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Written by: OpticNano CH

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Published: 18 May 2023

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Advancements in Refractive Index Refinement for Atomic and Molecular Physisorption on Thin Monolayers: Insights from Spectroscopic Ellipsometry Authors: Frederic Ferrieu (1), Christophe Vallee (2) Affiliations: 1. Opticnano Consulting, Origlio, Ticino, Switzerland 2. College of Nanotechnology, Science, and Engineering (CNSE), University at Albany, State University of New York, Albany, NY, United States Abstract: Spectroscopic Ellipsometry (SE) has advanced with integrated photonic no-moving-part designs, enhancing accuracy. Recent developments include IoT integration and cloud protocols (HTTP, MQTT), enabling automatic, remote control and analysis. SE serves as a versatile "Swiss knife" tool, optimized further with AI for full automation and deep learning. It is crucial for studying deposited or molecular beam epitaxy-grown monolayers, facing challenges in thickness and refractive index determination. It finds applications in biology and protein adsorption. SE competes with Surface Plasmon Resonance (SPR) in refractive index precision (~10^-3 to 10^-4). In situ SE acts as real-time process control, though very thin layer measurements often lack simultaneous thickness and refractive index correlation. This paper revisits P. Drude equations, approximating ellipsometry for ultra-thin layers with a first-order Taylor expansion. During growth or deposition involving atomic layers, SE excels. Unlike SPR, SE using discrete wavelengths offers broader applications with analytical indices law, enhanced by stable vacuum chamber configurations for precise refractive index and thickness measurements. Depolarization factor considerations give additional value, and SE's "no moving part" photonics provide superior capability over SPR, ideal for ALD, MBE, CVD, and PVD techniques. The instruments, while broad in spectroscopic range and angle techniques, face challenges detecting monolayers and ultra-thin layers. Ongoing advancements promise to address these limitations, reinforcing SE as a powerful tool for research and practical applications. This letter explores the future expanding capabilities and applications of SE, highlighting its pivotal role in advancing multi-technology tools. Introduction While easily detected, monolayers and thin layers below a few nanometers are challenging to analyze with Spectroscopic Ellipsometry (SE). Many examples exist from various fields, especially in biology, involving adsorbed monolayers. Initially described as a “transition layer” by P. Drude [1], this “top” monolayer can also be related to physisorption, porosimetry phenomena, and atomic layers deposited or grown by molecular beam epitaxy processing. However, even with a wide spectroscopic range and variable angle techniques, SE has not fully addressed this goal. The main issue for monolayers is determining two parameters simultaneously. As for porosimetry in biological applications, H. Arwin noted earlier: "it is often stated that it is impossible, or at least very hard, to resolve both tFt_F and nFn_F for a thin film in an ellipsometry experiment" [2-3]. Today, new photonic designs are implemented in SE instruments. The technique has been presented as a potential tool in parallel fields like immunology, particularly in testing the adsorption of proteins at solid surfaces [3-6]. This has become a crucial expectation in current immunology research as an antigen detection tool. Different methods, like surface plasmon resonance (SPR), measure optical thickness and refractive index variation [5][6], and significant efforts are made to increase their precision. The refractive index is expected to be known within almost 10^-3 to 10^-4 accuracy limits. Could ellipsometry be used as well? In fact, some developments based on the early Drude descriptions [1] have led research to reconsider the Fresnel equations. This approach should result in an unambiguous determination of both the refractive index (nFilmn_{Film}) and film thickness (tFilmt_{Film}) in the few nanometer range. Since several years, a recent publication has provided a promising answer [7], although a review and analysis of the theory are mandatory. Below 5 nanometers (nm), for most oxide layers grown from a substrate like silicon (Si), interlayer thickness determination generally involves considering a fixed value of the refractive index (r.i.), e.g., either 1.457 or 1.46 at 633nm, or less for native oxide (most native oxides are currently 1.0 to 2.5 nanometers thick). Early theories often described this as a “transition layer,” indicating that no discontinuities exist in nature. Classical models for native oxide typically use a parameterized Cauchy or Sellmeier law, as shown here: ξ(n0,λ)=n2(n0,λ)=1+n0λλ2−λ02\xi(n_0, \lambda) = n^2(n_0, \lambda) = 1 + \frac{n_0 \lambda}{\lambda^2 - \lambda_0^2} or an equivalent “absorption Urbach tail edge” formula associated with: n(\lambda) = n_{633nm} + n_{slope} \left(\frac{(1000⁄\lambda)^2 - (1000⁄633)^2}\right) with λ\lambda as the light wavelength, validity remains within a specified interval range (e.g., the Urbach absorption tail in the visible range). For example, we have n633nm=1.99n_{633nm} = 1.99 and nslope=0.03n_{slope} = 0.03 for zinc oxide (ZnO) [8]. These parameters are well-known from thicker sample works. In the 1990s, these models were refined, introducing a more or less densified material concept through the Effective Medium Approximation (EMA). The Lorentz-Lorenz equation for a mixture of materials, whose complex dielectric constants and volume fractions are ϵi\epsilon_i and fif_i, and the Bruggeman formula for computing ϵ\epsilon in terms of ϵi\epsilon_i and fif_i, is: 0=∑fi(ϵi−ϵϵi+θϵ)0 = \sum f_i \left(\frac{\epsilon_i - \epsilon}{\epsilon_i + \theta \epsilon}\right) where fif_i are the respective relative volume fractions for the host, the depolarizing electric field θ=2\theta = 2 with spherical voids, and the film optical index ϵf=nf2\epsilon_f = n_f^2. For calibrated samples, electron microscopy can then be used as references too. Methods Among SE candidates, “single shot SE” instruments are highly attractive. As a new generation of instruments, they provide real-time observation of phenomena within short time scales, less than 50 milliseconds (msec). Considering analytical models, a limited number of wavelengths is sufficient. Single shot SE instruments are thus highly promising. Currently, there are commercially available fast Wide Band Multi-Wavelength Ellipsometers, known as “no moving part” instruments [9]. However, this is not unique. In recent years, new systems are expected to be reported in literature. See the latest retrospective by R. A. Azzam [10]. These future designs can be referred to as “single shot ellipsometers” or “no moving parts” ellipsometers or polarimeters. They represent the near future in real-time dynamic processing. These instruments are also accurate, reaching the quantum noise “glass ceiling,” seen as the intrinsic source “photon noise limit” [11-a]. Only new quantum dots pulse light sources might overcome this limitation. Presently, SE instruments demonstrate the ability to control thin layer material growth, which is crucial for scaling down below 5 nm-thickness in the nano 3-D scale domain of IC technologies. Spectroscopic Ellipsometry (SE) must provide a fast and reliable real-time quality control tool. While spectroscopic measurements require the largest possible spectral range for new materials, this increases acquisition time. In industry, it is unnecessary to measure numerous wavelengths. Analytical models describing most dielectrics in the visible range are well-established since the 1990s and present databases available online [12]. The use of a “one single shot ellipsometer” is thus a promising approach. A multi-wavelength division-of-amplitude ellipsometer (DOA) is an old concept from the first papers by R. A. Azzam and G. Tompkins. Together with Ψ and Δ providing additional parameters, the degree of polarization d_pol is not yet well interpreted. The “no moving parts” aspect and the use of new LED sources prevent tedious alignments and limited lifetime source replacement procedures. Furthermore, LED sources produce less noise than the classical Xe (xenon) sources of the first instruments [10]. Each acquisition step displays in real-time the N, C, and S classical Stokes vector component values. A full description can be found in suppliers’ white papers and implicit patents [14]. With a limited number of four wavelengths, this concept enables fast acquisition without any moving optical elements in the beam, with an acquisition rate of roughly 50-100 ms, covering the visible range with wide LED bands at 463 nm, 524 nm, 595 nm, and 637 nm wavelengths. The number of wavelengths is not unique, as it has now increased to six in the latest instrument versions. These instruments also operate in very fast acquisition modes. The spectral range efficiently covers the visible range. This SE can be seen as a pioneering tool with up to six wavelengths available today. However, it is important to note that other solutions using new integrated photonic designs exist, and it is hoped that they will soon be available in commercial versions.
This paper delves into the significant advancements in Spectroscopic Ellipsometry (SE), particularly its application in refining the refractive index for atomic and molecular physisorption on thin monolayers. Here’s a brief summary:

Overview
The paper explores how Spectroscopic Ellipsometry (SE) has evolved with new integrated photonic designs, enhancing measurement accuracy and enabling IoT integration for remote control and analysis.

Key Points
Advances in SE: SE now incorporates photonic no-moving-part designs and AI for full automation, making it a versatile tool for real-time process control and analysis.

Challenges Addressed: It’s particularly effective for studying monolayers grown by molecular beam epitaxy, addressing the longstanding challenge of determining thickness and refractive index simultaneously.

Comparison with SPR: SE competes with Surface Plasmon Resonance (SPR) in terms of refractive index precision, offering broader applications through discrete wavelengths and stable vacuum chamber configurations.

Applications: SE is used across various fields, including biology for protein adsorption studies and industrial processes like ALD, MBE, CVD, and PVD.

Future Directions: Ongoing advancements aim to overcome current limitations in detecting ultra-thin layers, reinforcing SE’s role as a powerful research tool.

Implications
The paper emphasizes the future potential of SE as a comprehensive tool for multi-technology applications, thanks to its enhanced precision and real-time capabilities.