1. Introduction

Dynamically tunable nanophotonic devices are necessary for many applications including imaging, displays, and information processing [1–3]. Electrical tunability is preferred in many of these applications as it allows easy integration with control electronics. Electrically tunable optical materials form the core of such devices where small change in optical constants of the material can produce a large change in the overall functionality. Many such solid-state materials have been investigated before for visible and near-infrared applications, e.g., semiconductors [4, 5], transparent conducting oxides [6, 7], graphene [8, 9], MEMS devices [10] and thermal phase change materials such as chalcogenide glass [11]. However, their tunability is either small or requires large stimulus. In the case of field-effect tunable materials, large stimulus is also not anoption due to the limitation of electrical breakdown in the capacitive gap. In an attempt to overcome this limitation, here in this paper, we report a new class of material for such electrically tunable applications requiring only an in-plane bias. We study the electrically tunable optical properties of 1T-TaS₂, a quasi 2D material that exhibits strong correlation of charge density order [12].

Many materials supporting charge density waves (CDW) such as NbSe₃, TaS₃, and TiSe₂, exhibit strong correlation and CDW at low temperatures [13]. However, 1T-TaS₂ supports CDWs at room temperatures [14]. CDWs are a result of strong interaction between electrons and phonons of the material producing a condensate that rearranges the lattice and produces a nested Fermi surface. Depending on the extent of lattice reorganization or condensation, CDW materials exhibit different phases. For example, 1T-TaS₂ shows two phase transitions at 190 K and 348 K, separating three states: commensurate charge density wave (CCDW), near commensurate CDW (NCCDW) and incommensurate CDW (ICCDW) states [15]. The transition between NCCDW and ICCDW phases of 1T-TaS₂ above room temperature results in its extreme sensitivity to light [16], electrical bias [17] and temperature [18] making it a promising candidate for tunable nanophotonics.

Though previous demonstrations have shown that 1T-TaS₂ exhibits nonlinear conductance at room temperature[19], hysteresis behavior of electric resistance [15] and its phase transition that can be tuned by pressure [20], strain [21], thickness [22], gate voltage [23], and chemical doping [24, 25], its optical properties remain unexplored. Here in this paper, we characterize the anisotropic optical properties of 1T-TaS₂ thin films and demonstrate for the first time, an electrical bias dependent optical properties of a charge density wave material. By calculating the index change associated with the electrically tuned optical properties, we show that 1T-TaS₂ makes an excellent candidate for tunable nanophotonic devices.

2. Experimental methods

Pure 1T-TaS₂ crystals were purchased from 2D Semiconductors (www.2dsemicondcutors.com). Thin films of 1T-TaS₂ were obtained from bulk single crystals using mechanical exfoliation and subsequent transfer to substrates. Glass cover slides were chosen to be substrates due to their transparency in the visible spectrum. Thickness of 1T-TaS₂ after exfoliation were measured by Atomic Force Microscope (AFM) and profilometer. After exfoliation, electron beam lithography and electron beam evaporation were used to make top electrodes. The material quality of the sample was characterized by X-Ray diffraction (XRD) and Raman spectra. Cu K-α X-ray line is used for XRD, while a 532 nm wavelength CW laser was used for Raman scattering measurement.

 

Fig. 1 Material properties of exfoliated 1T-TaS₂ films: a) X-ray diffraction plot of 1T-TaS₂ showing four peaks corresponding to the planes indicated. b) Raman spectrum of exfoliated 1T-TaS₂ using 532 nm laser excitation. c) Nonlinear conductivity of 1T-TaS₂ measured at room temperature along with the theoretically predicted curve. The inset shows the crystal structure of a layer of 1T-TaS₂. When 1T-TaS₂ is in CDW phase, the Ta atoms on corners of the red star will move inwards making a 13-atom David-star cell. d) The magnitude of impedance spectrum of the 1T-TaS₂ film under an applied AC bias voltage at 500 mV. The inset shows the optical image of the device used for characterization.

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The electrical characterization of the exfoliated films were carried out using in-plane bias across the contacts prepared. DC and ac measurements were carried out using Keithley 2450 SMU and HF2LI from Zurich Instruments. Only DC transport measurements were carried out using a pulsed current source to avoid Joule heating in the sample, and rest all with unmodulated sources. The modulated DC current source for transport measurements had 1 ms pulse duration and 4 s period and was observed to cause negligible temperature rise.

Optical characterization was carried out with low intensity excitation and a microscope coupled to an imaging spectrophotometer. The reflectance and transmittance were measured using an excitation source of ps-pulsed supercontinuum laser with a repetition rate of 2.24 MHz. All other optical measurements were carried out using a low intensity white light excitation from a tungsten-halogen lamp. The imaging setup used an objective with 0.45 NA and 10×

magnification for all measurements except the angle dependent reflection. The angle resolved reflectances in TM and TE polarizations were measured using Fourier plane imaging technique through an oil-immersion objective of NA 1.45 and 100× magnification. The spectrum was collected by Princeton Instruments IsoPlane spectrometer and Pylon CCD. The resolution of the spectrometer was 0.2 nm and the estimated mean error in intensity measured is about 0.5%.

 

Fig. 2 Anisotropic optical properties of 1T-TaS₂ without any electrical bias: a) Normal incidence reflectance (left axis) and transmittance (right axis) spectra under low intensity white light excitation. b) Extracted real (${\epsilon }^{\prime }$) and imaginary (${\epsilon }^{″}$) permittivity functions in in-plane (ε_o) and out-of-plane (ε_e) directions. The out-of-plane permittivity function was extracted using angle dependent reflectance spectra measured in c) TE and d) TM polarizations.

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3. Results and discussion

The as-exfoliated 1T-TaS₂ films showed single crystalline characteristics as seen from XRD plot of Fig. 1(a). The four peaks at 14.99°, 30.26°, 46.13° and 62.97° correspond to 001, 002, 003 and 004 crystal planes respectively [26, 27]. Further, the crystal phase of the films was identified by Raman scattering spectra of Fig. 1(b). The Raman shifts at 254 cm⁻¹, 306 cm⁻¹ and 379 cm⁻¹ indicate crystalline 1T phase of TaS₂[28].

Since 1T phase of TaS₂ exhibits NCCDW order at room temperature, its DC conductivity is expected to show a non-linear dependence on bias. Electrical bias depins condensed CDW from the defects or impurities in the film and thereby results in a nonlinear increase in conductivity with bias. A semi-empirical equation, Eq. 1 captures the non-linear conductivity as a function of in-plane electric field E, a threshold depinning field of E_T and a saturation field of E₀ [12].

The measured DC conductivity of as-exfoliated 1T-TaS₂ film is shown in Fig. 1(c) along with the theoretical estimate for a film with a depinning threshold $E_T=$10 V/cm and $E_0=$83 V/cm. [19]. The non-linear DC conductivity confirms the presence of condensed CDWs in our 1T-TaS₂ film at room temperature. The measured magnitude of ac impedance of 1T-TaS₂ is shown in Fig. 1(d). The impedance is almost a constant up to about 10 kHz and increases like an inductor. The kinetic inductance of condensed charge carriers is much higher than free carriers leading to a much smaller frequency of transition to inductive behavior.

The presence of CDW influences the optical properties of the tantalum disulfide films and the depinning with bias enables electrical tuning of the optical properties. We characterize the optical properties of as-exfoliated 1T-TaS₂ films by measuring reflection and transmission spectra with and without electrical bias. At first, we measure the normal incidence reflectance and transmittance spectra at low intensity white light excitation without bias as shown in Fig. 2(a) for a film with an average thickness of 97 nm. Using these reflectance and transmittance spectra, the in-plane dielectric function (ε_o) of the 1T-TaS₂ film was extracted for every wavelength point and is plotted in Fig. 2(b). In the wavelength range of 540 to 840 nm, 1T-TaS₂ has both large real and imaginary dielectric constants making it a lossy high index dielectric material.

Since this quasi-2D layered material should possess uniaxial anisotropy [29], the dielectric function (ε_e) along c-axis or direction normal to layers is expected to be different from the in-plane dielectric function,ε_o. Angle dependent reflection measurements in both TE and TM polarization without bias, as shown in Fig. 2(c) and 2(d), were used to extract this c-axis dielectric function. Since only reflectance data was available for the extraction of dielectric function, a Lorentzian model was assumed for ${\epsilon }_e\left(\omega \right)$ and is plotted in Fig. 2(b).

Using the same optical measurement setup, we characterize the change in the optical properties of the 1T-TaS₂ film with both DC and AC biases. With an in-plane DC bias, the measured reflectance of 1T-TaS₂ film is as shown in Fig. 3(a). Reflectance monotonically decreases for wavelengths shorter than 700 nm with increasing bias up until 1.5 V. However, when the in-plane bias reaches 2 V, the 1T-TaS₂ transits from NCCDW to ICCDW phase resulting in a change in the shape of the reflectance spectrum. The phase transition was confirmed by DC conductivity measurements not shown here. We suspect that the observed changes in reflection are mainly due to Joule heating of the sample though there has been some recent evidence of DC bias reducing the phase transition temperature [30]. A simple estimation shows that the minimum temperature rise expected in our film at 0.5 and 2 V DC biases are about 2 and 20 K respectively. Thus, higher bias leads to higher temperatures which in turn create more free carriers leading to larger plasma frequency. Higher plasma frequency results in larger reflection at longer wavelengths and smaller reflection at wavelengths shorter than the plasma wavelength, thus explaining the observed trend in Fig. 2(a). The change in the reflection with bias plotted in Fig. 2(a) can be translated to a change in refractive index of the film. The projected change in the real index of the film is as shown in Fig. 3(b). Maximum index change of about 0.1 is observed with an in-plane bias of 2 V. The bump in $\mathrm{\Delta }n$ observed at around 570 nm could be due to interband transitions in ICCDW phase. The phase transition of 1T-TaS₂ from NCCDW phase to ICCDW phase would cause a reconfiguration of crystalline structure and change the electronic band structure [31].

 

Fig. 3 DC bias dependent optical properties of 1T-TaS₂ films: a) Relative change in reflectance spectrum of 1T-TaS₂ at room temperature under in-plane DC bias from 0.5 V to 2 V, and b) Corresponding absolute change in real refractive index.

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The CDWs in 1T-TaS₂ also respond to AC bias and hence are expected to exhibit frequency and amplitude dependent optical properties. Fig. 4 shows the measured changes in reflectance spectra of a near 125 nm thick film with different AC bias amplitudes at 1 MHz frequency. In contrast to the DC case, AC bias at 1 MHz causes the reflectance to increase with increasing amplitude (see Fig. 4(a)). The AC bias reinforces condensation of CDWs by causing them to slide and enhance coherence. Thus, the AC bias reduces the number of carriers available for optical conduction and hence increases reflectivity of the film. The initial decrease in reflectivity for 100 mV bias could be due to Joule heating. However for larger biases, the effect of additional Joule heating is negligible and the reflectance shows a monotonically increasing trend. (Our estimates show that the minimum temperature rise at 500 mV, 1 MHz AC bias is about 2.4 mK.) The corresponding change in real refractive index of the film is shown in Fig. 4(b). Except for 100 mV, all other curves show an increase in the index as expected. The largest change in index observed here is about 0.06 though higher bias amplitude can result in even larger change.

Similar to the AC bias amplitude, increasing frequency up to the saturation frequency ω_p usually in MHz, can also result in increasing reflection and thus increasing index [32]. The frequency dependence as shown in Fig. 4(c) for a constant amplitude of 500 mV shows a monotonic trend of increasing reflectance with frequency. CDWs are known to exhibit strong resonances in higher MHz frequency range and thus, increasing frequency reinforces their condensation and thus the observed trend in the reflectance. The corresponding change in real refractive index of the film is plotted in Fig. 4(d). Just by tuning the excitation AC frequency, the refractive index of 1T-TaS₂ films can be changed by about 0.06.

 

Fig. 4 AC bias dependent optical properties of 1T-TaS₂ films: a) Relative change in reflectance spectra and b) absolute change of refractive index of 1T-TaS₂ for different amplitudes of AC bias at 1 MHz. c) Relative change of reflection and d)absolute change of refractive index of 1T-TaS₂ for a constant AC bias amplitude of 500 mV.

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4. Conclusions

Mechanically exfoliated thin films of 1T-TaS₂ - a quasi 2D layered material - were observed to support CDWs at room temperature. The existence of CDWs results in interesting optical and electro-optical properties. We characterized the uniaxial anisotropy in this lossy dielectric material in the visible and demonstrated in-plane electrical bias tunable optical properties. While DC bias tuned the optical properties primarily from Joule heating, AC bias tuning was an outcome of changing condensation of charge density waves. Real refractive index change in the order of 0.1 was demonstrated with both DC and AC biases. Such large index change makes 1T-TaS₂ and such other strongly correlated materials promising for tunable nanophotonics.