## Single Wavelength Ellipsometry SWE

Ellipsometry was first practiced by Paul Drude (Ref 10) just prior to 1890. The name ellipsometry was introduced by A. Rothen (Ref 11) in 1945. Clearly, this is not a recently developed technique. Ellipsometry uses monochromatic light, optical elements that change the polarization state of the light, some sort of detector, and some calculation facilities. Although rudimentary forms of these requirements have been present throughout this century, the development of the photomultiplier, the laser, and the desktop computer have greatly enhanced the use of this technique to the point that it is now routinely used as a metrology tool in semiconductor wafer manufacturing.

Instrumentation. Figure 4 shows the basic requirements for SWE. The figure shows the arrangement of a manual null ellipsometer. The source generates monochromatic light, and the polarizer passes only light that is polarized in a particular direction. The quarter-wave plate (QWP) then converts the light to elliptically polarized light. If the polarizer and QWP are positioned correctly, the ellipticity is reversed by the reflection, giving linearly polarized light. The analyzer nulls out the light so that the intensity at the detector is zero. The optical elements used for the polarizer and analyzer are both polarizers. The terminology describes function, in that it is the function of the element called polarizer to cause the light to be polarized, and it is the function of the analyzer to determine the polarization state of the light.

Fig. 4 Schematic of manual null ellipsometer. The quarter-wave plate is fixed at either ± 45° and the polarizer and analyzer are rotated to find the null. The positions of the polarizer and analyzer are then used to calculate the ellipsometric parameters Del and Psi. Source: Ref 8

Operation of this instrument requires iterative adjustment of the polarizer and the analyzer until the null positions are located. The angular position of the polarizer and analyzer are then used to calculate the ellipsometric parameters, Del and Psi. Del is the reflection-induced phase shift between the waves that are perpendicular and parallel to the plane of incidence, and tan (Psi) is the amplitude attenuation ratio of the parallel wave to the perpendicular wave.

Although the manual null instrument illustrates the concepts reasonably well, most commercial instruments are rotating-element instruments. In some cases, the polarizer and analyzer are rotated by the instrument, under microprocessor control, until null is found. In other cases, only the analyzer is rotated, and Del and Psi are calculated from photometric measurements, rather than null positions.

Analysis of Films. Regardless of whether the measurement is made with a manual null instrument, a rotating-element null instrument, or a rotating-element photometric instrument, the parameters that an ellipsometer measures are Del and Psi. For a film-free surface (a substrate), Del and Psi can be converted to the values of the optical constants for the substrate material, N = n - jk. The value of Del for a substrate will be between zero and 180° and the value of Psi will be between zero and 45°. In Fig. 5, the film-free value of Del/Psi for silicon is about 178°/10.5°. If a dielectric film (i.e., k = 0) with index N = 1.46 is added, the location of the Del/Psi joint begins to change on the Del/Psi domain. When the film thickness is 20 nm, the Del/Psi location is about 129.9°/13.7°. As the thickness increases, the Del/Psi trajectory is traced out until the value of thickness reaches the period thickness. At this thickness, the Del/Psi point has returned to the filmfree location. For added thicknesses, the Del/Psi point simply retraces the trajectory. For the particular example given in the figure, the period thickness is 283.2 nm.

Fig. 5 The Del/Psi trajectory for silicon dioxide on silicon with angle of incidence of 70° and wavelength of 632.8 nm. Source: Ref 8

The physics and mathematics for converting ellipsometric measurements to optical constants and film thicknesses are beyond the scope of this article. The reader should refer to books by Azzam and Bashara (Ref 7) and Tompkins (Ref 8) for details. The important point to remember is that the technique relies on differences in phase shift and reflectance for the two directions of polarization, and on changes in these differences as a function of film thickness.

The trajectory that is traced out depends on the index of refraction of the film. Figure 6 shows the first part of trajectories for films on silicon, with n values 1.46, 1.6, 1.8, and 2.0. If an unknown film were measured and the resulting values of Del/Psi were 70.0°/28.9°, it could be determined by inspection from Fig. 6 that the Del/Psi point falls on the n = 1.8 trajectory, and the position on this trajectory indicates that the thickness is 60 nm. Although the calculations to plot these trajectories can be made (Ref 8), normally the microprocessor in the ellipsometer makes the calculations and provides the values of n and thickness. This has led to the common misconception that ellipsometers measure the index of refraction and thickness. In fact, ellipsometers measure Deland Psi, and the values of n and thickness are calculated based on a model. The model is implicitly chosen when the program on the microprocessor is chosen (e.g., single film or substrate).

Fig. 6 The Del/Psi trajectories for films with several different indices of refraction on single crystal silicon substrates. The first 80 nm is shown. Source: Ref 8

Because of the periodicity, the resulting thickness value is not unique. A Del/Psi point of 129.9°/13.7° could represent a film 20 nm thick, 283.2 + 20 nm thick, 2 x 283.2 + 20 nm thick, and so on. In many cases, other processing information can be used to deal with this matter. The deposition or film formation rate can often be used to estimate the film thickness to well within one period thickness. For a totally unknown film, however, other methods must be used. The period thickness depends on the index of refraction of the film, the angle of incidence, and the wavelength of light being used. By using another wavelength of light or another angle of incidence, the question of period can often be resolved. If unknown film stacks are routinely encountered, spectroscopic ellipsometry might be a more appropriate technique.

For non-dielectric films, the Del/Psi trajectory does not close on itself. An example is shown in Fig. 7. Conceptually, with no film present, the Del/Psi point represents the substrate. When there is a thick film of an opaque material present, the Del/Psi point will represent a substrate of the film material. The Del/Psi trajectory during film growth is simply the movement of the Del/Psi point between the location for the original substrate to the location for a substrate of the film material. In Fig. 7 the growth of a tungsten film on silicon is shown. As long as the film is thin enough that light reaches the silicon substrate, ellipsometry can be used for film thickness measurements. For tungsten, the method could be used for films up to about 20 nm thick. Beyond that, the points are too close together for the method to be useful.

Fig. 7 The Del/Psi trajectory when a film of tungsten is deposited onto silicon. The small dots are at 1 nm intervals. The large dots are at 5 nm intervals from zero thickness. Source: Ref 8

Areas of Applicability. Ellipsometers can measure Del/Psi to a few hundredths of a degree. A change in film thickness (with n = 2.0) of 0.1 nm represents about 0.25° in Del. This technique therefore can be used to measure monolayer changes. This is a particularly powerful technique in the thickness range from about 1 nm to a few hundred nanometers. When the thickness is greater than several period thicknesses, other techniques such as reflectometry may be more appropriate for thickness measurements. Even in this case, however, ellipsometry may be used to provide index of refraction information for the reflectometry instrument.

When multiple films are present, information about the top film can be determined if information is available for all of the underlying films. In metrology situations, this is often the case, but for totally unknown films, other methods normally must be used.

References cited in this section

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