A. C.HALL
1702
On the Use of Ellipsometry for Adsorption Measurements below Monolayer Coverage
by A. C. Hall Sowny MOW Oil Company, Inc., Field Research Laboratory, Dallas, Texas (Received July 1 , 1966)
It has been surmised that the ellipticity of light reflected from partially covered surfaces depends linearly on the fractional coverage. Adsorption studies based upon this conjecture may need to be revised, since it appears that ellipticity varies as the square root of fractional coverage.
Introduction Because of experimental limitations, adsorption measurements on solids, whether from the liquid, vapor, or gas phase, often require use of particulate adsorbents. There are at least two disadvantages inherent in this practice: it becomes difficult to distinguish between multilayer and capillary adsorption at relative pressures near unity, and particle surfaces have properties that are difficult to control. It is quite useful, therefore, to be able to measure adsorption on surfaces that are both flat and smooth, in the optical sense. Ellipsometry is probably the most versatile technique for making such studies. Under certain conditions this method permits adsorbed films to be measured both qualitatively (refractive index) and quantitatively (thickness).’ A problem of interpretation arises when coverages of less than a monolayer are considered. The model upon which the equations of ellipsometry are based assumes the adsorbed phase to be a homogeneous, plane, parallel-sided layer.2 How the ellipticity of the reflected light varies with coverage below a monolayer is the question to be answered.
T
=
tan (PO- cpl)/tan
S = -sin
(cpo (PO
+
PI),
and
- cpd/sin
(PO
+ cpd
(1)
Theory
T and S are the reflected amplitudes with planes of vibration parallel and perpendicular to the plane of incidence. cpo and cp1 are the angles of incidence and refraction. These formulas imply that linear polarization is preserved on reflection, and that for incident light of equal amplitudes parallel and perpendicular to the plane of incidence, the azimuth of the plane of vibration of the reflected beam ($ = arctan T / S ) depends upon cpo and cpl, or, via Snell’s law, upon cpo and n, the refractive index of the reflecting body. Also, at the polarizing-or Brewster’s-angle (tan cpo = n), T = 0. That is, a surface quite free of film will reflect no light vibrating in the plane of incidence if cpo = &. The reflected amplitude, if any, lies entirely in the perpendicular plane. The equations are confirmed by o b ~ e r v a t i o n . ~ ~ ~ If a surface film is present, the Fresnel equations must be modified to express the observed phenomenon, viz., that the reflected light is elliptically polarized. A t the polarizing angle, the component vibrating in the plane of incidence does not vanish, although its intensity, M 2 , is very small by comparison with S2. Furthermore, it is found to be 90” out of phase with the
T o approach the problem it is necessary to consider in turn the optics of film-free and of film-covered surfaces. In the case of film-free surfaces the transition between adjoining media (e.g., glass-vacuum) is discontinuous, and the reflection of incident linearly polarized light of unit amplitude is described by the Fresnel equations3
(1) A. Vasicek, J . Opt. SOC.Am., 37, 145 (1947). (2) P. Drude, “The Theory of Optics,” Longmans, Green and Co., New York, N. Y., 1920, p 287. (3) M. Born and E. Wolf, “Principles of Optics,” Pergamon Press Inc., New York, N. Y., 1959, p 39. (4) P. Drude, Ann. Phys., 36, 592 (1889). (5) Lord Rayleigh, Phil. Mag., 2 3 , 1 (1892).
The Journal of Physical Chemistry
USE OF ELLIPSOMETRY FOR ADSORPTION MEASUREMENTS
perpendicular component, and this is generally indithe resultant cated by writing it as iM where i = 47, being elliptically polarized light with the minor axis in the plane of incidence, the major axis in the perpendicular plane, and ellipticity defined as p = M / A Y . ~ What follows is simplified by imposing certain conditions: (1) observations are confined to the polarizing angle; ( 2 ) the incident linearly polarized beam vibrates at 45” to the plane of incidence; (3) the film thickness, d, and light wavelength, X, are such that d/X
