Ellipsometry is a technique of non-destructive measurement allowing optical characterisation of a sample having a specular or quasi-specular surface. The term ellipsometry is used as a collective term for denoting various methods for studying the physical properties of test samples by means of measuring the amount by which they change the polarization of a polarized light beam. In principle, a beam with a known state of polarization is reflected from or transmitted through the test sample. After reflection at the test sample or after the light has passed through the test sample, the physical properties of the test sample can be ascertained from the change in polarization, using optical calculations.
Ellipsometry is based on the fact that a monochromatic electromagnetic wave changes its intensity and state of polarization if it non-perpendicularly strikes the interface between two dielectric media (for example, a substrate coated with a film). The ellipsometer linearly polarizes the light beam before it strikes the sample surface; linear (or circular) polarization indicates that the light gets only two perpendicular components having the same amplitude. The beam, after going through the interface between the surface film and substrate, is reflected and changes its polarization, i.e. both the ratio amplitude of the two components (Ψ) and their phase (Δ) are modified. The two components of the reflected light are no longer mutually perpendicular and have a different amplitude; hence the polarization becomes elliptical and the technique is called ellipsometry. The ellipsometer measures the experimental values of the two components of the reflected light, giving the values Ψ and Δ. The value Ψ is calculated by multiplying the ratio of amplitudes of the incident beam by the amplitudes of the reflected beam; the value Δ comes from the difference of their phases.
Ellipsometry can be implemented in situ and therefore is well suited to the study of the mechanisms of thin layer growth, the formation of interfaces and the control of the processes used to form these layers and interfaces. For example, during semiconductor fabrication, thin films are deposited on a wafer. The thickness of the films is critical and may be readily determined from ellipsometric measurements. There are numerous other manufacturing processes that also require accurate deposition of thin films. Ellipsometers are routinely used to measure the quality of these processes by analyzing the film properties.
The ellipsometric measurements can be made at one fixed wavelength or at several wavelengths (i.e. spectroscopic ellipsometry). According to the wavelength region of the source (near ultra violet, visible, near infra red, infra red, etc.) it is possible to analyze different properties of layers or of bulk materials. In the ultra violet and visible regions, the depth of penetration of the radiation is often slight. These wavelengths are often used for the study of surfaces and interfaces. Generally this does not allow access to layer volumetric properties of materials which can, however, be obtained through measurements in the infra red region. Infra red is also well suited to measurements of vibrational absorption (chemical bonds).
In reflection ellipsometry, the test sample has a reflective surface on which the light beam impinges with an oblique angle of incidence. The ellipsometric data obtained can be used for ascertaining the refractive index and the extinction coefficient of the surface material of the test sample. If the test sample is covered with a dielectric film, it is possible to determine the thickness and the refractive index of the film. Reflection ellipsometry is the most sensitive and most accurate method for measuring such films or layers. Instead of using a reflected beam, it is also possible to analyze the light beam which is transmitted through the test sample. This method is referred to as transmission ellipsometry. The same procedure which is used for measuring the change in polarization in transmission ellipsometry can also be employed for studying bulk properties of transparent materials, for example the birefrigence of crystals or optical rotation of a sugar solution. The latter is conventionally referred to as polarimetry, but it falls within the general term of ellipsometry. For the sake of simplicity hereinafter, reference will primary be made to reflection ellipsometry but it should be appreciated that, unless stated otherwise, the information and procedures set forth herein also apply to transmission ellipsometry and polarimetry as referred to above.
In ellipsometry, the physical parameters of the test sample, which are the aspects of interest, simultaneously affect the relative intensity and the phase delay of the two polarization components of the light beam. As external influences affect the two polarization components to the same degree, ellipsometry is very insensitive with respect to such external influences. That also explains the extremely high degree of accuracy of ellipsometric measuring methods in conventional laboratory equipment.
An ellipsometer essentially comprises a light source for emitting polarized light, a test sample and an analyser which analyses polarization of the light after it has been reflected at the test sample or after it has been transmitted through the test sample. More particularly, an ellipsometer typically comprises a light source and a detector together with two polarizers, one of which is disposed near the light source and is conventionally referred to as the polarizer, while the other is disposed in the vicinity of the analyzing means and is generally referred to as the analyzer. The test sample is disposed between the polarizer and the analyzer, and the assembly may include one or two devices for altering or modifying the polarization of the light, referred to as polarization modifying devices or polarization modulating devices. The polarization modulating devices may be polarizers which produce a partial polarization effect, birefrigent devices (which are referred to as compensators), or optical rotators and/or geometrical rotators. If, for example, the polarizer is rotated relative to the test sample, that is a geometrical rotation. The differences between the individual kinds of ellipsometers arise out of the choice of the device used for modifying the state of polarization. By virtue of the particular design construction selected, ellipsometers have different properties, for example in regard to accuracy, high measuring speed and suitability for operation with multiple wavelengths.
Because of the non-directional nature of optical laws, the sequence in which the optical components are disposed may be interchanged between the two polarizers. The mode of operation of the overall assembly then remains the same.
In order to carry out ellipsometric measurements, the surface of a sample is illuminated by a light beam and the state of polarization of an incident beam i is compared with that of the reflected beam r or the transmitted beam. A polarization electric field vector E is generally represented by its projections ES and EP, respectively perpendicular and parallel to the plane of incidence. The projections ES and EP are complex amplitudes.
In the domain of linear ellipsometry, the polarization reflectance ratio is traditionally defined to be the ratio of the reflection coefficients p- to s-polarized lightρ=RP/RS=(EP/ES)r/(EP/ES)i  (1)and is indicative of the modifications to the state of polarization produced by the surface being studied. ρ is a complex number, therefore two ellipsometric parameters must be obtained in order to determine ρ, which is generally represented in the form:ρ=tan Ψ·eiΔ=(EP/ES)r/(EP/ES)i  (2)
The two parameters Ψ and Δ describing the change in polarization are thus combined in the complex quantity ρ. The parameter Ψ is a measure of the relative intensities (the amplitude ratio) of the p-to-s polarization states of the probe light beam, and the parameter Δ is a measure of the relative phase shift between the p and s polarization states. The parameters Ψ and Δ, and hence the number ρ, depend, at the same time, on the surface properties of the sample, the angle of incidence of a beam and the measurement wavelength. The expression of Ψ and Δ, or of ρ, as a function of these parameters, is given by the equations of Fresnel, as is well known in the art.
As a conventional method of obtaining these ellipsometric parameters Ψ and Δ, the null ellipsometry method is known. In null ellipsometry, the change in the state of polarization which is caused by the test sample is compensated by suitable adjustment of the polarization modulating device so that the light beam is extinguished by the analyser. Adjustment to a minimum level of received intensity may be effected either manually or automatically. The measurement result is then the position of the polarization modulating device upon extinction of the light beam. In this method, a polarized beam is radiated from a light source onto a measurement target at a predetermined angle with respect to the target, and a beam reflected by the target, which is elliptically polarized, is transmitted through a λ/4 (quarter wave) plate and an analyzer to be guided to a light-receiving unit. While optical intensity signals obtained by the light-receiving unit are observed through, e.g., a measuring unit, the λ/4 plate and the analyzer are rotated to obtain a rotational angle at which the minimum optical intensity is observed. The above-mentioned ellipsometric parameters are calculated on the basis of this rotational angle, as is known in the art.
Second harmonic generation (SHG) and sum-frequency generation (SFG), which are the respective frequency doubling and frequency mixing of light, have emerged as powerful ellipsometric probes for characterizing oriented surface systems. By nature of the unique symmetry of SHG and SFG measurements, the detected signals are often dominated by the oriented chromophores at interfaces and are largely insensitive to greater numbers of randomly oriented species in the bulk. This symmetry condition has been exploited with great success in surface-specific spectroscopic measurements by SHG and SFG at solid/liquid, liquid/liquid, liquid/air, solid/air, semi-conductor, polymer and biological interfaces.
The intensity of the second order nonlinear beam generated from an oriented uniaxial organic film between two isotropic media is dependent on the nonlinear optical susceptibility (described by the rank three x(2) tensor), the incident intensity or intensities, the polarization states of the incident and exigent light, and the linear optical properties of the interfacial system. A routine approach for isolating relative values of the x(2) tensor elements is to compare the intensities of the s- or p-polarized nonlinear beams measured as functions of the polarization state(s) of the incident beam(s). For example, the expressions in Eqs. 3 and 4 below (or variations thereof) are commonly used in reflection SHG measurements of achiral uniaxial interfacial films performed using linearly polarized incident light with the plane of polarization rotated away from purely p-polarized by the angle γ.Is2ω=C·¼ sin2(2γ)|s1xXXZ|2(Iω)2  (3)Ip2ω=C·|s6xZXX+cos2γ(−s3xXXZ+s5xZXX−s6xZXX+s7xZZZ)|2(Iω)2  (4)In standard reflection and transmission measurements of achiral films far from resonance, relative values of the tensor elements are easily obtained from the ratios of the second harmonic intensities measured under different polarization conditions or from nonlinear curve-fitting.
As new samples, unique substrates and diverse interfacial systems are increasingly investigated by SHG and SFG, many of the simplifying assumptions routinely used to treat polarization measurements may not hold. For example, the Fresnel factors that describe the electric fields at an interface will be complex-valued in studies conducted in total internal reflection or in studies of multilayer films. The Fresnel factors will also generally be complex in systems in which the nonlinear film, the substrate, or the ambient medium absorbs either the incident or exigent light (e.g., in spectroscopic studies). Finally, if the nonlinear surface layer absorbs one or more of the incident or exigent optical frequencies, the x(2) tensor elements themselves will also be complex-valued. In any or all of these instances, even the simple expressions in Eqs. 3 and 4 (or variations thereof) describing SHG can become complicated. Expansion of the expressions in Eqs. 3 and 4 in the most general case of SHG measurements with complex fitting coefficients and complex tensor elements yields the expressions in Eqs. 5 and 6.
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It is immediately apparent that extracting the real and imaginary components of the three independent tensor elements present in SHG from the second harmonic intensity measured as a function of γ is nontrivial. Even assuming the x(2) tensor elements are purely real, Eqs. 5 and 6 yield a minimum of two possible solutions for the relative tensor elements (for xZXX and xXXZ of like and opposite sign).
An alternative detection approach was pioneered during the emergence of nonlinear optical surface measurements of uniaxial films in which a rotating polarizer is placed between the sample and the detector. As described hereinabove, rather than compare normalized intensity ratios, the rotation angle of the polarizer that resulted in extinction of the nonlinear beam was used to determine relative values of the tensor elements and subsequently molecular orientation. Using this type of approach, the ambiguity regarding the relative sign between xZXX and xXXZ in principle can be removed. However, this rotating polarizer approach will only produce a true null provided the nonlinear beam is linearly polarized, which generally limits its reliable application to standard reflection and transmission measurements of vanishingly thin transparent films far from resonance (in which case both the x(2) tensor elements and the Fresnel factors are purely real).