflection spectroscopy has recently received increased attention as a method for investigating in situ the optical properties of surface films in the monolayer thickness rangel-lo). In the UV-visible wavelength region, this method is often comparable in sensitivity of film detection to classical ellipsometry [cf. Hayfieldii)] but has the significant advantage of much faster response (N lo-’ set), thus facilitating kinetic studies of very fast surface reactions. Owing to the influence of the substrate, however, reflection spectra often differ markedly in character from conventional transmission spectra63 ls). It is then necessary to evaluate the actual optical constants of the thin film before detailed information about its optical and electronic properties can be deduced. In the present communication, we describe a new differential spectrophotometric method for determining the optical constants of very thin surface films. The application of this method is illustrated by the determination of the spectral dependence of the optical constants of an adsorbed 0 layer formed anodically on a gold mirror electrode in acid solution.
2. Theory When
electromagnetic
* To whom correspondence
radiation
is incident
should be addressed. 321
on a multiphase
stratified
322
D.M.KOLB
AND J.D.E.MCINTYRE
system, conservation of energy requires that the sum of the energy fluxes in the reflected and transmitted beams, plus the sum of the rates of energy dissipation in any absorbing phases, be equal to the energy flux in the incident beam. For a beam of unit intensity, which is incident on a bare metallic substrate, L=R+A,+T,
(1)
where R and Tare, respectively, the reflected and transmitted beam intensities in the transparent ambient phase and A, is the rate of energy absorption by the metallic phase. If a thin film is deposited on the substrate surface 1 = R’ + A, + A:, + T’ ,
(2)
where the primed symbols denote terms analogous to those in eq. (1) and A, is the rate of energy dissipation in the surface film. For a thick strongly absorbing substrate, T=T’=O, and we have from eqs. (1) and (2) AR+A,+AA,=O.
(3)
The form of the differential reflection spectrum, AR versus /?w is thus governed by two factors - absorption in the thin surface film and the change in absorption in the bulk substrate phase caused by deposition of this film. Two limiting cases can be distinguished. (i) If the surface film is transparent, A,= 0 and AR= -AA,,,. (ii) If the substrate reflectivity is very high (i.e., Rz 1) there is very little energy dissipated in this phase and hence AA,zO. In this case, the differential reflection spectrum resembles a distorted transmission spectrum of the film material. Numerous examples of this type of behavior have been observed in infrared reflection studies of metal surfaces [cf. Poling 13)]. In intermediate cases where the film is absorbing but the substrate is only a moderately good reflector (Rx 0.5), the two effects are not readily separable. The reflectivity change produced by a weakly absorbing film may be dominated by effects due to absorption in the substrate. Such behavior is typified by the reflection spectra of surface films on noble metal substrates in the UVvisible wavelength region6). Since the absolute reflectivity of a surface enclosed in an experimental cell is very difficult to determine accurately, the normalized differential reflection spectrum, AR/R versus hw, is usually measured in practice. By measuring the ratio of two reflectivities, spurious effects from a number of common error sources can be cancelled 14*15). A number of noble metals (e.g., Cu, Ag, Au) exhibit pronounced structure in their visible-UV reflectivity spectra owing to the onset of interband transitions. Interpretation of AR/R spectra is thus further complicated by the inclusion of a factor due to the variable
background reflectivity of the substrate. In order to obtain the absorption spectrum of the thin film material per se, it is first necessary to determine the characteristic optical constants of the film. In the sections which follow, a procedure is developed for evaluating the complex dielectric constant of a surface film in the monolayer thickness range from polarized differential reflection spectra. This treatment, which is based on the linear approximation theory of McIntyre and Aspnesi2), assumes that the dielectric constants of the ambient and substrate phases are known from independent measurements. 2.1.
&NEAR
~PF~UX~M~T~~N
THEORY
When a film of thickness d is deposited on a bare substrate surface, the fractional reflectivity change is defined by
AR
R(d) - R(0)
-~~--“_=-----------__
R
R (0)
R(d) R(0)
1
’
where R(d) is the reflectivity of the stratified three-phase system (ambient, film, substrate) and R(O) is the reflectivity of the ambient-substrate interface. If the film thickness is very small relative to the vacuum wavelength 1Eof the incident light, the fractional reflectivity changes for radiation polarized perpendicular and parallel to the plane of incidence are given, to first order in C&U,byI%)
(5b)
In eqs. (.5), ‘pi is the angle of incidence of the light beam in the transparent ambient phase (1) with r-e& dielectric constant a1 and refractive index yti, and t2 and Z&are the complex dielectric constants of the absorbing thin film and substrate phases, respectively. These terms are defined in accordance with the Nebraska ~onven~on~6)~ The above relations provide a very good approximation for AR/R when d/A
324
D.M.KOLB
AND
J.D.E.MCINTYRE
(ii) Measurement of (AR/R), or (AR/R),, at two (or more) angles of incidence. These are referred to as single- and multiple-angle methods, respectively. 2.2. SINGLEANGLEOFINCIDENCE,TWO
POLARIZATIONS
With this method, values of ~AR~R)~ and (ARiR~,, are measured at a single angle of incidence, usually chosen to he between 45” and the pseudoBrewster angle of the ambient-substrate interface. Eqs. (5a) and (5b) can be inverted and solved simultaneously for the real and imaginary parts of &. Expressing the complex dielectric constant of phase j as gj = 8; - is;‘)
(6)
E; = a, - CQE;,
(7)
we find from eq. (5a)
where 1 El
-
El
&;“I --- (AWR)I
El&; - [(El - E;)' +
- E;
8nn,~l
@a)
(>jiq ’
E); a2 = ---‘-r’ Et -83 Letting u=sin2~, and v=cos2~,, third-order in E; and E; : p
WI
we obtain
from eq. (5b) an expression
’ +p
of
(9)
l&2
where fll =
VE[;
(E;’
+
E1;’
-
2X&),
p2 = ZI(E1- E;) (E;’ + f13
=
UEf&;
(EL2
+
p4 = Z&E1 ((E;2 + ____-.-I__
E;’ E1;‘)
~
E1;’
(loa) 2UErE;) +
-
-
2UQEj),
[IV
(&j2
U2Q
-
8;)’
+
+
E;‘)
-
El&;]
+
[(El -
E;)’
+
&1;‘]
[(?.tE1
U&f
EgElj
(&i2
-
-
+
(lob)
(&i2
+
y2”;2
+
y&
+
y4
=
+
&1;2
0,
(fad)
&Ij2)),
V&i)’
of &I;from eqs. (7) and (9) yields a cubic in y,g
&I;‘],
UOC)
-
Elimination
[(El
V’&:;‘]
2U&,&3
-
E;
Ooe)
:
011
where Yl = (1 + 6)
(PI -
a2Pz)T
(12a)
SPE~ROPHOTO~~IC
y2 = -
Zc+@l
34) B2 + (1 + 4) B5 9
+ a1 (1 +
Y3
=
&
-
3&M*
Y4
=
dPz
+
ad4
+ P3 - @A - 2%%& 7
+
&J
325
TECHNlQUE
*
(12b) (12cf VW
Eq. (11) has three roots. If yi, y2, y3, y4 are real, the following solutions are possible”*): (i) one real root and two conjugate imaginary roots; (ii) three real roots of which at least two are equal; (iii) three real and unequal roots. When the number of real roots of eq. (11) is greater than one, it is not always evident which is the physically meaningful value of 8;. Methods for distinguishing the pertinent value are discussed in a following section. Substitution of this value into eq. (7) then yields the corresponding value of &I;. The complex index of refraction of phase] is expressed as fij=nj-ikj,
(13)
where nj and kj are, respectively, the index of refraction coefficient of phase j. Since &j
=
AS
and extinction
) WQ
6;
~(ir
=
=
n;
-
kj” ,
2njkj,
04b)
(14c)
the equivalent set of optical constants n2, k2 of the thin-~lrn phase can be determined from the relations n2 = {J[E; i- (EL2+ E’;~)+]}*,
WW
k, = E;/2n2.
0 5b)
The optical behavior of a thin isotropic surface film is characterized by the three parameters: E;, E; and d (or n2, k2 and d). For a single angle of incidence, however, only two quantities can be measured spectrophotometrically, (AR/R), and (AR/R)/, . If the film is nonabsorbing, &;I= k2 =O, and these two measurements suffice to determine uniquely the values of E; = ~2; and d. If the film is absorbing, the value of d must be determined independently. In studies of heterogeneous electrochemical reactions, for example, d can be estimated from coulometric measurements of the charge passed during film formation or removal. In studies of adsorption on highly-reflecting metallic substrates (e.g., in the infrared), (AR/R), is very small compared to (AR/R),, since the component of the standing-wave electric field tangential to the surface has a node at the surface planel$). The single-angle method cannot be used in this case to evaluate the optical constants of the film. However, for a weakly absorbing
326
film on a highly-reflecting
D.M.KOLB
AND J.D.E.MCINTYRE
substrate,
8, %& and t3 %,~i, such that to a good
approximation
(16)
=-4sin2cp,
The quantity (djcos qpl) is the volume of film sampled by a light beam of unit cross-sectional area, while CI~is the absorption coefficient, defined by a2 = 4nkJl.
(17)
At a film-free surface (z=O) and for angles of incidence smaller than the principal angle, qDp,the value of the normal component of the mean square field strengthaa) in the standing wave in phase 1 is given by49 21)
(18) where (E1[12) is the field strength in the incident plane wave propagating in the positive z-direction. The fractional reflectivity change in this case is thus directly proportional to the energy absorbed by the film, as expressed by Poynting’s theorem. Since AR/R@ 1, it is simply related to the change in “reflection absorbance”, sic4) AA =log,,
by AR R
R (0) [R(d) 1’
= - 2.3 AA .
(19)
(20)
Eq. (16) is thus equivalent to an analagous expression for AA,, derived by Hansen4) (for ‘pr
INCIDENCE,SINGLEPOLARIZATION
Inspection of eqs. (5a) and @a) reveals that since (AR/R)I is directly proportional to the only angle-dependent term, cos ql, no evaluation of E; and sl; can be made using first-order theory and a multiple-angle technique with perpendicular polarization. Analogously, methods which involve a variation of film thickness are not applicable for either polarization.
SPECTROPHOTOMETRIC
TECHNIQUE
327
If measurements of (AR/R),, are made at two (or more) angles of incidence, E; and E; (and d) can be evaluated in principle from eq. (9), although analytical solution for these quantities does not appear feasible. This method will be insensitive when ‘pl <45”, since to a good approximation, (AR/R),, is directly proportional to (l/cos ‘p1)12). In view of the difficulties reported for multipleangle ellipsometric studies of very thin surface films22-24), we have not pursued this method further. In the UV-visible wavelength region, the single angle method discussed previously is more accurate, although an independent measurement of d is required for an absorbing film. In addition, it affords the possibility of detecting optical anisotropy in monolayer films@).
3. Experimental Polarized differential reflection spectra of adsorbed oxygen (or oxide) layers, formed anodically (Eu = 1.6 V) on vacuum-evaporated Au mirror electrodes in Ar-saturated 1.0 M HClO,, were measured in situ at vi =45” over the photon-energy range 1.6-5.5 eV. The film thickness was estimated by coulometry to be 6.0 A, assuming the composition to be Au,O, with a bulk density of ca. 6 g cmm3. Optical constants of the Au substrate were determined by a Kramers-Kronig analysis of normal incidence reflectivity data, measured in air. A detailed description of the experimental apparatus and procedures has been given previouslys).
4. Results and discussion The spectral variation of the optical constants of the vacuum-evaporated Au film substrate is shown in fig. 1. The results are in close agreement with recent measurements of Irani et al.25) and earlier data of Schulz et al.26t27). Illustrated in the inset is the normal incidence reflectivity of the Au film in air. The polarized differential reflection spectra (q)i =45”) of the 0 layer on Au are shown in fig. 2. The influence of the optical properties of the substrate is clearly evident. Using the measured optical constants of the Au film, values of R,(O) and RI, (0) were calculated as a function of photon energy for ~0, =45”, assuming n, to be constant (1.333). Fig. 3 illustrates the pronounced variation of the reciprocal reflectivity, R-l, with tto for these conditions. From the measured values of AR/R and the calculated values of R-“, the differential reflection spectra of AR versus ho were computed; these spectra are shown in fig. 4. Three main peaks are evident in these spectra near 2.35, 3.3, and 4.7 eV. On the basis of the single-angle method described in section 2.2, the dielectric constant of the 0 layer on Au was computed from the measured
328
D. M. KOLB
-24
I 1.6
I 2.4
1
AND J. D. E. MCINTYRE
I 3.2
I
hw
Fig. 1.
I 4.0
I
I 4.8
I 5.6
[ev]
Spectral dependence of the real and imaginary components of the dielectric constant of Au: 8 = E’--ie”. The normal incidence reflectivity of Au (in air) is shown in the inset.
8.0
cc 2 a N 0 7
6.0
4.0
2.0
'iw[ev] Fig. 2. Normalized differential reflection spectra, AR/R versus AU at ql= 45”, of the 0 layer formed anodically on an Au electrode at EH = 1.6 Vin 1.0 M HClOb(Ar saturated).
SPECTROPHOTOMETRIC
229
TECHNIQUE
6
0
1.0
2.0
3.0
4.0
5.0
6.0
Aw !ev) Fig. 3.
Reciprocal reflectivity spectra of Au in an aqueous electrolyte (m = 1.333) at ~1 = 45”.
I
I
I
3.0
[L 2.0 a N 0 T
1.0
0
, I.0
I
I
I
I
2.0
3.0
4.0
5.0
hw
Fig. 4.
0
(ev)
Differential reflection spectra, AR versus ftw at II= 45”, of the 0 layer on Au.
values of (AR/R),,, (AR/R),, 8, and d. As discussed previously, the firstorder theory for the single-angle method yields three solutions for each component of 6,. The frequency dependence of the three sets of roots is shown in fig. 5. At low energies, there are three pairs of real and unequal roots, but at 2.1 eV two of these sets become identical. For ku > 2.1 eV, there is only one set of real roots and this set must therefore correspond to the
D.M.ROLB
330
AND J.D.E.MClNTYRE
actual physical values of E; and 8:. Since these quantities are inherently continuous, their pertinent physical values can easily be distinguished in energy regions where more than one real solution exists. Examination of fig, 5 also reveals that the discarded sets of s; and E; are physically unrealistic
1.0
2.0
3.0
4.0
5.0
6.0
hw rev] Frequency dependence of the three possible solutions of the linear appro~~~~tion retationsl”) for the diekctric constant of the 0 layer on Au. The physicaily meaningful
Fig. 5.
set is w, I&“.
for a semiconducting oxide film and that these discarded values become identical just before turning imaginary. Several useful criteria thus exist for distinguishing the correct physical solution of the optical equations. The frequency dependence of the absorption coefficient of the 0 layer on Au is illustrated in Sg. 6. Also plotted for comparative purposes is the absorption coefkient of the Au substrate. On comparing figs. 2 and dl it becomes evident that the detailed features of the absorptjon spectrum of the
SPE~ROPHOTO,~ETRiC
331
TEC~QUE
0 layer on Au are concealed in the differential reflection spectrum; they can only be revealed by a computer analysis of the optical data. This is particularly evident for the case of the two prominent absorption bands at 4.2 and 4.9 eV. In the spectrum of AR(o), only a single broad maximum centered at 4.7 eV
8.0 -
- 1.0
\
I
I
2.0
3.0
I
I
4.0
5.0
\
6.0
hw [ev] Fig. 6.
Absorption
spectra of bulk Au and the anodic 0 layer on Au (assumed to be Au~03).
is apparent (cf. fig. 4). Similar behavior was observed in the analysis of the differential reflectivity spectra of the 0 layer on Pt mirror electrodes6). As discussed previously6) the very high magnitudes of CQindicate that charge-transfer or other fully-allowed transitions are responsible for the absorption. These processes are likely to be associated with transitions involving excitation of an electron from: (i) an oxygen ion, 02- (2p6), to vacant d levels of a nearest-neighbor gold ion, Au3+ (5d’); (ii) a 2p6 level of 02- to an unfilled 6s level of the Au3” ions; or, (iii) a filled 5d level of Au3’ to an unfilled 6p level of this ion. A more definitive assignment must await quantitative calculations that take specific ligand-field effects into account. Inspection of fig. 6 also reveals that the rapid rise in Q,, at low energies, characteristic of the free-electron behavior of metallic gold, is not duplicated by the thin-film absorption coefficient. The optical properties of the 0 layer on Au thus resemble those of a semiconductor. The results of this study provide an interesting contrast to infrared reflection studies. Fig. 7 illutrates the frequency dependence of the components of the mean square electric field strength in the ambient phase at a film-free
332
D.M.KOLB
AND J.D.E.MCINTYRE
Au surface (z=O), as computed from the exact relations of Hansen20); the maximum value of the ratio (Elf i )/( E,;:) 1z= o is 4. The boundary conditions of electromagnetic theory require that the tangential components of the displacement, D = b E, be continuous across the interface of two phases. In
3.6 3.2 28 t A
;'2.41? ,$2L)w
__
V
.
\
1.61.2cm0.4-
I
O.Ol.0
I
I 2.0
I 3.0
I 4.0
I 5.0
I 6.0
liw(eV)
Fig. 7. Spectral variation of the components of the meansquare electric field strength in the standing wave at the surface (z = 0) of a film-free Au substrate, relative to that of the incident beam, for PI= 45” and nl = 1.333.
the thin-film phase, since cfgi and the energy loss is small, the field strength is only slightly attenuated. Hence to a good approximation
= (E:z)
(E;,.J
= C&x)
E:.@;I,)
= M2
5
(214
2
@lb)
WC)
At the absorption maximum near 2.4 eV (cf. fig. 6), E; =2.3, s;‘=7.0 and hence l&l = 7.37. For an aqueous electrolyte, .si = 1.78, and hence (Eifzz) = =0.058
SPECTROPHOTOMETRIC
<~~,.J/@;;,2$z=,
TECHNIQUE
= 4/k:,
333 (22)
while (~~l,Y<~~~)~,=O
= 4 sin2’p1.
(18)
Thus even for very strong infrared absorption bands (k2 w l), the energy loss is almost entirely due to interaction of the molecules in the film with Ezz, the field-component normaE to the surface. A comparison of figs. 4 and 7 also reveals that the main peaks near 2.4 eV in the differential reflectivity spectra, AR,(w) and AR,, (o), occur near the energies at which both CC,, (Ei,) and (Ei,,) exhibit maxima. A similar peak occurs in the electroreflectance spectrum of Au at this energy”s). This energy corresponds to the onset of the interband transition 5d -+ 6s (Fermi surface) in Au metal. The prominent peak at 2.4 eV in fig. 4 is thus attributable to the combined effects of absorption in the film and a change in absorption by the metal substrate. The successful application of the above spectrophotometric method for determining the optical constants of very thin surface films depends upon the accuracy with which the ratio R(~)/R(O) can be measured. Owing to the cancellation of intensity loss factors in ratio measurements, the accuracy of determination of AR/R is limited primarily by the linearity and freedom from zero-level errors and noise of the photodetector and associated electronic amplification system. In cases where AA,+ Al, AR/R is primarily determined by the real part of the refractive index of the film and the absorptive properties of the substrate12). In order to deduce the true absorption spectrum of the film per se by computer analysis, highly accurate measurements of (AR/R), and (AR/R),, are required. Since the absolute reflectivity of a surface enclosed in an experimental cell of conventional design (cf. ref. 6) cannot be measured accurately, it is not possible to determine the optical constants of the film-free substrate in situ*. The calculation of the thin film optical constants therefore depends upon an external determination of 2,. In this respect, the spe~trophotometric method suffers by comparison with classical ellipsometry which permits an internal measurement of 6,. It has recently been recognized, however, that in optical studies of metal substrates in electrolyte solutions, significant errors in measurements of the apparent optical constants of the bulk substrate may result from neglect of electroreflectance effects. The latter arise primarily from a field-induced change in the free-electron surface charge distribution, which can produce large perturbations of the dielectric constant of the metal in its surface region3r). Ultimately, a combined application of in situ ellipsometry and differential * The use of cylindrical all-quartz cells 2Q*30) may facilitate such measurements.
334
D. M. KOLB
AND
J. D. E. MCINTYRE
reflection spectroscopy may prove most effective in surface studies. The technique described in the present communication promises to be of utility for in situ spectroscopic investigations of the optical properties of monomolecular films on metal surfaces, particularly in studies of the kinetics of rapid adsorption processes and the nature of the electronic interactions of adsorbed species with catalytic substrate materials.
References 1) D. F. A. Koch, Nature 202 (1964) 387. 2) D. F. A. Koch and D. E. Scaife, J. Electrochem. Sot. 113 (1966) 302. 3) T. Takamura, K. Takamura, W. Nippe and E. Yeager, J. Electrochem. Sot. 117 (1970) 626. 4) W. N. Hansen, Disc. Faraday Sot., in press. 5) M. A. Barrett and R. Parsons, Disc. Faraday Sot., in press. 6) J. D. E. McIntyre and D. M. Kolb, Disc. Faraday Sot., in press. 7) A. Bewick and A. M. Tuxford, Disc. Faraday Sot., in press. 8) W. J. Plieth, Disc. Faraday Sot., in press. 9) R. Memming and F. Mollers, Disc. Faraday Sot., in press. 10) H. B. Mark, Jr. and E. N. Randall, Disc. Faraday Sot., in press. 11) P. C. S. Hayfield, in: Surface Phenomena of Metals (Sot. Chem. Ind. Monograph No. 28, London, 1968) p. 128. 12) J. D. E. McIntyre and D. E. Aspnes, Surface Sci. 24 (1971) 417. 13) G. W. Poling, J. Colloid Interface Sci. 34 (1970) 365. 14) D. G. Avery, Proc. Phys. Sot. (London) B 65 (1952) 425. 15) H. E. Bennett and J. M. Bennett, in: Physics of Thin Films, Vol. 4, Eds. G. Hass and R. E. Thun (Academic Press, New York, 1967) p. 1. 16) R. H. Muller, Surface Sci. 16 (1969) 14. 17) S. P. F. Humphreys-Owen, Proc. Phys. Sot. (London) 77 (1961) 949. Ed. S. M. Selby (Chemical Rubber, Cleveland, 1970) 18) Handbook of Mathematics, 4th ed., p. 129. 19) R. G. Greenler, J. Chem. Phys. 44 (1966) 310. 20) W. N. Hansen, J. Opt. Sot. Am. 58 (1968) 380. 21) S. A. Francis and A. H. Ellison, J. Opt. Sot. Am. 49 (1959) 131. 22) F. L. McCrackin and J. P. Colson, in: Ellipsometry in the Measurement of Surfaces and Thin Films, Eds. E. Passaglia, R. R. Stromberg and J. Kruger (Nat]. Bur. Std. (U.S.) Misc. Publ. 256, U.S. Govt. Printing Office, Washington, 1964) p. 61. 23) D. G. Schueler, Surface Sci. 16 (1969) 104. 24) J. A. Johnson and N. M. Bashara, J. Opt. Sot. Am. 61(1971) 457. 25) G. B. Irani, T. Huen and F. Wooten, J. Opt. Sot. Am. 61(1971) 128. 26) L. G. Schulz, J. Opt. Sot. Am. 44 (1954) 357. 27) L. G. Schulz and F. R. Tangherlini, J. Opt. Sot. Am. 44 (1954) 362. 28) J. D. E. McIntyre, Paper (Abstract No. 231) presented at the 135th National Meeting of the Electrochemical Society, New York, May 7, 1969. 29) L. Masing, J. E. Orme, and L. Young, J. Electrochem. Sot. 108 (1961) 428. 30) B. D. Cahan, private communication. 31) J. D. E. McIntyre and D. E. Aspnes, Bull. Am. Phys. Sot. 15 (1970) 366.