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The current product line of Woollam spectroscopic ellipsometers (alpha-SE, VASE, M-2000, IR-VASE, and VUV-VASE) includes an optical compensator (retarder) element on every ellipsometer. In this article we address advantages of using and methods of incorporating a compensator element into the optical design of an ellipsometer. We believe that this review of compensator technology will help you understand the operation of your ellipsometer and unlock its full potential for your application.

What is a Retarder (Compensator)?
A retarder is an optical element that changes the phase of an incident wave, delaying one of the two orthogonal light constituents. This delay is caused by optical anisotropy (no ≠ ne) in the retarder. Each of the two orthogonal electric fields sees a different index which produces a different phase velocity.

Figure 1. Retarder element introducing a phase shift between the two light constituents.

A compensator introduces a 90° phase change. Therefore, if linearly polarized light is put in, it will exit the compensator as circularly polarized light.

Why use a Compensator in an Ellipsometer?
Compensators are used in ellipsometry to enhance measurement accuracy.

Rotating Analyzer and Polarizer ellipsometers (RAE and RPE) are very simple to construct and can be highly accurate over a wide spectral range. However, they have the following limitations:

1. Cannot determine the “handedness” of the phase term Δ. In other words, they measure from 0° to 180° when in reality Δ varies from 0° to 360°.

2. Their precision and accuracy are poor when Δ is near 0° or 180°.

For many applications, these limitations are inconsequential. However, accurate Δ near 0° and 180° can be helpful if measurements are not possible near the Brewster condition. For instance, in-situ ellipsometry is often limited to a fixed angle. This means that the angle cannot be adjusted until Δ in the optimized measurement region. For other samples, such as thin layers or index-matched layers on transparent substrates, Δ does not stay in an optimal region except for a very narrow range of angles.

Null ellipsometers measure ψ and Δ with high precision and accuracy over the entire range. However, the null configuration is not generally employed in spectroscopic systems because it is slower.

Phase modulation ellipsometers (PME) measure Δ accurately over the full 0-360° range, but suffer from ψ accuracy problems when ψ is near 0° or 45°, depending on the particular instrument configuration. Usuallly, this limitation can be overcome by the additional complexity of a dual channel detection system. PME ellipsometer systems use inherently chromatic optical elements as photoelastic modulators; the drive voltage must be accurately adjusted at each wavelength during a spectroscopic scan. Furthermore, due to the high modulation frequency of the existing diode array spectrometer technology, it is not possible to construct a PME system which could implement true parallel signal acquisition and readout with existing diode array spectrometer technology.

 Compensator ellipsometers measure both ψ and Δ accurately over their full ranges. Δ values near 0° or 180° correspond to linearly polarized light. Δ has its highest sensitivity when the light is circularly polarized (Δ=90°). A compensator placed in the light path converts the polarization state to circularly polarized (or an elliptical state, nearly circular) ensuring the measurement is always acquired in a region of highest sensitivity.

At the Woollam Company, two different compensator designs are used:
  1) RAE with adjustable retarder [VASE and VUV-VASE].
  2) Rotating compensator ellipsometer (RCE) [alpha-SE, M-2000 and IR-VASE].

Rotating Analyzer Ellipsometer (RAE) with Adjustable Retarder (AutoRetarder)
In theory, the RAE and RPE ‘Δ’ can be eliminated simply by adding a compensator to the beam path (either before or after the sample). However, this is more challenging than it sounds, for several reasons: 1) a perfectly ideal spectroscopic compensator element does not exist; 2) compensator elements which can be used spectroscopically (such as Fresnel Rhombs) are only pseudo-achromatic, can be bulky, and difficult to align; and 3) if the retardance of the compensator is not meticulously calibrated throughout the entire spectral range, or if the compensator is not properly aligned, the accuracy of the ellipsometric data will be degraded (instead of enhanced) by the introduction of the compensator element.

In spite of these challenges, our VASE and VUV-VASE do integrate a compensating element with a high accuracy RAE. In these systems, a computer-controlled MgF2 Berek waveplate is used to introduce retardance into the beam path accurately. Since the retarder is under computer control, it is possible to generate appropriate retardance values (0 - 90°) over a broad (150- 1700 nm) spectral range. Figures 2 and 3 show examples of variable angle and spectroscopic ellipsometric data which was acquired with such systems. In these examples, it is the accurate measurement of the ellipsometric parameter near 0° and 180° that enables a determination of the thickness and index of a dielectric film deposited on a polycarbonate substrate and finds the optical constants and surface roughness layer on a glass microscope slide.

Figure 2a (left) and 2b (right). Ellipsometric Ψ (not shown) and Δ (a) data acquired with a retarder-equipped RAE system on a polycarbonate lens with a thick (4.35mm) hard coating.  Accurate measurement of the period and amplitude of oscillations in both Ψ and Δ  (notice it is very close to zero)  enabled accurate determination of the film thickness and optical constants (b).

Rotating Compensator Ellipsometers (RCE)

Another approach to introduce a compensator into the ellipsometer beam path is to implement the Rotating Compensator Ellipsometer (RCE) configuration. There are many advantages to the RCE configuration, including: accurate measurement of the ellipsometric Ψ and Δ parameters over the complete measurement range (=0-90°, Δ=0-360°), no residual input or output polarization sensitivity (due to a fixed polarizer on input, and a fixed analyzer on the output), and the capability to directly measure depolarization effects. However, only recently have Spectroscopic RCE systems been constructed. The prior lack of spectroscopic RCE systems, in spite of the well known advantages to this configuration, was mainly due to the perceived difficulty of constructing a mechanically rotatable compensator element which behaves ideally (retardance »90°) over a wide spectral range. Recently, this challenge has been successfully addressed in a number of ways: 1) a special rhomb-like prism retarder has been used to implement a Fourier Transform Infrared (FTIR) RCE system [IR-VASE] 2) a realization that ellipsometric data can still be acquired (albeit with reduced measurement capability) even as the retardance of the compensator passes through 180° in part of the spectrum (which is inevitable when using standard waveplates for compensator elements, as their retardance exhibits a 1/λ dependence), and 3) development of multi-element, pseudo-achromatic compensators coupled with a rigorous calibration methodology. The M-2000 also employs a CCD array detector making simultaneous acquisition of spectroscopic ellipsometric data possible. In addition, by switching the light source and/or diode array detector, it is possible to cover a variety of spectral ranges, from the DUV (190nm) to the NIR (1700nm).

Figure 3a (left) and 3b (right). Accurate measurement of variable angle ellipsometric data near the Brewster angle on a glass microscope slide, using VASE with AutoRetarder. This very accurate measurement of would not be possible with a standard RAE or RPE system