### High Sensitivity

The most well known advantage of ellipsometry is its extreme sensitivity to very thin films. This advantage derives from the ellipsometric Δ (Delta) parameter, which is a phase quantity. By measuring the phase between p- and s-polarized reflected beams, ellipsometry provides precise determination of film thickness, down to sub-monolayer film thicknesses, even though the wavelength of the measuring beam (≈ 500 nm) is very long compared to the film thickness (which can be < 0.1 nm). With the FS‑1 Banded Wavelength Ellipsometer, thickness precisions of better than 0.001 nm can be achieved on a wide range of samples, ranging in thickness from 0 to 1000 nm.

### Increased Information Content

When compared to a simple sample reflectivity measurement (which just measures the intensity of light reflected from a sample), the ellipsometric measurement (which utilizes polarized light) is certainly more complex. However, the complexities of the ellipsometric measurement can be offset by the additional information contained in the ellipsometric parameters: 2 ellipsometric values are measured at each wavelength (and the degree of polarization **P** can provide a 3rd value), while reflectivity only measures 1 value.

#### Direct Determination of Substrate Optical Constants

An example which directly utilizes the information content in the 2 ellipsometric parameters **Ψ** (Psi) and** Δ** (Delta) is the calculation of the pseudo-dielectric function **<****ε>** of a substrate. The dielectric function **ε **is one way of characterizing the optical properties of a material, and it is a complex value, with a real part **ε _{1}**, and an imaginary part

**ε**. The dielectric function is also the square of the complex index of refraction

_{2}**ñ**(the real part of

**ñ**is the index of refraction

**n**, and the imaginary part of

**ñ**is the extinction coefficient

**k**). Assuming the measured sample is a substrate with no overlayers or roughness, the pseudo-dielectric function for the substrate

**<**

**ε>**can be calculated from the ellipsometrically measured

**Ψ**(Psi) and

**Δ**(Delta) values, using the formula below (the parameter θ is the angle of incidence of the measurement beam). Since the preceding assumptions are not always rigorously satisfied, the prefix of “pseudo-” is applied, as denoted by the <brackets>.

Obtaining the real and imaginary parts of the dielectric function of a substrate (or equivalently, **n** and **k** for the substrate) from reflectivity data would require measurements over a wide spectral range, combined with data analysis with an appropriate dispersion model. With ellipsometric data, the dielectric function (or equivalently, **n** and **k**) for a substrate can be directly calculated.

#### Determination of Film Thickness and Index of Refraction

Another example which demonstrates the information content advantage of ellipsometry is the determination of the thickness and index of refraction of a transparent thin film on a substrate. Since ellipsometry measures 2 parameters, **Ψ** (Psi) and** Δ** (Delta), it is possible to directly determine 2 sample related parameters, which in this case are the thickness of the film ** d**, and index of refraction

**n**of the film. This is done by numerically inverting the thin film interference equation shown below. In this equation, the reflection coefficients

_{1}**at each interface and the film phase factor**

*r*_{p,s}**β**are calculated using the index of refraction for each media, the angle of incidence θ, the Fresnel equations, and Snell’s law (the FS‑1 software handles all these calculations internally).

While there are some limitations in this analysis for very thin films less than 10 nm in thickness (due to correlation between the film thickness and index), ellipsometry is superior to reflectometry when determining the index of refraction of films less than 25 nm in thickness. Another limitation arises if the film thickness determination is done with a traditional single wavelength ellipsometer: multiple thickness values can satisfy the thin film equation, leading to a thickness “periodicity” problem. With the FS‑1 Banded Wavelength Ellipsometer, the thickness periodicity problem is eliminated by the multiple measurement wavelengths.

### Intensity Independent

As an optical technique, ellipsometry is fast and non-destructive, and can be performed in a wide range of environments: in the lab, on a factory floor, in a vacuum chamber, or even with a liquid ambient. A unique advantage of ellipsometry is that the measured parameters are *not* dependent on the intensity of the measurement beam. This advantage comes from the definition of the ellipsometric parameters by a ratio. The beam *intensity* *independent* property of the ellipsometric measurement can be very beneficial in situations where maintaining constant beam intensity would be challenging, such as *in situ *measurements, or long term measurements requiring high stability. Ellipsometry is also less susceptible to many types of sample non-idealities, such as scratches, dust, defects, and macroscopic roughness. These types of sample non-idealities scatter the measurement beam, such that light scattered from these non-idealities does not enter the ellipsometer’s Polarization State Detector (which collects only the ideal, specularly reflected light from the sample).