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Abstract
There has been a renewed and strong interest in phase change materials (PCMs) in many fields beyond traditional memories, due to their optical and electrical tunability aspect. Given their unique characteristic of changing phase and refractive index on-demand from amorphous to crystalline and vice versa via optical or electrical switching, they can be employed in many applications ranging from optical filters to rewritable metasurfaces. Patterning PCMs into self-assembled nanorod structures much smaller than the wavelength in diameter could potentially lead to interesting applications such as controlled chirality, birefringence and anisotropy. Additionally, such nanorod geometries may potentially lead to robust switching over multiple cycles for films of thicknesses well beyond those that are switchable in bulk thin film geometries. In this work, we grow and characterize self-assembled nanorods of antimony selenide PCM, and we characterize the nanostrucutres using ellipsometry and X-ray diffraction. We additionally provide an effective medium approximation (EMA) fit that greatly simplifies future macroscopic devices based on the underlying PCM nanorod geometry.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The use of phase change materials (PCMs) for tuning optical devices has been gathering steam in the last few years, mainly due to the large index contrast upon phase transition that could be accomplished electrically, thermally or optically [1–3]. Due to the large index contrast, actively tunable devices could be readily achieved in an incredibly small footprint on the order of a single wavelength [4–8]. Generally, these devices have been dedicated to intensity or amplitude modulation of light due to two major drawbacks of PCMs [9,10]: 1) Losses are generally non-negligible for traditional PCMs such as germanium antimony telluride and its derivatives (GeTe, Ge$_2$Sb$_2$Se$_4$Te$_1$) [11,12], and 2) switching large volumes of PCMs is tricky due to thermal constraints [5,13]. One key aspect is that phase modulation devices generally require up to $2\pi$ phase contrast upon actuation [1]:
where $\Delta n$ is the index contrast between the two states, $\lambda$ is the operating wavelength, and $L_{eff}$ is the effective length that takes into account any resonant or slow-light effects. This can be achieved through switching the PCM between its two states. Hence, for a PCM device capable of full $2\pi$ phase modulation, we require an index contrast on the order of $\Delta n = 1$, an effective height on the order of $L_{eff} = \lambda$, and minimal absorption in both states ($k \approx 0$, where $k$ is the extinction coefficient). One promising path to this problem recently appeared through the emerging field of wide bandgap PCMs, such as Antimony Selenide (Sb$_2$Se$_3$) or Antimony Sulfide (Sb$_2$S$_3$), whereby losses near the telecom band could be reduced to near 0 in both states [14]. As shown in most literature, however, the thicknesses that could be reliably switched limit phase accumulation to a fraction of $\pi$, which again, has led to most of the work relying on highly resonant structures with narrow functionality [15].In recent work, we showed that self-assembled chiral nanorods in Germanium Antimony Telluride Ge$_2$Sb$_2$Te$_5$ (GST) offer a path towards fully cyclable 250 nm thick films due to improved thermal dissipation and other geometrical considerations [16]. Inspired by those earlier results, our goal here is two-pronged: First, to show that the same fabrication techniques can be used to create a thick, large-scale film of Sb$_2$Se$_3$ nanorods with transparency from the mid-IR all the way to the near-visible. Second, to show through both metrology and modeling that these nanostructures can form the foundation for future devices based on macroscopic (effective medium) behavior without necessitating first-principles calculations for each design. While showing multiple cycling of the nanostructures is beyond the scope of this work, we believe the behavior should be consistent with results for GST-based nanorods in which optical switching over thousands of cycles did not degrade the optical performance [16].
2. Nanostructure growth
To deposit helical nanorod structures, critical mask design and lithography techniques are not necessary. Instead, a simple oblique angle deposition (OAD) technique with sample rotation suffices. The oblique angle is used to enable the shadowing effect on adatoms, thereby causing the formation of the nanorod structures [17,18]. As for the helical structures, a continuous rotation of the sample is necessary [19,20]. The rotation speed can be controlled in order to define the pitch and diameter of the rods while the oblique angle defines the structure of the rods to either be more compact or sparsed. This technique is more commonly referred to as the glancing angle deposition (GLAD) technique. The fabrication process is reliable and repeatable. By fixing the incident particle flux angle, rotation speed, and deposition rate the nanorod pitch and diameter remain the same.
In this work, GLAD is performed using the electron beam (e-beam) evaporation deposition method. Glass cover slips and silicon (Si) substrates are mounted on the motor-controlled sample mount that rotates continuously at a rate $\frac {d\phi }{dt}$. Additionally, an oblique angle, measured from the surface normal to the incident evaporated Sb$_2$Se$_3$ particle flux, defined by $\alpha$, is chosen to achieve the desired nanostructure geometry. A schematic of the mounting configuration in the e-beam evaporation tool is shown in Fig. 1(a). The deposition parameters were set to the following: 7.5 kV e-beam voltage, 2mA e-beam current, 15 inch crucible to substrate distance, 85$^{\circ }$ oblique angle, and 1.6 rpm angular rotation. The helical nanostructures fabricated is depicted in Fig. 1(b) with a cross-sectional and top view scanning electron microscopy (SEM) image shown in Fig. 1(c). The cross-sectional view (left) captures the helical features achieved while the top view (right) captures a fill factor in the range of 60-70%. Additionally, Fig. 2 shows the three samples fabricated with SbSe thicknesses of 400 nm, 500 nm, and 600 nm before employing a protective capping layer of indium tin oxide (ITO).
Fig. 1. (a) A schematic depicting the GLAD technique showing that the evaporated particle flux are incident on the substrate at an angle $\alpha$ while the sample rotates at an angle $\phi$. (b) Schematic of the helical structures that can be achieved as a result of GLAD. (c) Cross-sectional view and top view SEM images of the fabricated nanostructures.
3. Antimony selenide nanorod material properties
The molecular structure between the phase states of chalcogenide PCMs induces different optical properties which can be of use in many tunable applications. Although GST has been the most commonly used PCM due to its high refractive index modulation ($\Delta$n $\approx$ 2.5 at $\lambda$ = 1550 nm) between the amorphous and crystalline phases, a major drawback of GST is the absorption losses caused when switching the material to its crystalline phase ($\Delta$k $\approx$ 1 at $\lambda$ = 1550 nm) making phase modulation independent of amplitude modulation unachievable [21]. Therefore, Sb$_2$S$_3$ and Sb$_2$Se$_3$, have been studied as new low-loss PCM options [22]. In this work, Sb$_2$Se$_3$ was the material of choice as it has been shown to be more durable than Sb$_2$S$_3$ for laser-induced crystallization [14,23] and outperforms GST optically [24].
The effective optical constants for all three samples in both the amorphous and crystalline phase were obtained through ellipsometry techniques. By performing these very sensitive measurements using polarized light, thin films, substrates, and nanostructures are characterized on the order of angstroms to microns in single or multi-layer objects. In this work, ellipsometer measurements were taken at several angles (55°, 60°, 65°, 70°, and 75°) using the variable angle spectroscopic ellipsometry technique.
To fit the ellipsometric measurement to the fabricated sample, a silicon substrate and a bulk film of Sb$_2$Se$_3$ representing the helical layer are loaded from the standard library. The bulk film is then converted into an Effective Medium Approximation (EMA) layer which is converted into an anisotropic Bruggeman EMA [25,26]. The EMA layer is used to account for the material voids given that the helical structure fabricated during the deposition process is about 30-40% void and 60-70% Sb$_2$Se$_3$. The structure is broken into three segments. The "nucleation layer", "bulk layer", and "surface roughness". The Bruggeman EMA models the surface roughness by setting the grade type of the "void" material in your "bulk layer" to parametric. The fits are then achieved by splitting the layers into multiple slices to account for the layers previously stated allowing for a more precise fitting throughout the film layer.
Lastly, to improve the fit results, the Sb$_2$Se$_3$ layer is converted into a basis-spline (b-spline) in order to ensure compliance with the Kramers-Kronig relations [27]. Kramers-Kronig allows for the real part to be calculated after oscillators are used to describe the imaginary part of the refractive index. This makes for more physical validity of the model’s optical constants. The EMA fits of the amorphous and crystalline Sb$_2$Se$_3$ for 400-600 nm helical nanostructures is shown in Fig. 3 below. It is clear from the results that the fits for the 500 and 600 nm nanorod samples are in closer agreement than those for the 400 nm-tall structures (potentially due to fabrication differences). A conclusion from this observation is that the EMA fits for films of thickness 500+ nm can be used as a basis for thick film calculations.
Fig. 3. Ellipsometry optical constant fits for (a) 400 nm, (b) 500 nm, and (c) 600 nm helical Sb$_2$Se$_3$.
Figure 4(a) shows as-deposited amorphous Sb$_2$Se$_3$ (aSb$_2$Se$_3$) while Fig. 4(b) shows crystalline Sb$_2$Se$_3$ (cSb$_2$Se$_3$) which was achieved after annealing the sample at 200$^{\circ }$C (The slight deformation is a feature of using a hotplate vs. high speed switching and is consistent with earlier observations [16]). The thickness decreased by 2% as well which is typical for crystallized PCMs [12,28]. In order to assure that the different thickness samples are materially and stoichiometrically consistent, crystallographic structure analysis of the film was performed for all 3 thicknesses considered (400 nm, 500 nm, and 600 nm) through x-ray diffraction (XRD) measurements using the Cu K-$\alpha$ 1 8.04 keV x-ray energy (Fig. 5). The notable peak at 33.038$^{\circ }$ is the (112) Si peak coming from the Si substrate used in these measurements. With the strong peak at 33$^{\circ }$ disregarded, however, the results match expectations where aSb$_2$Se$_3$ only exhibits broad features while cSb$_2$Se$_3$ exhibits narrow peaks. The consistency among the three samples confirmed that all three undergo the same crystallographic structural change upon crystallization.
4. Finite-difference time-domain model
To confirm that the EMA fits are a good approximation of the effective index of the actual sample, a finite-difference time-domain (FDTD) simulation was performed as a first-principles simulation of the nanorod geometry. In this work, the helical nanostructures grown have voids causing the effective index of the film to reduce, in addition to potential anisotropy and scattering effects, which cause the EMA fit to deviate from a simple "fill factor" approximation. On the other hand, FDTD simulations fail to capture inhomogeneities as well as effects below the smallest scale achievable in a reasonable run time. However, we anticipate that first-principle FDTD simulations should reasonably match the EMA model, which would allow us in the future to design macroscopic structures based on the EMA approximation rather than resorting to FDTD or other models that are far more complicated and time-consuming.
Therefore, the optical transmission through the helical nanostructures were modelled using FDTD and the helical structure’s geometrical parameters were based on scanning electron microscopy. As an example, the 500 nm Sb$_2$Se$_3$ values for rod diameter, pitch, and film thickness were 22 nm, 82 nm, and 500 nm, respectively. These values were averaged from several measurements of these parameters performed on the sample using the SEM. The resulting transmission for the wavelengths $\lambda$ = 200-1200 nm is shown in Fig. 6 (red). Additionally, using the extracted EMA values for the index of refraction of the film, the transfer matrix method (TMM) was used to model the transmission through the nanostructures and compared against the FDTD simulations (Fig. 6(b) blue). As expected, these two plots closely matched each other with some amplitude mismatches that can be attributed to the non-periodicity and inhomogeneities that are not captured in the FDTD model, as well as potential polarization effects caused by the chiral nature of the nanostructures which may not have been fully captured during the index fitting process.
Fig. 6. Transmittance through the 500 nm helical nanostructures simulated using FDTD (blue) and TMM (red) methods for both aSb$_2$Se$_3$ (solid lines) and cSb$_2$Se$_3$ (dashed lines).
5. Optical switching and transmission measurements
The helical nanostructures were in the amorphous state in the as-deposited form. Therefore, a thermal stimulus above 200$^{\circ }$C is needed in order to switch the structures into the crystalline phase [21]. To do so, an in-house optical switching setup was used (Fig. 7).
A 532 nm laser passing through an acousto-optic modulator (AOM) was focused on the sample using a 100X 1.3 NA oil immersion objective. By running a LabVIEW program, the voltage and pulse width of the laser pulse were specified and the AOM was driven. This allowed for the helical structures to be switched to the crystalline phase (Fig. 8).
Fig. 8. Optical microscope image showing as-deposited amorphous Sb$_2$Se$_3$ and a portion of the crystallized Sb$_2$Se$_3$.
Although an ellipsometry measurement of a large-area crystallized Sb$_2$Se$_3$ would be ideal, we note here that by matching the tone in Fig. 8 to that of the previously annealed (via hotplate) film, and matching the transmission data, we believe that the film is fully crystallized upon optical switching, at thicknesses far exceeding the absorption depth at 532 nm. This remarkable feature is due to the nanostructured nature of the film that allows transmission of the excitation pulse whereas the bulk medium would be opaque. Using optical switching, a variety of optical structures can be "written" into the film at high, diffraction-limited resolutions (< 300 nm), in which a crystallized region with a higher index can be printed into a lower-index region.
6. Discussion
For many years, Sb$_2$Se$_3$ has been used as photovoltaic absorbers and thin-film solar cells due to its high absorption coefficient in the visible spectrum [29,30]. However, being a low-loss chalcogenide material that can observe phase change with the correct thermal stimulus, it has recently received a lot of attention in the photonics industry [31,32]. The main limitation of PCMs, however, has been the thickness at which these materials can be grown and fully switched between the amorphous and crystalline phases [33]. Due to void formation and material decomposition when the material changes phase from amorphous to crystalline, a thick PCM film cracks and fails to switch [34]. Additionally, fully optical switching the material is limited by the absorption coefficient at different depths of the film. This, hence, prevents thicker PCM films to be completely switched [13].
In this work, however, the growth technique of the PCM film allows for thick films to be fabricated and crystallized. This creates the possibility of achieving a large variety of tunable devices that can be used for long-wavelength applications using only a single material. Applications for such a film are boundless, such as optical limiters [35] and phase shifters [1], among many others. In order to simplify future modeling, an effective medium was employed to extract the refractive index and extinction coefficient in the two states, allowing us to design complex devices without necessitating first-principle modeling at every step.
The difficulty of reverse switching of the PCM, however, will need further work. Our first attempt at reversibly switching the sample were not consistent, with irreversible damage occurring most of the time. This can be attributed to the heat trapped within the rods which fails to dissipate quickly enough, leading to the partial/complete melting of the rods rather than quenching into the amorphous state. One solution to this problem would be to use a material with a higher thermal conductivity than air as the surrounding medium, enabling fast quenching before structural deformation occurs. This can be applied using the atomic layer deposition technique where the nanorods can be encapsulated with the desired thermal dissipation layer allowing for the melt-quench process to occur as a result of the quick outward diffusion of the heat trapped inside the nanorods. On the other hand, if operation in the short and mid-wave infrared is desired, the PCM choice can also be altered. In previous work, helical Ge$_2$Sb$_2$Te$_5$ have shown the ability of reversible switching making it a more desired material to use for applications where low-losses in the near-IR and visible wavelength bands are not crucial [16].
7. Conclusions
Helical amorphous Sb$_2$Se$_3$ with 400-600 nm thicknesses were fabricated and optically switched to a crystalline phase using a 532 nm laser. The nanostructures were characterized under the SEM and using the XRD to confirm expected geometry and crystallographic structure, respectively. EMA refractive index fits were performed using an ellipsometer and the extracted (n,k) data was used in TMM simulations in order to simulate the transmission of the film. This data showed a close match to the FDTD transmission simulations that require high computer power and can be costly. Therefore, these fits can be used along with simple thin film modelling in order to design any desired filter. Re-amorphization of the helical rods was not achievable, however, but solutions were presented in Section 6 with further work being performed in the future.
Funding
Defense Associated Graduate Student Innovators; Hibbitt Fellowship Program in the School of Engineering at Brown University; Air Force Office of Scientific Research (FA9550-20RYCOR059).
Acknowledgments
R. L. acknowledges Dylan Morden for useful discussions on FDTD simulations.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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