Thickness Identification of 2D Materials by Optical Imaging

 

Physik  |  Technik

 

Elias Baumann, 2006 | Zürich, ZH

 

In recent years, 2D materials have been studied extensively for their exceptional properties and diverse applications. Since their thickness strongly influences their characteristics, it must be determined prior to any experiment. This paper examines the approach of thickness identification by optical imaging on behalf of a theoretical model and experimental data, and tests its reliability for application in research, for both the insulating material FePS3 and the conductive metallic NbSe2.

The results confirm that the theoretical model accurately describes the contrast and colour of an insulator on a SiO2/Si substrate up to 200nm. This correlation validates the model’s underlying assumptions. As expected, the experimental results of the conductive material diverge significantly from the theoretical model, for which insulation is assumed.

The experimental results are used to develop an application, which is capable to yield, from a list of RGB values, the thicknesses, to which they are likely to correspond. The application is evaluated and its reliability is demonstrated. This report therefore confirms the high practicality of thickness identification by optical imaging, providing a fast, non-invasive, large-scale and cheap method to determine the thickness of 2D materials.

Introduction

2D Materials are crystals with a thickness of a few molecular layers. Before conducting experiments, their thickness must be determined, as it strongly influences their properties. The conventional method relies on an Atomic Force Microscope (AFM), which is slow and expensive. This work explores an alternative colour-based approach: can images of a standard optical microscope be used to identify the thickness of 2D Materials?

Methods

Initially, the 2D flakes were created by exfoliation and deposited on freshly cleaned substrate chips. Then, optical microscope and AFM images of the flakes were taken. Finally, the acquired data were processed using Gwyddion and Python to extract and process the flake thicknesses and the corresponding RGB colours.

Results

The results depict a sinusoidal dependence of the colour on thickness for flakes of the insulating material up to 200nm, with r^2 values up to 0.91. For the red colour component, maxima were found at 3.0nm and 123.3nm, with minima at 63.2nm and 183.4nm, while the green and blue components have slightly smaller periodic intervals. The colours are changing significantly, enabling thickness differentiation with a precision of 0.5-2.5nm. In contrast, for the conducting flakes, the sinusoidal dependence is dampened 5-10 times faster, which makes color-based thickness identification unreliable above 50nm.

Additionally, a theoretical model for the reflectivity of 2D Materials on SiO2/Si substrate as a function of the wavelength, the materials’ thickness and its refractive index, was derived from Maxwell’s equations.

Discussion

For thin flakes, the theoretical model describes the contrast and colour of the insulating FePS3 accurately. From 125nm onwards, the divergence between the results becomes significant. In depth analysis of the contrast showed that the theoretical model has a slightly shorter period (contrast per thickness) than the experimental data – likely due to fitting errors, which might have been mitigated through more extensive preliminary experiments or an additional dataset.

The results of the metallic NbSe2 deviate from the theoretical model already at thicknesses above 50nm. This was expected, and it shows that the assumption of insulation, on which the theoretical model is based, is indispensable.

For ultrathin thicknesses (<10nm), both theoretical and experimental results match previous findings from other research groups. For thicker flakes, no data were found in literature.

Conclusions

To answer the research question, a theoretical model for the contrast and colour of flakes on substrate was derived from Maxwell’s equations and experimental data were collected and evaluated. The results depict a sinusoidal dependence of colour on the thickness of the flake and confirm that the theoretical models underlying assumptions were well chosen.

Moreover, an application was written to enable the integration of thickness identification by optical imaging in the production workflow of researchers, allowing a precision of 0.5-2.5nm. I am proud, that the application is now used in the Department of Material Science at ETH, where it speeds up thickness determination of FePS3 flakes, reduces the lab costs by using the AFM only for calibration, and may eventually be expanded to include other insulating materials.

 

 

Würdigung durch den Experten

Dr. Dimitri Vanhecke

Elias Baumann hat eine Methode zur Dickenmessung von 2D-Materialien entwickelt. Das in Eigenarbeit entwickelte Modell basiert auf eigenen experimentellen Daten und der theoretischen Wechselwirkung von elektrischen und magnetischen Feldern. Bemerkenswert ist insbesondere die Möglichkeit, die Dicke von NbSe2 aus einem Farbbild bis auf ein paar Nanometern genau abzuleiten. Seine Methode ist schnell, kostengünstig und nicht-invasiv und hat bereits Anwendung in der Forschung gefunden. Sie stellt einen signifikanten Fortschritt in der Materialanalyse von 2D-Materialien dar.

Prädikat:

hervorragend

Sonderpreis «Taiwan International Science Fair (TISF)» gestiftet von den Odd Fellows, Helvetia Loge Nr. 1

 

 

 

Realgymnasium Rämibühl, Zürich
Lehrerin: Yee Ling Willems-Ong