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Abstract
Ultrathin planar transparent conducting oxide (TCO) films are commonly used to enhance the optical response of epsilon-near-zero (ENZ) devices; however, our results suggest that thickness-dependent loss renders them ineffective. Here, we investigated the thickness-dependent loss of indium tin oxide (ITO) films and their effect on the ENZ-enhanced optical responses of ITO and ITO/SiO2 multilayer stacks. The experimental and computational results show that the optical loss of ITO films increases from 0.47 to 0.70 as the thickness decreases from 235 to 52 nm, which results in a reduction of 60% and 45% in the maximum field enhancement factor of a 52-nm monolayer ITO and 4-layer ITO/SiO2 multilayer stack, respectively. The experimental results show that the ENZ-enhanced nonlinear absorption coefficient of the 52-nm single-layer ITO film is -1.6 × 103 cm GW-1, which is 81% lower than that of the 235-nm ITO film (-8.6 × 103 cm GW-1), indicating that the thickness-dependent loss makes the ultrathin TCO films unable to obtain greater nonlinear responses. In addition, the increased loss reduces the cascading Berreman transmission valley intensity of the 4-layer ITO/SiO2 multilayer stack, resulting in a 42% reduction in the ENZ-enhanced nonlinear absorption coefficient compared to the 235-nm ITO film and a faster hot electron relaxation time. Our results suggest that the thickness and loss trade-off is an intrinsic property of TCO films and that the low-loss ultrathin TCO films are the key to the robust design and fabrication of novel ENZ devices based on flat ultrathin TCO films.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Epsilon-near-zero (ENZ) materials with a zero-crossing real part of the dielectric constant have emerged as a new material platform for integrated photonic and nanophotonic devices [1] and are being used to develop a variety of ENZ-enhanced linear and nonlinear optical devices [2–11]. From an optical point of view, the unique ENZ field enhancement effect and slow light effect in the ENZ region lay the foundation for the application of planar ENZ devices [12–15]. However, the ENZ behavior is greatly compromised by the loss problem in practical ENZ materials [16], which is the result of a mutual repulsion between the field enhancement and material loss in planar ENZ films [17]. To overcome the field enhancement limitation caused by intrinsic loss in isotropic ENZ materials, longitudinal [18] and ultrathin ENZ films [19] have theoretically been proposed to achieve large field enhancements. The theoretical results indicate that the electric field strength inside ENZ films is inversely proportional to the film thickness, making significant field enhancement dependent on the ultrathin ENZ films with thicknesses below 30 or even 10 nm [18,19]. In addition, stacked metamaterials composed of alternating layers of ENZ materials and dielectric layers have theoretically shown to achieve ENZ-enhanced linear absorption and nonlinear responses through the cascade or coupling of resonant modes at multiple interfaces [20,21]. These theoretical results are promising for the realization of high-performance lithography-free planar ENZ devices.
However, a common feature of these theoretical schemes is that the effect of the thickness variation on material loss is ignored [18–21], and significant field enhancements are realized based on zero-loss or low-loss (Im(ε) ∼ 0.001) ENZ materials [18,19], which makes their attainment challenging. To the best of our knowledge, the heavily doped semiconductor materials in transparent conductive oxide (TCO) materials are near-infrared natural ENZ materials with low optical losses [12]. Although the imaginary part of the dielectric constant at the ENZ point of highly crystalline ITO [22], AZO [23], and Y-doped CdO [24] films, with thicknesses greater than 300 nm, can be as low as 0.35, 0.27, and 0.05, respectively, the values are significantly higher than the theoretical requirements. The experimental results of ultrathin TCO materials show that ultrathin ITO nanofilms transform into discontinuous islands at thicknesses below 15 nm [25]. Moreover, the imaginary part of the dielectric constant at the ENZ point of 78-nm thick AZO films is as high as 0.9 [26], indicating that thickness-dependent loss is a distinguishing feature of ultrathin ENZ films. In addition, the latest research shows that tailoring the film thickness can help directly control the optical properties and ENZ behavior of ENZ films [27]; for example, the ENZ wavelength of ultrathin AZO films below 70 nm red-shifts significantly with decreasing thickness. Therefore, ignoring the thickness-dependent loss of ENZ films, such as in the equivalent replacement of 310-nm, 40-nm, or even 12-nm thick ITO films [21,28], may not lead to a robust ENZ device design. Existing research focuses on the evolution of the structural, optical, and electrical properties of TCO films with thickness [25–27,29], which is critical for an in-depth understanding and preparation of high-performance TCO films. However, further studies on the effects of loss caused by thickness variations on the ENZ-enhanced linear and nonlinear optical responses are lacking, which is another key issue in the use of TCO thin films in device applications, covering the design and fabrication of high-performance ENZ photonic devices.
Here, we used ITO as a representative for investigating the thickness-dependent loss of TCO materials and the effects on the ENZ-enhanced optical responses of monolayer ITO and ITO/SiO2 multilayer stacks. The experimental results show that the optical loss of ITO films increases from 0.47 to 0.70 as the thickness decreases from 235 to 52 nm, which is a result of the decrease in grain size and carrier mobility. The calculated results show that the thickness-dependent loss reduces the field enhancement factor of a 52-nm thick single-layer ITO film and 4-layer ITO/SiO2 multilayer stack by 60% and 45%, respectively, invalidating the cascading ENZ effect. The experimental results show that the ENZ-enhanced nonlinear absorption coefficient of a single-layer ITO film at 1240 nm rapidly decreases from -8.6 × 103 to -1.6 × 103 cm GW-1 as the thickness decreases from 235 to 52 nm. In addition, the cascading Berreman transmission valley intensity of the ITO/SiO2 multilayer stack with a total ITO thickness of 240 nm decreases with the number of layers, resulting in a decrease in the ENZ-enhanced nonlinear absorption coefficient for the 4-layer stack sample to -5.0× 103 cm GW-1, which is 42% lower than that of the 235-nm ITO film. In addition, the hot-electron relaxation time at 1450 nm is reduced from 69.8 to 55.2 fs. These results confirm that the intrinsic thickness-dependent loss of TCO thin films prevents ultrathin films and stacking schemes from achieving greater ENZ-enhanced optical responses, resulting in a trade-off between thickness and loss. Therefore, the preparation of low-loss ultrathin TCO films is key to designing and fabricating high-performance novel ENZ devices based on ultrathin TCO films, which should attract more attention.
2. Results and discussion
2.1 Thickness-dependent optical and electrical characteristics of ITO films
As an oxide material, the performance indicators of ITO films are closely related to the preparation conditions, such as the doping concentration [30], deposition oxygen flux [31], and substrate temperature [32]. Here, we focus on the effect of the thickness variation on the crystalline quality and the optical and electrical properties of ITO thin films under the same process conditions. To explore the effect of thickness on the crystalline quality of ITO films, we fabricated single-layer ITO films with thicknesses ranging from 52 to 235 nm based on electron beam evaporation (see Methods) and measured their XRD patterns, as shown in Fig. 1(a). The as-prepared ITO films exhibit a notable (222) preferred orientation and have significant thickness-dependent properties; in particular, the intensity of the diffraction peaks decreases significantly when the thickness is less than 100 nm. A quantitative analysis of the crystallinity of ITO films with different thicknesses was obtained by calculating the grain size of the strongest diffraction peak (222) using the Scherrer formula [33], as shown in Fig. 1(b). As the thickness decreases from 235 to 52 nm, the grain size decreases from 20.6 to 17.6 nm (a 15% decrease), indicating that a decrease in thickness leads to a decrease in crystalline quality, which is consistent with previous reports [25]. It is worth noting that there is an anomaly in the grain size of the 103-nm ITO film, which may be related to an unavoidable process instability.
Fig. 1. (a) XRD patterns of samples with different thicknesses. (b) Crystallite size calculated from the full width at half maximum of the (222) diffraction peak in (a).
The crystalline properties of ITO thin films inevitably affect their optical properties. The TM-polarized light transmission spectrum at an oblique incident angle shows a characteristic Berreman or Brewster absorption peak (transmission valley) near the ENZ point of the material [34,35], which can realize ENZ-enhanced nonlinearity [22] and can be applied in perfect absorbers [3], ultrafast all-optical switching [6], and directional thermal radiation [4]. Interestingly, this characteristic absorption peak can also be used to obtain high-precision optical constants for ENZ thin films through spectral fitting, which is simpler than traditional ellipsometry [36]. Figure 2(a) shows the experimentally measured TM-polarized light transmission spectra (solid line) of samples with different thicknesses for an incident angle of 60° and the fitted curve (dotted line) based on the Drude model and transmission matrix method [36]. The transmission spectrum of the ITO films decreases with an increase in the thickness, and the characteristic transmission valleys are all located near 1250 nm, indicating that the samples have similar ENZ wavelengths. It is worth noting that the spectral characteristics caused by the Berreman mode in the single-layer ITO film are mainly reflected in the transmission spectrum, which is represented by the Berreman transmission valley [36]. Therefore, spectral fitting of the Berreman transmission valley is the key to obtaining the optical constants of ITO films. To obtain the optical constants of ITO films of different thicknesses, we carried out spectral fitting based on the models and methods in the literature [36]. The fitting process can be summarized as follows: Firstly, the theoretical transmission spectra of single-layer ITO films are obtained by the Drude model and transmission matrix method. Secondly, the Drude parameters are obtained by fitting the experimental spectral curves with fmincon function, including the high-frequency dielectric constant (ε∞), bulk plasma frequency (ωp)and Drude loss (γ). Finally, the optical constant of ITO film is obtained by $\tilde{n} = \sqrt \varepsilon $.
Fig. 2. Transmission spectra and optical constants of monolayer ITO films with different thicknesses. (a) TM-polarized light transmission spectrum and fitting curve for an incident angle of 60°. (b) Thickness-dependent ENZ wavelengths and extinction coefficients obtained from transmission spectrum fitting.
Figure 2(b) shows the ENZ wavelengths and corresponding extinction coefficients k (${\textrm{k}_{ENZ}} = \sqrt {\varepsilon ^{\prime\prime}/2} $) of ITO films of different thicknesses, which were extracted from the optical constants of the ITO films (see inset in Fig. 2(b)). Although the thickness of the ITO films was reduced from 235 to 52 nm, the ENZ wavelengths were all distributed within a narrow wavelength range (1225–1255 nm) with a width of approximately 30 nm, indicating that the ENZ wavelength of ITO films above 50 nm is not sensitive to thickness. However, the recent experimental results of Saha et al. [27] show that the ENZ point of AZO film will significantly redshift from 1470 nm to 1750nm as the thickness is reduced from 63 nm to 27 nm. This strong thickness-dependent ENZ wavelength is significantly different from our experimental results, which may originate from differences in the film thickness, materials, and fabrication methods. Unlike the ENZ wavelength, as the thickness of the ITO film decreases from 235 to 52 nm, k at the ENZ wavelength increases significantly from 0.47 to 0.70, showing a remarkable thickness dependency. Notably, the k value of 235-nm ITO is 0.47, which is close to the value 0.42 reported for 310-nm ITO films [22]; it indicates that the thickness dependence of loss under the same preparation conditions is an essential feature of the film-growth law.
The dispersion relationship of ITO materials in the near-infrared band can be described by the classic Drude model [37],
To further investigate the fundamental reason for the thickness dependence of the optical constants, the electrical parameters of ITO films with different thicknesses were measured using the Hall effect, as shown in Table 1. When the thickness of the ITO film was reduced from 235 to 52 nm, its carrier concentration remained at approximately 1021 cm-3, showing thickness-insensitive features; whereas the mobility decreased from ∼30 to ∼15 cm2v-1s-1 (a 50% decrease), showing significant thickness-dependent characteristics, which is consistent with the reported results [25]. The resistivity ($\rho = 1/ne{\mathrm{\mu}}$) and sheet resistance (${R_{\square} } = \rho /d$) also exhibited a thickness dependence because they are directly related to the carrier concentration and mobility. It is worth noting that mobility is inversely proportional to the effective mass and scattering probability of the carriers. The former is determined by the material itself, whereas the latter is related to ionized impurities and grain boundaries [38]. Therefore, for the same preparation process conditions and doping concentration, the larger optical loss of the low-thickness ITO films can be mainly attributed to the reduced carrier mobility caused by a deterioration in the crystalline quality. It is worth noting that since the growth mechanism of thin films involves the adsorption, diffusion, condensation, nucleation, and growth of deposited atoms on the substrate surface, we refer to the loss due to this thickness variation as the intrinsic loss arising from the film growth law, which is significantly different from the loss determined by the preparation process.
Table 1. Basic electrical specifications of ITO films of different thicknesses measured using the Hall effect
2.2 Loss-dependent field enhancement in a monolayer ITO and ITO/SiO2 multilayer stack
Although planar ENZ materials have no mechanism other than the ENZ field-enhancement effect for enhancing the coupling of light and matter, theoretical studies suggest that multilayer ITO thin-film metamaterials composed of ITO and dielectric materials can be engineered to achieve ENZ-enhanced linear and nonlinear optical behaviors [20,21]. The experimental results in the previous section show that the optical loss of ITO films has a significant thickness dependence, which makes ultrathin monolayer and multilayer ENZ films unavoidable owing to the loss problem. Therefore, further investigation of the effect of thickness-dependent loss on the field enhancement of single-layer and multilayer ENZ thin films is of great significance for the design and fabrication of planar ENZ devices. To this end, we used the finite-difference time-domain (FDTD) algorithm for calculating the field enhancement factor of monolayer ITO and 2- and 4-layer ITO/SiO2 multilayer stacks for a 60° incidence of TM-polarized light.
For ease of comparison, we selected the midpoint of the ENZ wavelength distribution region (1225–1255 nm) at 1240 nm as the calculation point and used the optical constants of 80 and 235 nm to represent high-loss and normal-loss ITO films, respectively. Computational models of the single-layer and multilayer structures are shown in Fig. 3. Monolayer films (Fig. 3(a)) ranged in thickness from 52 to 235 nm, whereas multilayer films (as an example of the cascade ENZ effect) were constructed with a silicon dioxide dielectric layer inserted into an ITO film with a thickness of approximately 240 nm. Specifically, the bottom and top ITO layer thicknesses of the 2-layer sample (Fig. 3(b)) were 180 and 60 nm, respectively, and the dielectric layer was 220-nm thick. The thicknesses of the ITO layer and dielectric layer of the 4-layer ITO/SiO2 multilayer stack sample (Fig. 3(c)) were 60 and 110 nm, respectively. The thicker ITO layers of the multilayer samples were primarily used to avoid the strong thickness dependence of the optical constants of ITO thin films at low thicknesses [25], whereas the thicker dielectric layers were used to avoid the effect of mode coupling of adjacent interfaces on the investigated loss.
Fig. 3. Schematic of the structure of single-layer ITO and an ITO/SiO2 multilayer stack. (a) Single-layer ITO film (dITO = 52, 80, 103, 113, 235 nm). (b) 2-layer ITO/SiO2 multilayer stack (dITO_down = 180 nm; dSiO2 = 220 nm; dITO_top = 60 nm). (c) 4-layer ITO/SiO2 multilayer stack (dITO = 60 nm; dSiO2 = 110 nm).
Figure 4(a) shows the optical constants of ITO films with different thicknesses at 1240 nm. Although 1240 nm deviates to different degrees from the ENZ point (Fig. 2(b)) for ITO films with different thicknesses, it is still representative of the thickness-dependent loss problem. Figure 4(b) shows the maximum field enhancement factor of the monolayer ITO films for samples with different thicknesses, which occurred at the air/ITO interface position (shown in the inset). The maximum field enhancement factor calculated based on the constant optical loss (Normal loss) and actual loss (Actual loss) is shown in black and red curves respectively. The results show that if the thickness-dependent loss (black curve) is ignored, the field enhancement factor increases significantly from 1.36 to 2.32 as the thickness decreases, in correlation with the literature’s idea of ${(E/{E_0})^2} \propto 1/t^2$ [19]. However, if thickness-dependent loss (red curve) is considered, the field enhancement factor decreases from 1.36 to 0.84, which deviates significantly from theoretical expectations. It is worth noting that the field enhancement factor of the 52-nm thick ITO film is significantly reduced from the theoretically predicted 2.32 times to 0.84 times, indicating that the thickness-dependent loss results in the field enhancement advantage of the ultrathin film completely disappearing. Figures 4(c) and 4(d) show the field enhancement distributions of the 2-layer and 4-layer ITO/SiO2 multilayer stack samples without considering the interface loss, which is distributed across the ITO film in the form of exponential decay, indicating that the dielectric layer effectively avoids the coupling of modes in adjacent ITO layers. It is worth noting that the exponential distribution of field enhancement is mainly because the thickness of ITO films in each layer of the multilayer stack structure is smaller than the skin depth (normal loss ∼278 nm, high loss ∼332 nm). For the 2-layer ITO/SiO2 multilayer stack sample, the maximum field enhancement factor calculated based on the high-loss ITO film is only 1.73, which is 45% lower than the result calculated by the normal loss (3.16). Similarly, the maximum field enhancement factor of the 4-layer ITO/SiO2 multilayer stack sample is also reduced by 46% from 2.34 to 1.26 due to thickness-dependent loss. Furthermore, the maximum field enhancement factor (1.26) of the 4-layer ITO/SiO2 multilayer stack was lower than that of the 235-nm thick single-layer ITO film (1.36), indicating that thickness-dependent losses may lead to the failure of ENZ- enhanced linear and nonlinear optical responses in multilayer stacks.
Fig. 4. Calculated field enhancement factors at 1240 nm of monolayer ITO and ITO/SiO2 multilayer stack for 60° incidence of TM-polarized light. (a) Thickness-dependent optical constants of ITO films at 1240 nm. (b) Field enhancement factors of ITO monolayers with different thicknesses at the air/ITO interface; the inset shows the typical field enhancement distribution in 235-nm ITO films. Distribution of enhancement factors in 2-layer (c) and 4-layer (d) ITO/SiO2 multilayer stack calculated based on the optical constants of high-loss (80 nm) and normal-loss (235 nm) ITO films. The label “2L_Normal&High loss” means that normal loss is used for the bottom thick ITO film and high loss is used for the top thin film of the 2-layer ITO/SiO2 multilayer stack sample.
2.3 Loss-dependent linear optical properties of an ITO/SiO2 multilayer stack
Field enhancement is critical for ENZ-enhanced linear and nonlinear optical responses [13,35]. Here, we investigate the effects of loss on the linear optical responses of an ITO/SiO2 multilayer stack from an experimental perspective. The ITO/SiO2 multilayer stack samples were prepared using the electron beam evaporation technique (see Methods). Figures 5(a)–(c) show the cross-sectional morphologies of the 235-nm thick monolayer and ITO/SiO2 multilayer stack samples prepared under the same experimental conditions. It should be noted that the 60-nm thick single-layer ITO marked in the 4-layer ITO/SiO2 multilayer stack represents the average thickness, ignoring the thickness differences among the layers. Figure 5(d) shows the experimentally measured TM-polarized light transmittance spectra of ITO thin-film samples with different layers for an incident angle of 60°. The transmission spectra of the 1-layer ITO and 2-layer ITO/SiO2 multilayer stack samples were nearly identical, whereas the 4-layer ITO/SiO2 multilayer stack sample had a higher transmittance. The characteristic transmission valleys of the three samples are located near 1250 nm, and the 4-layer stack samples show more evident transmission valley characteristics, which can be attributed to the cascading Berreman modes introduced by the multiple ENZ/dielectric interfaces. This phenomenon is similar to that of the Ferrell–Berreman modes excited in Ag/SiO2 multilayer metamaterials [34]. In addition, the Berreman transmission valley of the 4-layer ITO/SiO2 multilayer stack sample was significantly blue-shifted compared to the single-layer and 2-layer ITO/SiO2 multilayer stack samples, which can be attributed to the blue-shift of the ENZ point of the ultrathin ITO films (Fig. 2(b)).
Fig. 5. Morphology and transmission spectra of samples with different multilayer structures. (a)–(c) cross-sectional views of the 1-layer ITO, 2-layer ITO/SiO2, and 4-layer ITO/SiO2 multilayer stack samples, respectively. (d) TM-polarized light transmission spectra of different samples for an incident angle of 60°. TM polarized transmission spectra of (e) 2-layer and (f) 4-layer ITO/SiO2 multilayer stack samples calculated based on different optical constants.
To further explore the effect of loss on the linear optical response of the ITO/SiO2 multilayer stack, we calculated the transmission spectra of multilayer samples based on the optical constants of 80-nm and 235-nm single-layer ITO films, as shown in Figs. 5(e) and (f). For the 2-layer ITO/SiO2 multilayer stack sample, the calculated transmission spectra based on the normal-loss ITO thin film are nearly consistent with those calculated based on the high-loss (top layer) and normal-loss (bottom layer) ITO films and in good agreement with the short-wavelength experimental values. Compared with the calculated Berreman transmission valley, the experimental value appears to be wider, which may occur from the interfacial loss introduced by the dielectric layer. The experimentally measured Berreman transmission valley of the 4-layer ITO/SiO2 multilayer stack sample in Fig. 5(f) is 13.0%, whereas the theoretical values calculated from the high-loss and normal-loss ITO films are 8.4% and 3.6%, respectively. This indicates that the thickness-dependent loss significantly reduces the intensity of the Berreman mode, which is a result of the Berreman mode originating from field enhancement [35]. Furthermore, unlike the 2-layer ITO/SiO2 multilayer stack sample, the calculated transmission spectrum of the 4-layer ITO/SiO2 multilayer stack sample is lower than the experimental value in the short-wave direction, indicating that the effective ITO layer thickness of the 4-layer ITO/SiO2 multilayer stack sample is lower than 240 nm, which is attributable to the multiple interfaces introduced in the non-conductive layer (dead layer) [25].
2.4 Effect of loss on nonlinear absorption response
The ENZ-enhanced nonlinearities in planar ENZ materials exhibit significant polarization-dependent and angle-dependent properties. According to the experimental results on the ENZ-enhanced nonlinearity of ITO thin films reported by Alam et al. [22], the excitation conditions for significant ENZ-enhanced nonlinearity are TM-polarized light at the ENZ wavelength and an incident angle of 60°. To study the effects of loss on the nonlinear response, we measured the nonlinear absorption response of single-layer ITO and ITO/SiO2 multilayer stacks at 1240 nm using the open-aperture Z-scan technique [39,40]. The femtosecond pump pulse used in the Z-scan measurement had a repetition rate of 1 kHz, pulse width of 186 fs, and peak pulse power density of 80 GW cm-2 at the focal point, which was generated by an optical parametric amplifier. Figure 6(a) shows the normalized transmission spectra of single-layer ITO films of different thicknesses. Under the same excitation conditions, the maximum normalized transmittance increased from 1.2 to 3.2 with the increase in thickness, exhibiting evident thickness-dependent properties. Figure 6(b) shows the nonlinear absorption response of an ITO/SiO2 multilayer stack; with a total thickness of approximately 240 nm, the maximum normalized transmittance decreased from 3.2 to 2.5 with an increase in the number of ITO layers. Although multilayer ITO/SiO2 hyperbolic metamaterials have theoretically been shown to enhance nonlinear responses [21], these experimental results show that it is difficult to achieve ENZ-enhanced nonlinearity by relying on a cascade of Berreman modes at multiple interfaces, which is different from the enhanced linear optical response of multilayer ENZ materials [20,41,42].
Fig. 6. Nonlinear absorption responses of monolayer and multilayer films at 1240 nm with TM-polarized light at a 60° incident angle. (a) Thickness-dependent nonlinear absorption response of a monolayer film. (b) Nonlinear absorption response of ITO/SiO2 multilayer stack. Thickness-dependent (c) and layer-number-dependent (d) nonlinear absorption coefficients.
The nonlinear absorption coefficient was obtained by fitting normalized transmittance curves. The normalized transmittance of the open-aperture Z-scan is expressed as [39,43]
where TOA, ΔΨ, and Leff are the normalized transmittance, imaginary part of the nonlinear phase shift, and effective interaction length, respectively. Equations (4)–(6) show that the normalized transmittance is determined by the distance from the focal point (z), Rayleigh length (z0), nonlinear absorption coefficient (z), peak pulse power density (I0), linear absorption coefficient (α0), and film thickness (L). It is worth noting that all parameters except β can be measured experimentally, which allows β to be directly extracted by fitting of the normalized curve of the experiment.The theoretical normalized transmission curves, shown as solid lines in Figs. 6(a) and 6(b), agree well with the experimental results. The effective nonlinear absorption coefficients of single-layer ITO films with different thicknesses in Fig. 6(c) are as high as 103 cm GW-1, which is consistent with previously reported results [22]. The nonlinear absorption coefficient decreased rapidly from -8.6 × 103 cm GW-1 to -1.6 × 103 cm GW-1 with decreasing thickness, indicating that thickness-dependent loss significantly reduces the nonlinear absorption response in ultrathin films. Compared with the 80-nm thick ITO film (low loss), the 103-nm thick ITO film (high loss) had a lower nonlinear absorption coefficient, further confirming that high loss significantly reduced the ENZ-enhanced nonlinear absorption response. In addition, the thicker thickness and greater loss of 103-nm thick ITO films imply higher linear absorption, however, this does not bring a larger nonlinear absorption coefficient, suggesting that the intensity of the ENZ-enhanced nonlinear response is dominated by the ENZ field enhancement rather than linear absorption. Figure 6(d) shows the layer-number-dependent nonlinear absorption coefficient. Under the same thickness condition, the nonlinear absorption coefficients of the 1-layer ITO, 2-layer ITO/SiO2, and 4-layer ITO/SiO2 multilayer stacks are -8.6 × 103 cm GW-1, -7.9 × 103 cm GW-1, and -5.0 × 103 cm GW-1, respectively, which can be attributed to an increased loss. The nonlinear absorption coefficient of the 4-layer ITO/SiO2 multilayer stack is 3.13 times that of the 52-nm single-layer ITO film, but only 0.58 times that of the 235-nm thick ITO film, indicating that taking the ultrathin single-layer as a reference will lead to an overestimation of the ENZ enhancement nonlinearity of multilayer films, which was ignored in previous studies [21,43]. These results confirm that the thickness-dependent loss significantly reduces the ENZ-enhanced nonlinear response, and thus the enhanced nonlinear response theoretically present in ultrathin ENZ films may encounter experimental challenges.
2.5 Effect of loss on transient nonlinear absorption response
To explore the effects of loss on the intra-band nonlinear response time, we measured the transient nonlinear response at 1450 nm (60 fs, 1 kHz) for a single-layer ITO and ITO/SiO2 multilayer stacks using a degenerate pump-probe technique, as shown in Fig. 7(a). The pump and probe light was TM-polarized light with an included angle of 5°, and the incident angle of the pump light was approximately 60°. To avoid a nonlinear response due to the probe light, the single-pulse energy of the probe light was attenuated to 50 nJ. The bandgap of the ITO film was 3.7–4.0 eV [44], and the low single-photon energy (0.88 eV) of the pump light caused the nonlinear response process to only involve the conduction band hot-electron behavior. Limited by the experimental conditions, this section explores the effect of loss on the transient nonlinear response at 1450 nm rather than at 1240 nm in the ENZ region. As the thickness-dependent loss law at 1450 nm (Fig. 2(b)) is similar to that at 1240 nm (Fig. 4(a)), it can be inferred that the loss-dependent hot-electron relaxation at 1450 nm reflects the intra-band hot-electron relaxation behavior in the ENZ region.
Fig. 7. (a) Schematic of the degenerate pump-probe measurement setup. (b) Ultrafast transient responses of single-layer ITO films with different thicknesses at a pump flux of 18.5 mJ cm-2; the solid black line is the fitted curve based on a single exponential decay function. (c) Ultrafast transient responses of the ITO/SiO2 multilayer stack at a pump flux of 18.5 mJ cm-2.
Figure 7(b) shows the ultrafast transient optical responses of single-layer ITO thin film samples with different thicknesses at a pump flux of 18.5 mJ cm-2. Consistent with the above nonlinear absorption response law, the modulation depth of the single-layer ITO film increased from 3.9% for a 52-nm thick ITO film to 17.5% for a 235-nm thick single-layer ITO film. The hot-electron relaxation times of ITO films with different thicknesses were obtained by fitting the experimental data with a single exponential decay function [45], which increased from 43.6 to 69.8 fs with the thickness increasing from 52 to 235 nm. Figure 7(c) shows the transient nonlinear responses of different layers of the ITO/SiO2 multilayer stacks. Compared with the 235-nm single-layer ITO films, the hot-electron relaxation time of 4-layer ITO/SiO2 multilayer stacks was reduced to 55.2 fs. These experimental results indicate that the thickness-dependent loss is beneficial for reducing the hot-electron relaxation time. Many experimental studies have shown that the strength of the electron–phonon coupling affects the hot-electron relaxation time, which increases with pump power [23,45,46]. Therefore, the longer relaxation time of the low-loss sample can be attributed to the stronger electron–phonon coupling caused by the higher field enhancement in the sample. In addition, the inferior crystalline properties of the high-loss samples may introduce a higher trapped state density and defect scattering [45,47], resulting in faster relaxation times for ultrathin ITO films and ITO/SiO2 multilayer stacks. Notably, although loss-accelerated hot-electron relaxation is beneficial for obtaining faster response times, the low nonlinear response strength limits the nonlinear applications of high-loss planar ENZ materials.
2.6 Ideal and actual losses of ultrathin ENZ films
To more intuitively reflect the thickness-dependent loss at the ENZ point of TCO films, we summarize the reported experimental results and theoretical requirements for loss at the ENZ point of typical TCO films with different thicknesses, as shown in the white and gray areas in Fig. 8. Compared with the reported ITO films with different thicknesses based on pulsed laser deposition [7,38] and magnetron sputtering [22,48–51], the ITO films prepared in this study based on electron beam evaporation have larger overall losses; however, the similar thickness-dependent losses further confirm that the high losses are intrinsic characteristics of ultrathin films. The typical losses at the ENZ point of the ITO [38], AZO [23], and GZO [52] films with thicknesses greater than 200 nm are 0.39, 0.37, and 0.54, respectively. They increase significantly with decreasing thickness and reach a value close to 0.7 at approximately 50-nm thickness [26,50,52], indicating that thickness-dependent loss is a common problem in TCO films. Notably, intrinsic and doped CdO [6,24] films exhibit lower losses (< 0.3) at the ENZ point than ITO, AZO, and GZO films, which is a result of their higher carrier mobility. Furthermore, the reported losses of ultrathin TCO films are significantly higher than the theoretical requirements of high-performance ENZ photonic devices [18,21,28,53], suggesting that devices designed by ignoring thickness-dependent losses are at risk of not being realized. Therefore, the low-loss ultrathin (< 50 nm) ENZ films is the basis for the realization of high-performance lithography-free planar ENZ devices.
Fig. 8. Experimental results and theoretical requirements for thickness-dependent loss at the ENZ point of typical TCO films. The loss at the ENZ point is represented by the extinction coefficient k (${k_{ENZ}} = \sqrt {\varepsilon ^{\prime\prime}/2} $) calculated from the imaginary part of the dielectric constant. Different physical vapor deposition techniques are represented by the background color of the material name, with green, red, blue, and magenta representing magnetron sputtering (MS), pulsed laser deposition (PLD), atomic layer deposition (ALD), and electron beam evaporation (EBE), respectively.
These theoretical and experimental results suggest that the loss originating from the crystalline quality of the thin film significantly reduces the field enhancement, which, in turn, deteriorates the ENZ-enhanced linear and nonlinear responses. Although the minimum film thickness involved in this study was only 52 nm, it was sufficient to demonstrate that the thickness-dependent loss of ITO films grown by electron beam evaporation is an intrinsic property derived from the film-growth law, which greatly hinders the field enhancement advantage of ultrathin ITO films. These results demonstrate the challenges in achieving ideal ENZ-enhanced linear and nonlinear responses based on native planar ultrathin TCO materials without addressing the loss of ultrathin films. According to recent reports on TCO materials, several potential approaches can be used to obtain low-loss ENZ films. One is doping engineering [54,55]; for example, transition metal-doped In2O3 can achieve an electron mobility as high as 75 cm2v-1s-1 [55], which is significantly higher than that of conventional ITO films (35 cm2v-1s-1). The second is the preparation process, for example, the electron mobility of epitaxially grown ITO thin films can also be as high as 67 cm2v-1s-1 [38]. The third is the post-annealing process, such as thermal annealing or laser annealing [56–58], which has been proven to effectively tune the optoelectronic properties of TCO thin films. The fourth is the selection of low-loss ENZ films; for example, doped-CdO is a very potential low-loss mid-infrared ENZ material [6,24]. However, it is worth noting that the existing technical means of obtaining high mobility can lead to a decrease in the carrier concentration of the material, causing the ENZ point to deviate from the important telecom band [38,55]. Therefore, the preparation of low-loss ultrathin ENZ thin films in the telecom band is still a technical challenge that must be overcome to achieve high-performance lithography-free planar ENZ devices, which provides potential opportunities for the exploration of new preparation processes and even new material designs.
3. Conclusion
In conclusion, the thickness-dependent loss of ITO films and their effects on the ENZ-enhanced optical responses of monolayer ITO and ITO/SiO2 multilayer stacks were investigated. The crystal quality and optical and electrical properties of monolayer ITO films show that reducing the thickness of ITO from 235 to 52 nm results in 15% and 50% reductions in grain size and carrier mobility, respectively, corresponding to an increase in the optical loss at the ENZ point from 0.47 to 0.70. The thickness-dependent loss reduces the maximum field enhancement factor of the 52-nm single-layer ITO film and 4-layer ITO/SiO2 multilayer stack by 60% and 45%, respectively, rendering the field enhancement effect of the ultrathin monolayer and cascade ENZ effect of the ITO/SiO2 multilayer stack futile. The experimental results show that the ENZ-enhanced nonlinear absorption coefficient of the 52-nm single-layer ITO film is -1.6 × 103 cm GW-1, which is 81% lower than that of the 235-nm ITO film (-8.6 × 103 cm GW-1), confirming that thickness-dependent loss prevents ultrathin TCO films from obtaining a more enhanced nonlinear response. In addition, the experimental results of the ITO/SiO2 multilayer stack show that the intensity of the cascaded Berreman transmission valleys decreases with an increase in the number of layers, resulting in the ENZ-enhanced nonlinear absorption coefficient of the 4-layer stack sample decreasing to -5.0 × 103 cm GW-1, which is 42% lower than that of the 235-nm ITO film. In addition, this results in a faster hot-electron relaxation time, confirming that it is challenging to obtain a larger ENZ-enhanced optical response. Our results indicate that the intrinsic thickness-dependent loss of the TCO film leads to a trade-off between the thickness and loss; thus, the preparation of ultrathin TCO films with low loss is key for realizing the robust design and fabrication of novel ENZ devices based on ultrathin TCO films, which should be potentially explored in the future studies.
Appendix
Methods
Fabrication. ITO films with different thicknesses were prepared on 1-mm thick fused silica substrates by electron-beam evaporation of ITO targets with a Sn doping ratio of 10%. The basic pressure of the chamber was 2.1 × 10−3 Pa, deposition pressure was stabilized at 1.6 × 10−2 Pa by controlling the oxygen flow, and temperature of the fused silica substrate was 250 °C. The deposition rate and sample thickness of the ITO films were monitored using quartz crystal control. The deposition parameters of the ITO layer of the ITO/SiO2 multilayer sample were consistent with those of the single-layer ITO layer film, whereas the deposition pressure of the SiO2 layer was stabilized at 2.0 × 10−2 Pa by controlling the oxygen flow, and the deposition rate was increased from 0.3 Å/s for the ITO film to 3.5 Å/s. Characterization. The TM-polarized static transmission spectra of all samples were measured using a Lambda 1050 ultraviolet-visible-near-infrared spectrophotometer (PerkinElmer). Optical set-up. For the open-aperture Z-scan measurements, we used a femtosecond laser (Light Conversion, CB5-05) with a center wavelength of 1030 nm, pulse duration of 230 fs, and repetition frequency of 1 kHz to feed the optical parametric amplifier (OPA). The collimated femtosecond laser (1240 nm, TM-polarized) output by the OPA was divided into a signal light part and reference light part by a beam splitter. The signal light was focused on the sample using a focusing lens with a focal length of 150 mm at an incident angle of 60° and collected by an optical power meter after transmission. The sample was scanned along the Z-axis using an electronically controlled displacement stage.
Funding
National Key Research and Development Program of China (2018YFE0115900); National Natural Science Foundation of China (11874369, 52002271); China Postdoctoral Science Foundation (2021M703326); Key Foreign Cooperation Projects of the Bureau of International Cooperation of the Chinese Academy of Sciences (181231KYSB20210001).
Acknowledgments
We thank Kui Yi, for the preparation and technical support for sample fabrication in this study, and Yun Cui, for providing technical support for the characterization of the microscopic morphology of the samples.
Disclosures
The authors declare no competing interests.
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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