Determining Optical Material Parameters With Motion in Structured Illumination

A set of power measurements as a function of controlled nanopositioner movement of a planar film arrangement in a standing wave field is presented as a means to obtain the thicknesses and the dielectric constants to a precision dictated by noise in an exciting laser beam, and the positioning and detector process, all of which can be refined with averaging.

September 1, 2023

Purdue University, West Lafayette, IN

Figure 1. (a) The simulated measurement arrangement has a plane wave incident from the top, with the free-space wavelength as λ=1.5μm. Two dielectric slabs act as partially reflecting mirrors and form a low-Q cavity with a length of 2.7λ (inner face-to-face distance). (b) An illustration of the magnitude of the background electric field in which the film and substrate are placed and moved (not drawn to scale).

The broad need for determining the optical properties of thin films in a multitude of applications is usually served by ellipsometry. Practical application of ellipsometry generally requires prior constraints, typically in the form of a frequency-dependent model. To provide for a suitable solution of the inverse problem, where film parameters are determined from a set of optical measurements. We present motion in structured illumination as a means to obtain additional information and hence avoid the need for a material response model. Using this approach, inversion for multiple parameters at each wavelength becomes possible, and in a mutual information sense, this is achieved by taking intensity measurements at a known set of displacements in a cavity.

Ellipsometry measures the amplitude ratio and the phase difference between polarized light reflected from the surface of a film and determines the refractive index or thickness by fitting the experimental data to an optical model that represents an approximated sample structure. Generally, a model of the frequency-dependent dielectric constant is used for successful parameter extraction, in order to constrain the inversion. For example, such a model may represent a Lorentzian resonance or impose a Drude model. While simplifying the extraction, this imposes an approximate but not necessarily the correct description. Otherwise, a careful choice of the initial variables is needed in ellipsometry.

There is a long history of using interferometers to determine the relative position of a surface, and to determine the refractive index of gases, and in fuel cells, including water content changes in membrane fuel cells. White-light interferometry has been used to retrieve the thickness of thin films, under the assumption that the frequency-dependent dielectric constant is known.

We present the concept of an interferometer arrangement where intensity measurements as a function of controlled position of the sample, as could be achieved with a piezoelectric positioner, allow extraction of both the thickness and dielectric constant based on transmission measurements. The simple intensity-based measurement required avoids the alignment and multiple polarization data typical of ellipsometry. Here, the film is moved in a structured background field in steps, and the total power due to the background and scattered fields is measured. The method relies on cost-function minimization using a forward model to compare the measurements to a set of forward model data corresponding to different sample structures rather than repeated corrections to the theoretical dielectric function and initial values in order to fit the experimental data.

An illustration of the arrangement used to obtain simulated data is shown in Fig. 1(a). The 1D object to be characterized is located and scanned within a cavity having a low quality (Q) factor that provides the structured field, as illustrated in Fig. 1(b). Two dielectric slabs forming the partially reflective mirrors have a refractive index of 1.5 (simulating crown glass) and a thickness of λ/5/5, with λ being the free-space wavelength, 1.5μ1.5m. The mirrors are separated by 2.7λ (inner face-to-face distance). Note that the length of the cavity was not tuned to resonance. An object of total thickness λ/5/5 is comprised of two layers of different materials: a slab with a known refractive index of 1.5 and a thin film on top with a thickness L and refractive index n. Both L and n are to be determined simultaneously at the single frequency of the measurement, at a free-space wavelength of λ.

This work was performed by Dergan Lin, Vivek Raghuram, and Kevin J. Webb for the National Science Foundation and the Air Force Office of Scientific Research. For more information, download the Technical Support Package (free white paper) below. ADT-09233