Thermal tuning capabilities of semiconductor metasurface resonators

1 Introduction

Metasurfaces are planar optical structures composed of ordered subwavelength resonators, designed to manipulate light through arbitrary wavefront shaping [1], [2], [3], [4]. Recently, this field has witnessed tremendous progress by adopting an all-dielectric approach [2], giving rise to several dielectric metasurface demonstrations, including achromatic and broadband metalenses [5], [6], [7], axicon lenses [8], sub-diffraction focusing [9], nonlinear generation [10], [11], [12], beam deflectors [8], [13], [14], wave plates and beam converters [15], [16], [17], [18], holograms [19], [20], [21], antireflection coatings [22], and magnetic mirrors [23], to name a few. So far, however, most metasurfaces are implemented for static operation and optimized for limited bandwidth of operation. To reach the next level of dynamic control over light, metasurfaces must include active and reconfigurable functionality that will drastically increase their potential and unlock a vast array of new application possibilities.

The fundamental challenge for achieving reconfigurable operation is to obtain large and continuous modulation of optical properties within subwavelength and low-Q meta-atom resonators [24], [25]. Desirable tuning mechanisms continuously shift the resonance frequency of the metastructure with at least one linewidth of maximal shift, thus enabling significant modulation of both amplitude and phase. These challenges have motivated several studies exploring different approaches, designs, and materials that provide extreme tunability. Previous investigations of active tuning in dielectric metasurfaces and meta-atoms have focused on ultrafast free-carrier injection [26], [27], [28], [29], [30]; coupling to liquid crystals [31], [32], to atomic vapor [33] or to epsilon-near zero materials [34], [35]; phase change materials [36], [37]; and MEMS [38], [39], [40]. However, none of these approaches provide a viable solution for a fully reconfigurable metadevice where at each subwavelength meta-atom, the phase and amplitude can be individually and continuously tuned to provide an arbitrary phase profile. Free-carrier approaches have shown only sub-linewidth resonance tuning, along with severe losses, as they require exceptionally high carrier generation rates. Phase change materials allow non-continuous switching between two distinct states while coupling to background media, and MEMS-based approaches do not provide direct modulation of the resonator itself but rely on mechanical actuation or index modulation of substrates. Recent studies have showed that the thermo-optic effect (TOE), i.e. refractive index variation with temperature dn/dT can be used to induce large (Δn~1) and continuous index shifts in materials having extraordinary thermal dependence [41], [42]. Recently, the TOE was also used to actively tune Si metasurfaces, but only at a limited temperature range (273–573 K) [43]. Here, we present a thorough study of the thermal tunability of Ge and Si meta-atoms and metasurfaces over a large temperature range 80–900 K. We demonstrate thermal tuning of Mie resonances due to the normal positive thermo-optic coefficient (TOC) (dn/dT>0) over a wide infrared range. At higher temperatures and longer wavelengths, we show that thermal excitation of free carriers (FCs) becomes significant due to the bandgap shrinkage of the semiconductors, causing a reduction in dn/dT. With further increased temperatures, the sign of TOC is reversed (dn/dT<0) culminating in a total negative induced index. We also demonstrate the tuning of high-order Mie resonances by several resonance linewidths with a temperature swing of ΔT<100 K. Finally, we exploit the larger TOC of Si at near-infrared (NIR) wavelengths for realizing amplitude modulators and tunable metafilters with Si metasurfaces.

Thermo-optic (TO) effects provide an ideal test bed for demonstrating and elucidating reconfigurable metasurface properties. TO tuning can provide large index shifts with no added losses and be integrated into electrically controlled architectures [44], [45]. Thus, TO tunability forms the basis for many reconfigurable integrated photonic devices [44], [45], [46], [47]. However, the TOC of most materials is small for subwavelength applications; hence, typical TO applications exploit small index changes acting over distances much larger than a wavelength to achieve useful modulation. For efficient modulation of subwavelength resonators, the maximally induced index shift Δn should tune the resonance wavelength by more than its linewidth (Δλ/FWHM>1, where Δλ is the resonance wavelength shift and FWHM is the full width at half max of the linewidth). The route for achieving this tunability is by maximizing the TOE using extraordinary materials [41], [42], [48], [49] and/or narrowing the resonance linewidth using high-Q modes [41], such as supported by asymmetric [32] or fano-resonant [10] metasurfaces or originating from bound states in the continuum [50]. Here, we study the TO tuning capabilities of Si and Ge – the most commonly used materials for dielectric metasurfaces and nanophotonics. The TO coefficients of these semiconductors are among the highest of natural materials [51], which, along with their high refractive indices and CMOS compatibility, makes them very attractive materials for reconfigurable metasurfaces. However, the typical TOC values (~1–5×10⁻⁴ K⁻¹) requires large temperature modulation, which may cause problems if the TOC is strongly temperature dependent [41], [42]. In the mid-infrared (MIR) range; for instance, working at high temperatures can generate FC densities in semiconductors that dramatically alter the optical constants due to Dude-like dispersion. The total induced index shift of the semiconductor due to a positive temperature gradient is the sum of contributions from the normal TO effect and the thermal FC effect: Δn=Δn_TO+Δn_FC. In vast majority of materials, the TOC is positive; hence, Δn_TO>0, while the FC term has a negative contribution Δn_FC<0 (due to the plasma frequency blue shift caused by FCs, in a Drude model). The thermal FC term (Δn_FC) is particularly strong for low bandgap semiconductors with small effective masses [24], [41], [42] (Supporting Information), but in most semiconductors is negligible below ~500 K.

2 Results and discussion

The induced index shift of Si and Ge as a function of wavelength (2–16 μm) and temperature (80–850 K) is presented in Figure 1A and B. Refractive index shifts Δn are calculated with respect to index values at room temperature (RT). The index shifts in Si are almost wavelength independent for ~T<700 K, where the normal positive dn/dT is responsible for a near linear increase in Δn with temperature. For T>700 K, Δn is wavelength dispersive since the density of thermally generated FCs is no longer negligible (Supporting Information Figures S1 and S2). Extracted dn/dT linecuts at different temperatures (Figure 1C) illustrate the temperature dependence and chromatic dispersion of dn/dT at various temperature regimes, specifically when dn/dT switches signs, i.e. dn/dT<0, for T=800 K (orange line). The strong dn/dT wavelength dispersion at 800 K (orange line) is due to a 15% decrease in bandgap, which generates an intrinsic FC density of n_i~10¹⁷ cm⁻³ (Supporting Information Figures S1 and S2) and associated negative Δn_FC. Thus, there is a point where both effects perfectly cancel out Δn_TO=−Δn_FC and the total Δn is zero. In Ge, these thermal FC effects are further accentuated, as seen in Figure 1B and D. The smaller bandgap of Ge (0.66 eV at RT) compared to Si (1.12 eV at RT) and the lower FC effective mass cause a stronger FC contribution for the same temperature gradients. Therefore, FC effects play a significant role even at 500 K. For more elevated temperatures and longer wavelengths, FC effects dominate over normal TO effects, leading to a negative and highly dispersive dn/dT at MIR and LWIR wavelengths. For example, at T=800 K (orange line), dn/dT is almost an order of magnitude larger in magnitude at λ=14 μm (−18×10⁻⁴ K⁻¹) compared to λ=2 μm (2×10⁻⁴ K⁻¹).

Figure 1:

Temperature and wavelength dispersion of n and dn/dT in Silicon and Germanium.

Thermally induced index shifts in Si (A) and Ge (B) as a function of wavelength (2–16 μm) and temperature (80–850 K). (C) and (D) The chromatic dispersion of dn/dT at various temperatures in Si (C) and Ge (D). Each color plot corresponds to dn/dT at different temperatures as detailed in the legend of (D).

To investigate thermal tunability capabilities, we study Si and Ge single spherical meta-atom resonators fabricated by laser ablation [24], [52]. Examples of Si (r=1.9 μm) and Ge (r=1.54 μm) meta-atom Mie resonators are illustrated in Figure 2A and B. A series of multipolar Mie resonances in the range 4–14 μm are observed using both analytical calculations (red dashed), FDTD simulations (red) and single particle infrared microspectroscopy (black). These multipolar resonances are labeled (see panels 2c and 2d) according to their polarization (magnetic or electric) and mode order (dipole, quadrupole, hexapole, etc.). The temperature-dependent spectra of these resonators (80–873 K for Si and 123–773 K for Ge, see experimental section for more details) are presented in Figure 2C and D. Spectral shifts are observed for all resonances as a response to the thermal modulation of the refractive index of the resonators.

Figure 2:

Thermal tunability in single semiconductor meta-atom resonators.

(A) and (B) Infrared spectra of Si (a, r=1.9 μm) and Ge (b, r=1.54 μm) spherical Mie resonators. Experimental spectra show good agreement with the calculated Mie scattering and FDTD cross-sections σ_sca normalized to the geometric cross-section σ_geo. A series of multipolar resonance peaks are visible in the spectra and correspond to dipole, quadrupole, hexapole, octapole, etc. (C) and (D) Temperature-dependent spectra of the spherical resonators between 80 K and 900 K. The spectral shifts of magnetic and electric dipole (MD and ED) and quadrupole (MQ and EQ) modes are highlighted. The dashed lines track the temperature-dependent resonance peaks and are a guide to the eye. The MO shift is also highlighted in the Ge resonator and is elaborated on in Figure 3. (E) and (F) The extracted induced index and resonance wavelength shifts as a function of temperature for MD and ED modes in Si (E) and Ge (F). Dots are experimentally extracted values, while solid lines are calculated shifts based on Mie theory.

When thermally generated FCs are negligible, all resonances are expected to red shift in response to a positive thermal gradient due to the normal positive dn/dT in both Si and Ge. This behavior is confirmed for both particles between cryogenic temperatures and up to 500 K. For more elevated temperatures, the shift in the long wavelength dipole modes deviates from the near-linear increase in wavelength. This behavior is more prominent in Ge due to its smaller bandgap and lighter effective mass (Supporting Information Section 1), which respectively facilitates higher FC concentrations at each given temperature and a larger index shift for a given carrier density. In Figure 2E and F, we track the temperature-dependent resonance wavelength shifts of the MD and ED, with respect to the RT resonance wavelength, and extract the corresponding index shifts Δn. Using our model for the temperature-dependent permittivity of the semiconductors (Supporting Information Section 1), we compare ex periments to calculated resonance and index shifts of the ED and MD modes (also see Figure S3, Supporting Information). For Si, the curvature of dn/dT significantly changes only above ~770 K and exclusively for the MD mode (due to its longer wavelength), as seen by the peak in both Δn and Δλ at ~800 K. Above the peak, the induced index and resonance wavelength decrease due to the generation of n_i>10¹⁷ cm³ FCs; the sign of dn/dT has reversed (dn/dT<0) and now causes a slight blue shift for the MD mode (at this point, the curvature of the ED mode is also affected as it starts to flatten).

For the Ge resonator (Figure 2F), FC effects are more prominent and emerge at lower temperatures. Due to its smaller bandgap and lower effective masses, the dispersion of the induced index Δn of the MD mode starts to flatten at ~550 K, peaks at 600 K, then decreases at higher temperatures (dn/dT<0). For even more elevated temperatures, FCs dominate the index change, giving rise to a larger magnitude |dn/dT|. The behavior of the ED is similar, but the change in curvature of Δn is shifted to higher temperature T~675 K since the FC effect is smaller at shorter wavelengths. Altogether, these results show that the dispersion, the sign, and magnitude of dn/dT can be controlled with temperature in low and moderate bandgap semiconductor resonators through the generation of FCs. This can be used to engineer the dispersion of dn/dT and for tuning of infrared meta-atoms and resonators.

The ability to maximize the control over the phase and amplitude of incident light depends on the capability of tuning resonance wavelengths by more than one linewidth Δλ/FWHM>1. Figure 3 presents the normalized tunability (Δλ/FWHM) of a high-order magnetic octapole (MO) mode that is tuned by ~4.5 normalized linewidths across the 123–773 K temperature range. This wide normalized tunability becomes possible due to an order of magnitude increase in the resonance Q-factor of Q_MO=88.1 compared with Q_MD=8.2 for the MD mode. As evident from Figure 3A, the normalized tunability exhibits a linear like dependence up to 675 K, with almost one normalized linewidth per 100 K. For ~T>675 K, the linear dependence breaks as FC effects become significant, which leads to a rapid saturation of tunability with increased temperature. Figure 3B presents the spectral shift of Δλ/FWHM=1.2 with a temperature gradient of ΔT=100 K. Such tunability with a practical temperature difference of ΔT=100 K would be useful for implementing reconfigurable high-Q Ge metasurfaces.

Figure 3:

Normalized tunability (Δλ/FWHM) of high-order MO mode in the Ge resonator.

(A) Temperature-dependent MO shifts normalized to the resonance linewidth. (B) Tuning by more than one resonance linewidth (Δλ/FWHM=1.2) with a ΔT=100 K temperature gradient.

A different route for increasing the TO normalized tunability is to exploit the larger TOC at shorter wavelengths in the vicinity of the material bandgap. As seen in Figure 1C, the dn/dT values are up to 50% larger in Si around 1 μm. Below, we demonstrate thermally reconfigurable metasurfaces in the NIR range using a Si disk array on SiO₂ substrate. Figure 4A shows experimental and FDTD reflection spectra of a silicon disk array with disk diameter and height of d=290 nm and h=280 nm, respectively, and periodicity a=590 nm. Both experimental and FDTD spectra show pronounced MD and ED resonances (Q~21) at λ=1.12 μm and λ=0.95 μm, respectively. The experimental temperature dependence of these resonances is presented in Figure 4B (the spectra are vertically shifted along the y-axis for visibility), where both dipole modes are continuously red shifted with increasing temperatures. The extracted index and resonance wavelength shifts Δn and Δλ are presented in Figure 4C for both dipole modes (Δn and Δλ are calculated with respect to index and resonance wavelengths values at RT). The higher TOC at shorter wavelengths is evinced by a larger induced index shift Δn for the ED mode compared to the MD mode. Extracted dn/dT values for both MD and ED modes are similar or slightly higher than reported values [51]. These high dn/dT values at the ED resonance wavelengths, combined with relatively narrow linewidths (Q~21), allows for tunable metafilter operation (Figure 4D) with amplitude modulation of more than 95% (13 dB) for ΔT=380 K at λ=950 nm [60% (4 dB) amplitude modulation for ΔT=280 K]. Further reduction in the required temperature modulation may be achieved by engineering ultrahigh-Q metasurfaces (such as the high-order Mie resonance presented in Figure 3) that enable normalized tunability Δλ/FWHM>1 with temperature modulation of tens of kelvin or less [32], [41]. Importantly, thermal tunability in Si metasurfaces can be extended to the visible range, with improved performance due to the expected increase of dn/dT at shorter wavelengths. Also, thermal tuning can be implemented using electrically controlled architectures with independent control for each element [45], [48].

Figure 4:

Thermally reconfigurable Si metasurfaces.

(A) RT NIR reflection spectra of a Si metasurface disk array with disk diameter and height of d=290 nm and h=280 nm, respectively, and periodicity a=590 nm on a SiO2 substrate. Experimentally measured (black) and FDTD (red) spectra are in good match showing the fundamental MD and ED modes. The inset presents an SEM image of the metasurface. (B) Temperature-dependent spectra exhibiting continuously red-shifted MD and ED resonances with increasing temperature. The spectra are vertically shifted along the y-axis for visibility. (C) Thermally induced index and wavelength shifts of MD and ED modes. (D) Thermally reconfigurable metafilter demonstration, exhibiting 4 dB and 13 dB amplitude modulation when a temperature gradient of ΔT=280 K and ΔT=380 K is applied, respectively.

3 Conclusions

In summary, we studied the thermal tuning capabilities of Si and Ge single resonators and metasurfaces over the large temperature range 80–873 K. We demonstrated temperature-dependent resonance frequency shifts that follow a modified model of the traditional TOE that takes into account effects of thermally generated FCs. We showed that at low and intermediate temperatures, all resonances red-shift according to the normal positive dispersion of TOC (dn/dT>0). At higher temperatures and longer wavelengths, however, thermally generated FCs contribute a negative component to the total TOC and can reverse its sign, i.e. yielding a dn/dT<0. This dispersion anomaly is evinced by a continuous change in the resonance shift from red- to blue-shift. We also demonstrated more than a unit of normalized tunability Δλ/FWHM=1.2 of high-order octapole modes in Ge resonators with a temperature gradient of ΔT<100 K. Ultimately, we exploit the larger TOC at short NIR wavelengths in Si to demonstrate thermally reconfigurable metasurface functionality such as amplitude modulators and tunable metafilters. This work highlights the opportunities and potential of thermally tunable semiconductor metasurfaces and can pave the way to efficient high-Q reconfigurable metadevices.

4 Methods