Optimization of the Saturable Absorption of 2D Bi2Te3 Layers

Nayla Jimenez de la Vega, Arjun Karimbana Kandy, Fabien Lemarchand, Andrea Campos, Martiane Cabié, Carine Perrin-Pellegrino, Julien Lumeau, Jean-Yves Natoli, Konstantinos Iliopoulos

► To cite this version:

Nayla Jimenez de la Vega, Arjun Karimbana Kandy, Fabien Lemarchand, Andrea Campos, Martiane Cabié, et al. Optimization of the Saturable Absorption of 2D Bi2Te3 Layers. Photonics, 2025, 12 (8), pp.822. 10.3390/photonics12080822. [hal-05215214](https://hal HAL Id: hal-05215214)

https://amu.hal.science/hal-05215214v1

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# Optimization of the Saturable Absorption of 2D Bi₂Te₃ Layers

Nayla Jimenez de la Vega <fnref n="1" />,*, Arjun Karimbana Kandy <fnref n="1" />,*, Fabien Lemarchand <fnref n="1" />, Andrea Campos <fnref n="2" />, Martiane Cabié <fnref n="2" />, Carine Perrin-Pellegrino <fnref n="3" />, Julien Lumeau <fnref n="1" />,*, Jean-Yves Natoli <fnref n="1" /> and Konstantinos Iliopoulos <fnref n="1" />,*,

## Abstract

The saturable absorption of 2D Bi₂Te₃ layers is studied by using the Z-scan technique employing infrared 400 fs laser pulses. Optimization of the nonlinearities has been carried out by measuring the third-order nonlinear susceptibilities as a function of the film thickness. A thorough optimization of the thin film annealing conditions has been performed and is presented. For each thickness, the annealing parameters have been separately investigated. Scanning electron microscopy, X-ray diffraction, and UV-Vis spectrophotometry studies have also been performed on the as-deposited and crystallized 2D layers.

**Keywords:** ultrafast optics; saturable absorption; 2D materials; topological insulators; thin films; chalcogenides; Z-scan

## 1. Introduction

Two-dimensional materials currently play a very important role in photonics [1–3]. In particular, a family of 2D materials including Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃ [4] exhibit excellent optical nonlinearities due to their topological insulator characteristic [5–7]. These materials are widely studied nowadays, especially regarding their saturable absorption efficiency, which can be employed for laser mode-locking [8–10]. The Bi₂Te₃ material has been found to exhibit high mode-locking performances while employed alone or combined with other materials such as graphene [11–13]. For this reason, the nonlinear absorption properties of Bi₂Te₃ are extensively investigated [14–19]. For the last few years, the focus of our research group is on the nonlinear optical (NLO) responses of such chalcogenide topological insulators that strongly depend on several parameters, such as the film thickness, the annealing conditions, and the pulse duration [6,20–23]. Therefore, to employ the chalcogenide topological insulators for applications, it is extremely important to optimize and adjust the NLO responses with respect to such physical parameters. In this study, our focus is on the thickness-dependent nonlinearities of 2D annealed Bi₂Te₃ films which have been deposited by means of the electron beam deposition technique. The annealing of the thin films allows for the acquisition of a well-defined crystalline structure, while adjusting the thickness in the case of topological insulators is of very high importance because it allows for the optimization of the saturable absorption emanating from the Pauli blocking that renders the material more transparent [6]. The nonlinear optical investigations were performed by using the popular Z-scan technique [24] employing an

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Received: 3 June 2025

Revised: 15 August 2025

Accepted: 15 August 2025

Published: 19 August 2025

**Citation:** Jimenez de la Vega, N.; Karimbana Kandy, A.; Lemarchand, F.; Campos, A.; Cabié, M.; Perrin-Pellegrino, C.; Lumeau, J.; Natoli, J.-Y.; Iliopoulos, K. Optimization of the Saturable Absorption of 2D Bi₂Te₃ Layers. *Photonics* **2025**, 12, 822. https://doi.org/10.3390/photonics12080822

**Copyright:** © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

<footnote n="1">¹ Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, AMUTech, Marseille, France; nayla.jimenez@desy.de (N.J.d.l.V.); fabien.lemarchand@fresnel.fr (F.L.); julien.lumeau@fresnel.fr (J.L.); jean-yves.natoli@fresnel.fr (J.-Y.N.)</footnote>

<footnote n="2">² Aix Marseille Univ, CNRS, Centrale Med, FSCM, Marseille, France; andrea.campos@univ-amu.fr (A.C.); martiane.cabie@univ-amu.fr (M.C.)</footnote>

<footnote n="3">³ Aix Marseille Univ, CNRS, Univ Toulon IM2NP UMR, 7334, AMUTech, Marseille, France; carine.perrin@univ-amu.fr</footnote>

<footnote>* Correspondence: konstantinos.iliopoulos@fresnel.fr</footnote>
infrared femtosecond fiber laser as the source. These studies allowed for the determination of the third-order nonlinear optical susceptibilities as a function of the film thickness. An optimization of the annealing conditions is necessary and has been performed by depositing several identical layers, annealing each one at different temperatures and finally studying their nonlinearities. The nonlinear optical studies have been coupled with additional investigations including scanning electron microscopy (SEM), X-ray diffraction (XRD) and UV-Vis spectrophotometry. These studies shed light on the crystalline structure and the optical properties of the 2D layers which strongly vary with the layer thickness. The results obtained during this study are compared with previously published results in the literature for the same family of topological insulators. We also provide a comparison with the nonlinear optical properties of the Bi₂Se₃ and Sb₂Te₃ topological insulators all investigated under identical experimental conditions, which will allow for an evaluation of their saturable absorption efficiencies.

## 2. Materials and Characterizations

### 2.1. Thin-Film Deposition and Annealing

High-quality Bi₂Te₃ thin films were deposited on 1 mm thick B270 glass substrates. The Bi₂Te₃ material was obtained from Codex company (Saint-Désir, France) in 2–10 mm pellets with a purity of 99.99%. The films were deposited using the e-beam evaporation deposition technique (EBD) in a Buhler SYRUSpro 710 machine (Alzenau, Germany), with a deposition rate of 0.5 nm/s. Initially, thicknesses ranging from 1 to 100 nm were deposited for the needs of this study. During the NLO investigations, it was found that thicknesses higher than 70 nm were exhibiting high losses and low nonlinearities, so they were not further investigated. Consequently, the layers that will be presented in this article will have a maximum thickness of 70 nm. The layer thickness was in all cases monitored during deposition by means of a quartz microbalance offering a precision of ±0.2 nm. To prevent oxidation of the Bi₂Te₃ layer after deposition, an additional 2 nm SiO₂ protective layer was deposited over the Bi₂Te₃ layers using the same technology/machine as the one used for the Bi₂Te₃ layer.

As has been previously demonstrated by our group, as well as by other groups working in the field of topological insulators, these materials can be crystallized by annealing at an appropriate temperature [6,25]. This crystallization is necessary in order to achieve significant optical nonlinearities. In the current study, it has been found that the optimal annealing temperature was 300 °C for all the studied thin films. It has to be mentioned that increasing the temperature higher than 350 °C resulted in slight degradation of the thin film layers. The annealing duration for all the thin films studied in this paper was one hour. This choice will be explained in the next paragraphs.

### 2.2. UV-Vis Spectrophotometry

The optical properties of the annealed films were analyzed over the spectral range of 320 nm to 2500 nm using a Perkin-Elmer Lambda 1050 spectrophotometer (Villebon-sur-Yvette, France). Representative curves for the investigated 2D layers are shown in Figure 1. Specifically, the spectral dependence of the transmittance (Figure 1a) and reflectance (Figure 1b) is presented for samples with thicknesses ranging from 10 to 70 nm, annealed at a temperature of 300 °C. A clear wavelength dependence is observed, with a minimum transmittance around 600 nm, regardless of the film thickness. Reflectance generally increases with thickness, which is typical for non-transparent materials.

The measured data were fitted using a global optimization algorithm, applying the Forouhi-Bloomer model combined with a Drude model [26], allowing the convergence to move towards an optimal solution. This enabled the determination of the refractive index
(n) and extinction coefficient (k). Figure 1c,d shows representative results: the refractive index increases from the visible range to the near-infrared region (around 1000 nm) before slightly decreasing, reaching a value of n ≈ 5.5 near 2500 nm. The extinction coefficient (k) peaks around 600 nm, followed by an exponential decay until 2500 nm, where k approaches zero, indicating that the annealed material becomes nearly transparent. The variation in n and k with film thickness for very thin layers is consistent with a potential porosity of thinner (e.g., 10 nm thick) films compared to thicker ones.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Transmittance (a) and reflectance (b) spectra in the range of 320 nm to 2500 nm for different sample thicknesses. Refractive index (c) and extinction coefficient (d) for different film thicknesses. (e) n and k values as a function of the annealing temperature for the same film thickness (10 nm).</figcaption></figure>

Additionally, a study of the n and k values was conducted for three different annealing temperatures (150 °C, 240 °C, and 300 °C). In this study, three separate samples with the same thickness of 10 nm were annealed for one hour at the aforementioned temperatures, followed by spectrophotometric measurements. The n and k values were then calculated as a function of the wavelength and are presented in Figure 1e. For annealing temperatures of 150 °C and 240 °C, no significant changes in the n and k values were observed compared to the as-deposited layers, indicating insufficient annealing. However, at higher annealing temperatures (notably 300 °C), the n and k values were significantly altered due to the increased crystal density in the 2D layers.

## 2.3. Structural Characterization of Bi₂Te₃ Thin Films

SEM studies were performed on many of the layers examined in this study using a field emission ZEISS Gemini 500 electron microscope (Oberkochen, Germany). SEM images were acquired with a four-quadrant backscatter electron detector at an acceleration voltage of 10 kV, which was the optimal value at which to observe the Bi₂Te₃ surface between the silica protection layer and the substrate.

In Figure 2, representative SEM images of different crystalline thin layers (10 nm, 50 nm, and 70 nm) are presented. All the thin films have been annealed under identical conditions. Moreover, the experimental parameters employed for the SEM studies are the same for all the samples in order to render the comparison between them feasible. It
can be seen that increasing the thickness of the sample results in a higher crystal grain
density. This was expected, as in thicker layers, there is more matter available, increasing
the probability of crystal formation compared to thinner films. Statistics performed on the
SEM images showed that the surface covered by Bi₂Te₃ was 1%, 5%, and 15% for the 10 nm,
50 nm, and 70 nm thin films, respectively. The average crystal size was 37 nm, 93 nm, and
92 nm for the same thin films.

<figure><img src="image_4.png" /><figcaption>**Figure 2.** SEM images of (a) 10 nm, (b) 50 nm, and (c) 70 nm Bi₂Te₃ layers.</figcaption></figure>

XRD studies have been additionally performed on several 2D layers. Representative
results are shown in Figure 3 for films having the same thicknesses as those presented in
Figure 2. As can be seen in Figure 3, in the case of the 10 nm XRD, the peaks are not visible.
This is attributed to the low quantity of matter, which results in a low signal-to-noise ratio
during the XRD studies. However, this film is crystallized, as shown in Figure 2a and
confirmed by the Z-scan measurements (see Section 3. Thicker layers present clear XRD
peaks, which have been identified using a rhombohedral structure from the PDF2 database
JCPDS 15-0863. These peaks have also been compared with previous results published in
the literature [27,28].

<figure><img src="image_5.png" /><figcaption>**Figure 3.** X-ray diffraction data obtained for three different 2D layers (10 nm, 50 nm, and 70 nm).</figcaption></figure>

**3. Nonlinear Optical Studies and Discussion**

The NLO parameters of the Bi₂Te₃ layers have been studied by the Z-scan technique, which allows for a simultaneous detection of the real and imaginary parts of the third-order nonlinear susceptibility (Reχ⁽³⁾ and Imχ⁽³⁾, respectively). The studies have been carried out by a passively mode-locked laser delivering 400 fs duration pulses at 1030 nm with a tunable repetition rate. A 100 Hz repetition rate has been chosen for this study in order to avoid measuring nonlinearities having thermal origins. These Z-scan studies are performed by moving the sample along the propagation axis of a focused laser beam while measuring the transmission with two different experimental arms, the “closed aperture” and “open
aperture" Z-scans, respectively. The beam waist at the focus has been measured to be 20 µm. The laser energies employed for this study were between 5 nJ and 30 nJ. The corresponding peak intensities have been calculated and are given with the experimental data below. In this study, we mainly focused on examining the imaginary part of $\chi^{(3)}$, since the real part has been found to be negligible for the 2D layers. The dominating characteristic of the saturable absorption over the nonlinear refraction has been previously demonstrated by our group for another topological insulator, the Sb₂Te₃ material [6]. For this reason, the "open aperture" Z-scan configuration is mainly employed for the nonlinear optical investigation of this category of materials [19,29]. Moreover, the optical nonlinearities of the as-deposited layers were negligible under the same experimental conditions. The contribution of the substrate has been separately tested and found to be negligible.

The analysis of the experimental data has been carried out by using the optical parameters (refraction and absorption coefficients) presented in the previous paragraphs. More specifically, the nonlinear absorption coefficient was determined by fitting the "open aperture" Z-scan data with the following equation:

$$T = \frac{1}{\sqrt{\pi} \left( \frac{\beta I_0 L_{\text{eff}}}{1+z^2/z_0^2} \right)} \int_{-\infty}^{\infty} \ln \left[ 1 + \frac{\beta I_0 L_{\text{eff}}}{1+z^2/z_0^2} \exp(-t^2) \right] dt \quad (1)$$

In this expression, $I_0$ is the on-axis irradiance at the focus, $L_{\text{eff}}$ is given as $L_{\text{eff}} = (1 - \exp(-\alpha_0 L))/\alpha_0$, and $\alpha_0$ is the linear absorption coefficient of the sample at 1030 nm. The $\text{Im}\chi^{(3)}$ is related to the nonlinear absorption coefficient by means of the following relationship:

$$\text{Im}\chi^{(3)}(\text{esu}) = \frac{10^{-7} c^2 n_0^2}{96\pi^2\omega} \beta (\text{cm W}^{-1}) \quad (2)$$

where c is the speed of light in cm s⁻¹, $n_0$ is the linear refractive index, and $\omega$ is the fundamental frequency in cycles per sec [6].

Thickness-dependent nonlinear optical studies have been performed in order to enhance as much as possible the saturable absorption behavior of the Bi₂Te₃ samples. These studies have been coupled with an investigation of the saturable absorption as a function of the annealing temperature and the annealing duration employed to crystallize the layers.

The first priority of this study was to determine the ideal annealing temperature for the layers. For this reason, "open aperture" Z-scans have been performed on different films having the same thickness but were annealed at different temperatures. Representative curves can be seen in Figure 4, both obtained at a peak intensity of 6 GW/cm² in the case of the 30 nm thin film. As can be seen in this figure, a transmission peak appears at the focal plane (Z = 0), which indicates the saturable absorption characteristic of the films when they are irradiated with intense laser irradiation. It is also obvious that the annealed film crystallized at 300 °C has a higher nonlinearity compared with the film annealed at 240 °C. Similar behaviors have been observed for the other thicknesses studied in this article. As mentioned in the previous paragraphs, the maximum annealing temperatures employed have been under 350 °C in order to avoid the slight degradation of the layers, which has been observed for annealing temperatures higher than this limit. A common point between all the layers was that an annealing temperature of about 300 °C was enough to obtain the fewest defect states and consequently the best crystallization, resulting in the highest nonlinearities achieved during this study. For this reason, this temperature has been chosen for the annealing of all the 2D layer studies. A study of the nonlinear optical parameters as a function of the annealing duration has also been performed. It has been found that one-hour annealing is sufficient to obtain the maximum nonlinear optical values. Studies
performed with longer annealing durations (i.e., 3 h and 20 h annealing) have shown that additional annealing time did not result in further enhancement of the NLO properties.

<figure><img src="image_6.png" /><figcaption>**Figure 4.** "Open aperture" Z-scans of two films of the same thickness which have been annealed at different temperatures.</figcaption></figure>

After establishing the ideal annealing temperature and duration, several annealed 2D Bi₂Te₃ layers having different thicknesses ranging from 5 nm to 70 nm have been studied by the Z-scan setup. Thicker layers have been avoided as they exhibited high optical losses and negligible optical nonlinearities, at least under the same experimental conditions employed for the other thin films. Figure 5a represents "open aperture" Z-scan curves for four different films having different thicknesses. All the curves have been recorded using a 2 GW/cm² peak intensity. Two different facts can be noted in Figure 5a. Firstly, a saturable absorption character is present for all layers. Additionally, a small modification of the thicknesses can result in a significant change in the nonlinear optical responses. Consequently, the film thickness is the most important parameter that has to be adjusted in order to enhance the optical nonlinearities of this material for a given laser excitation wavelength. This fact has been previously reported by our group for other topological insulators [6,22]. In this study, we have maintained a precision in thickness of 1 ± 0.2 nm between 8 nm and 12 nm thickness, since the NLO parameters were found to be at their maximum there (Figure 5b). This gave the possibility to precisely pinpoint the thickness with maximum saturable absorption efficiency.

<figure><img src="image_7.png" /><figcaption>**Figure 5.** (a) "Open aperture" Z-scans of films having the same thicknesses, all annealed under the same conditions. (b) Nonlinear absorption coefficient and (c) imaginary part of the third-order nonlinear optical susceptibility as a function of the thickness of the 2D layers.</figcaption></figure>

From the many different curves obtained for every sample, the nonlinear absorption coefficient (β) and the imaginary part of the third-order nonlinear susceptibility
(Imχ⁽³⁾) have been plotted as a function of the film thickness, and they are presented in Figures 5b and 5c, respectively. The figure of merit, defined as the Imχ⁽³⁾ divided by the linear absorption coefficient at 1030 nm, is also provided in Figure 5c. In all cases, the maximum nonlinear optical response is obtained for the 11 nm thick sample. More specifically, the highest values of β and Imχ⁽³⁾ have been measured to be −7.9 × 10⁻⁷ mW⁻¹ and −16.1 × 10⁻⁸ esu, respectively. For lower and higher thicknesses, the nonlinear optical responses are gradually decreasing.

This significant influence of the thickness on the nonlinear optical properties can be expected for materials exhibiting topological insulator characteristics. In such nano-layers, the surface state wave functions from the two surfaces of the thin film overlap [30]. This has a strong impact on the electronic properties of the layers, which are directly related to the optical and nonlinear optical properties. This can be better understood if one takes into account the fact that the saturable absorption of these systems is emanating from bleaching of the material due to the Pauli blocking, which arises when all energy states of the material are occupied [31]. This bleaching results in a decrease in the absorption and increase in the transmission, giving rise to saturable absorption. Consequently, a slight change in the thickness is able to significantly modify the properties of the material. The strong link between the electronic properties of topological insulators and their thicknesses has been previously demonstrated [32].

These underlying mechanisms can explain the experimental finding that the thickest films studied (50 nm and 70 nm) having the highest density of crystals result in the lowest nonlinearities. The highest density of crystals results at the same time in thicker crystals, which in turn leads to a gradual loss of the overlapping of the surface state wave functions. Consequently, the 2D characteristic of the nanolayers is gradually lost and the saturable absorption performance is significantly decreased for thick films.

Very few reports exist in the literature concerning the optical nonlinearities of the Bi₂Te₃ material. Recently, Kim et al. [5] investigated the nonlinear optical properties of Bi₂Te₃ nanoparticles in the spectral range of 400 nm–1000 nm. The nonlinear absorption coefficient was found therein for an excitation wavelength at 1000 nm, which is the closest wavelength with respect to the one used in this study, which was −1.5 × 10⁻⁵ cmW⁻¹. This value is about five times lower with respect to the maximum value reported in this study, obtained after the optimization of the layer thickness.

In another study [15], Bi₂Te₃ thin films were investigated with a pump probe experiment in order to find the dependence of multiple relaxation processes on the thickness of the films. A significant difference in the relaxation time was observed while changing the film thickness from 10 to 25 nm. This difference between the ultrafast dynamics of layers having different thicknesses can give rise to significant modification of the third-order nonlinearities. Other articles focused on studying the mode-locking efficiency of Bi₂Te₃ layers, either undoped, doped, or combined with different materials [11,12,14].

Our group has previously performed thickness-dependent NLO studies on two other topological insulators, Sb₂Te₃ and Bi₂Se₃, which are also very promising candidates for mode-locking applications, employing identical experimental conditions [6,22]. Our studies on the Sb₂Te₃ material have shown that a 9 nm layer thickness gave rise to a nonlinear absorption coefficient value of −15.30 × 10⁻⁷ mW⁻¹ [6], which was the highest nonlinearity measured during our study. This value is higher by about a factor of two compared with the values reported in the current study. Another thickness-dependent study carried out by our group at 1030 nm [22] on the Bi₂Se₃ material revealed that the Bi₂Se₃ layers having 30 nm thicknesses held the highest β value, equal to −2.12 × 10⁻⁷ mW⁻¹, which is about four times lower than the values reported herein. These comparisons are crucial as they allow for a direct comparison between the optical nonlinearities of three very
popular topological insulators, which have been studied with the same femtosecond laser system and experimental setup. Indeed, it is well known that the NLO parameters of photonic materials depend not only on the material properties but also on the laser excitation parameters and the employed setups. Comparing results obtained for non-identical experimental parameters is often ambiguous. In this regard, our studies allow for a comparison of the third-order optical nonlinearities. However, they cannot provide all the information needed for a comparative evaluation of the samples in terms of their mode-locking efficiencies. This requires an investigation of the influence of the thickness of the 2D layers on other parameters such as the saturation intensity, modulation depth, and laser damage threshold. These studies will be performed by our group in the near future.

## 4. Conclusions

The thickness-dependent nonlinearities of 2D Bi₂Te₃ layers have been studied in the ultrafast regime employing 1030 nm irradiation. Our studies revealed that a fine adjustment of the 2D layer thickness is of high importance for the enhancement of the third-order nonlinear optical response. The highest nonlinear absorption coefficients have been observed for the 11 nm thin film and the measured values were $-7.9 \times 10^{-7}$ mW⁻¹. Our findings have been compared with previously published results concerning other topological insulators, which are important candidates in several fields of photonics.

**Author Contributions:** Conceptualization, K.I.; methodology, K.I., J.-Y.N. and J.L.; validation, K.I., J.-Y.N. and J.L.; formal analysis, N.J.d.I.V. and A.K.K.; investigation, N.J.d.I.V., A.K.K., F.L., A.C., M.C., C.P.-P. and K.I.; data curation, A.K.K. and K.I.; writing—original draft preparation, N.J.d.I.V., A.K.K., F.L., A.C., M.C., C.P.-P., J.L., J.-Y.N. and K.I.; writing—review and editing, K.I.; supervision, K.I., J.-Y.N. and J.L.; project administration, K.I.; funding acquisition, K.I. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the French National Research Agency (ANR-19-CE09-0002-01). This study received support from the French government under the France 2030 investment plan as part of the Initiative d'Excellence d'Aix-Marseille Université—A*MIDEX. (AMX-20-IET-015).

**Data Availability Statement:** Data are contained within the article.

**Conflicts of Interest:** The authors declare no conflicts of interest.

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