Ellipsometry for Thin-Film and Surface Analysis Robed W. Wlm* and Yeon-Taik Khn‘ Materials R e d Laboratory The Pennsylvania State Vnlwrslty Unlverstiy park, PA 16802
Ellipsometry, in its broadest sense, entails measurement of the polarization state of light, which is in general elliptical. Although the term ellipsometry was coined in 1944, the principle of ellipsometry was fmt applied just over 100 years ago when Paul Drude in Germany and Lord Ftayleigh in Great Britain studied the polarization state of liiht reflected from thin-film-coated solid and liquid surfaces, respectively. Drude is credited with the development of the fundamental equations of eUipsometry, which demonstrated potential monolayer sensitivity for the detection and characterization of thin films on specular surfaces (I). When a polarized light heam reflects from any specular surface, changes occur in both the amplitude and phase of the willating parallel and perpendicular vector components of the electric field associated with the beam. As shown in Figure 1 @. 889 A), p and s *&withthtIkpartmentofPhysies. Present addrew Department of Chemistry, Universityof Tern &Austin, Austin,TX 78712
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0003-2700/90/0362-887A/$02.50/0 0 1990 American chemical Society
refer to the spatial directions parallel and perpendicular (in German, senkrecht) to the plane of incidence, which contains both incident and reflected beams. The goal of an ellipsometry experiment is to measure these amplitude and phase changes, which provide researchers with information about the reflecting surface (2). If the incident light wave is linearly polarized with the electric field oscillating along the s direction, and it strikes a dielectric (nonabsorbing)material at an angle of incidence, Bi, then the phase change is 180’. and the direc-
Bremter’s angle. The planes indicated bythe dottedlinesrepresent the planes of polarization of the heam just hefore and just after reflection from the surface. Because of the different phase and amplitude changes that the p and s electric field components incur upon reflection, the direction of the linear polarization changes in the manner shown qualitatively in the figure. Although Figure 1depicts the easily visualized case of linearly polarized light, it demonstrates the essence of ellipsometry. More commonly, the incident light is elliptically polarized and
lNSTRLJMEN7ATlON tion of the electric field vector is reversed upon reflection. On the other hand, if the liiht wave is linearly polarized along the p direction, the phase change upon reflection is either 0’ or 180° depending on whether Bi is less than or greater than the polarization, or Brewater’s angle, respectively. (At Brewster’s angle the p component is completely transmitted.) In the simple example of Figure 1, the incident beam is linearly polarized at an angle with respect to the p and s directions, with p and s electric field vector componentsthat are in phase. In the figure, Bi is assumed to be less than
the surface is ahsorbing. Then the phase difference between the two incident components as well as the phase change upon reflection is neither Oo nor 180° for each of the two components. It is impossible to discuss ellipsometric instrumentation and applications without fmst introducing the complex amplitude, or Fresnel, reflection coefficients (see Glossary) and the measured ellipsometry angles J. and A (2). The Fresnel reflection coefficients, rp and r,, are defined as ratios of the reflected and incident electric fields (including both the amplitude and complex phase factors) for the p and s components.
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For reflection from a single interface between two media, the Fresnel equations allow one to calculate r,, and r. from Bi and from the optical properties of the two media. Furthermore, for any sample with multiple interfaces, rpand r. can be calculated by multilayer optical analysis using the incidence angle: the optical properties of the ambient, substrate, and each layer; the layer thicknesses; and the wavelength. The ratio of the p and s Fresnel reflection coefficients, rp/rs, defines the complex parameter p. The amplitude of p in turn defmes the tangent of the ellipsometryangle $, and the phase of p defines the other ellipsometry angle A. Thus, $ and A provide a measure of the amplitude ratio and the phase difference between the two components upon reflection. Figure 1 summarizes these relationships. Within the realm of tools available for surface and thin-film characterization, ellipsometry fills a special niche. Its primary advantage is that it can be applied to study surfaces in real time in a variety of adverse environments including reactive gases, ion beams and plasmas, laboratory air, and transparent liquids. Surface probes that rely on the detection of electrons or ions from the surface, such as Auger electron spectroscopy, X-ray photoelectron spectroscopy, reflection high-energy electron diffraction, and secondary ion mass spectrometry, require ultrahighvacuum techniques and cannot be used to study many important problems, such 88 c o m i o n or chemical vapor deposition, that occur in reactive environments. Although scanning tunneling microscopy is a highly effective probe of surface processes in electrochemistry and can provide a more direct picture of atomic-scale structure of surfaces in liquid environments, it cannot be used to investigatevapor deposition in real time. As discussed below, ellipsometry as an optical spectroscopy provides information on the electronic transitions in the solid and on the overall structure of the sample, including film thicknesses, density, and microstructure, the latter on scales much smaller than the wavelength of light in the solid. Thus, it is complementaryto other more common optical techniques including IR reflection and Raman spectroscopy, which prohe vibrations of the solid, and diffuse light scattering, which tends to probe larger scale microstructure. In fact, ellipsometryalso bas been used in the IR range (3),but discussion of such instrumentation, which is continuing to advance. is bevond the scoDe of this article. Ellipsometry tends to be more pow-
erful than simpler optical measurements. In contrast to a reflectance experiment, which provides one measured parameter, the ratio of the reflected and incident irradiances, an ellipsometry experiment provides two, $and A,which are ultimately related to the change in tilt angle and ellipticity of the polarization state. For example, a measurement of a nonabsorbing (film-free) solid by reflection spectroscopy gives the index of refraction (n), whereas ellipsometry gives both n and the extinction (k)or absorption coefficient (a)of any f h - f r e e solid. Thus, ellipsometry provides a complete description of the optical properties of absorbing bulk materials. Because 0 the extreme surface sensitivity of ellip sometry, however, the problem of determining accurate optical properties of solids becomes one of preparing clean, atomically smooth surfaces so that application of the Fresnel equations for a single interface is valid. One limitation of ellipsometry is its inability to measure low absorption coefficients for weakly absorbing bulk samples. In contrast to a transmittance experiment in which the sample thickness can often be increased to detect increasingly lower values of a,ellipsometry in the visible range can only detect values of a > 1-10 em-' (4). To determine polarization state changes, an ellipsometer must consist of a series of optical elements that serve as a polarization state generator mounted before the sample, followec by elements that serve as a polarizatioi state detector, mounted after the sample. The variations in ellipsometer design arise from differences in the methods used to generate and detect polarized light. Advances in ellipsometry to dah have been stimulated by sweeping ad vances in instrumentation of genera utility: after World War 11, the photo multiplier tube (PMT) for high-semi tivity detection of photons; in tL 196Os,the microcomputer for laborato ry automation; and about 15 years lat er, the optical spectrometric multi channel analyzer for near-simulta neous acquisition of entire spectra. Manual null elllpwnetef Manual ellipsometers of the null design benefited from the development of the PMT. Although they continue to be available commercially and are still used in research laboratories, these ellipsometers are gradually being replaced by various automatic systems. Those who have had passing contact with ellipsometers are probably most familiar with the operation of the null instrument.
Figure 2 shows a schematic of the optical elements for the null ellipsometer and the polarization of the beam as it progresses through the instrument. The polarization state generator consists of a collimated monochromatic light source, a polarizer, and a quarter-wave plate (QWP) in succession. The polarization state detector consists of a second polarizer (or analyzer) and PMT. The QWP uses a birefringent material (e.g., crystal quartz or mica) to impose a 90° phase shift between two orthogonal electric field components. The phase shift occura hecause the electric field component along one axis 11 (slow axis) expariena
higher index of rehction than the component along the orthogonal axis (fast axis). This leads to a reduced speed for the former component, and hence the term slow axis. The combination polarizer4WP allows one to generate any elliptical polarization state by adjusting the angles of the poLarizer and QWP appropriately (measured counterclockwisefrom the plene of incidence when looking into the beam; see Figure 2). For example, circularly polarized light is generated when the light incident on the QWP is linearly polarizedat 45' with respect to the fast and slow axes. In null ellipmeter operation, the polarizer angle is adjusted 80 that th
Flgure 1. The geometry of reflectlon and the deflnklon of $ and A.
me sltvatiMl here 1s typical d a nonabsablngmatau wdl asdiamondIn mevislbk spemun aIa M)' angle of lncldsnur ( b l o w Brewaer's -le). F a an absubing1-, he nwectsd llpmwould bdllp tically polsriled.
Figure 2. A schematic of the progression of optical elements and the evolutim of
the polarization atate for the null ellipsometer. angk d the quulsr-wan, plate (QWP)taSt axkmca8ued wm rsape*totheplane Ot Inoldenos. r s p s s e m me powm and analper anoh ~1me cull pornlon. F a me rsiatlamhips ahom, 00 5 h 5 900. CIS
me sminga (P,,&)
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ellipticity imparted to the polarization state by the polarizer4WP is cancelled by the sample. Then the reflected beam is linearly polarized, and the output of the PMT can be completely nulled by adjustment of the analyzer orientation. Figure 2 includes the relationship between $ and A and the polarizer and analyzer angles at the null, when the analyzer angle is in the first quadrant. In practice, the angles P and A are suceeasively adjusted to minimize the PMT output until (PO& is reached (5). The key to the surface sensitivity of any ellipsometer is the ability to resolve small angular differencesin P and A. For the typical null ellipsometer,the angular resolution is mechanically limited to 4.02O. It may be recalled that in thin-film interference phenomena, an increase in f i thickness equal to lh the wavelength of light in the f h generatea an added phase shift of 180° between beams reflected from the top and bottom f i surfaces. This results in a shift from maximum to minimum in the irradiance distribution of the interference pattern. Correspondingly, the ability to detect a phase change of 0.02' implies a sensitivity tofh thickness, d, of 6d (0.02°/1800)(X/4nl cos 03, where X is the vacuum wavelength, nl is the index of refraction of the film, and Bt is the transmitted an-
-
-- -
gle. For X = 400 nm and other typical values (nl 1.5, St 40°), this corre0.1 A, about 'Im of a soonds to 6d monolayer. Accurate determination of ($, A) in the manual null ellipsometer requires a minute or more of tedious manipulation of the optical elements. This discourages the operator from performing detailed spectroscopic measurements in which the wavelength of the incident light is varied. A spectrum of 100points represents several hours of continuous, eye-straining work. Furthermore it is impossible to follow dynamic phenomena such as thin-film growth even at slow, Klmin rates. In spite of these limitations, the null ellipsometer has been widely used to study the optical properties of bulk materials and determine the thickness and propertiea of thin films in numerous static and quasi-static applications (2). In electrochemistry, applications of null ellipsometry have included characterization of surfaces and thin films in studies of adsorption, oddation, passivation, electrodeposition, and electropolishing. In medicine and biology, applications have included adsorption of proteins on surfaces, immunological reactions, and measurement of cell surface materials. In physic8 and materials science, null ellipsometryhas been used to determine optical proper~~
Figure 3. optical configuration and detector irradiance, 4.as a function of time, t,
for the rotating analyzer ellipsometer. me SCglSs (#.A)are dstermlned W a n !Ae numallzed 2 0 Fowler OoBfflcW ol tha detscta i d l a n c e
M. tlms. Ths angle $ I5 a phase angle that io required became at t = 0, M i n e d as me time -1atSd wlth tha fhst data pint. amyzer mission axis Is not necessarily ap h of incldenca. This phaas angle b delemined in callbrath.
me
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Flgure 4. The slgie-layer (three-mediurn) problem usually encwntered in eliipsometly.
ties; to characterize monolayers and thin films, particularly dielectrics used in semiconductor fabrication; and to study surface modification in materials processing. Null ellipsometry is a powerful in situ probe of reactions at solid-mlid, solid-liquid, solid-gas, and even biological interfaces, but its power is limited to quasi-static situations at a single wavelength (selectable for some instruments). Hence in situ ellipsometryis an appropriate term to describe such experiments, although the same term is also applied to the dynamic situations discussed below. Aut~nnaNcelllpoometers Since about 1960, automatic ellipsometers have been developed and perfected using a number of polarization generation and detection schemes (6). As the sixties proceeded, newly introduced laboratory computers were exploited for data collection and analysis. The process was in full swing by 1968, when five different instruments were described at the Symposium on Recent Developments in Ellipmetry, held at the University of Nebraska (7).In the most straightforward design, the null ellipsometer was automated using computer-controlled stepping motors to rotate the polarizer and analyzer. The motors were driven by control sign& derived from the PMT output. This reduced the single measurement time by a factor of 100 to -1 s (8). More complicated schemesused Faraday or Pockela cell polarization mcdulators that were placed just after the polarizer and just before the analyzer. Otherwise the configuration of optical elements was the same as that of the null ellipsometer. The Faraday cell employs the effect of the same name, in which the direction of linear polarization of a beam traversing a material such as flint glass can be rotated by application of a magnetic field along the beam direction. To construct the Faraday cell, the flint glass is formed into a rod that is used as the core of a
