1. Introduction

Metamaterials are artificial media whose electromagnetic response can be precisely controlled by the arrangement and geometry of resonant metallic structures with feature sizes much smaller than the incident wavelength [1–6]. Dynamic tuning of the electromagnetic response by means of external stimuli of either optical [7], mechanical [8], electric [9] or magnetic origin [10], offers a novel path towards metamaterial-based adaptive optics. Optically tunable metamaterials typically rely on spatially dependent excitation of free carriers in semiconductors embedded in plasmonic metamaterial structures and thus on dynamic reshaping of the electrically conducting areas in the metamaterial structure [7]. Such approaches enable spectral THz band-stop filters with a red-shift [7] or blue-shift [11] of the resonance frequency, switching between different unit cell designs [12], or switching the handedness in THz chiral molecules [13].

In the past, most fabrication methods for optically tunable metamaterial devices followed a very simple approach for the embedding of semiconductors in the metamaterial. Basically, the plasmonic metamaterial structure was fabricated on top of a thick semi-conductor substrate as e.g. silicon-on-sapphire (SOS) [7, 11–13] or other bulk semiconductor wafers like GaAs [14]. In such devices, free carriers are typically excited by inter-band transitions which occur e.g. at a wavelength of the tuning laser of around 800nm. Moreover, the photo-excitation requires high pulse energies that can be usually delivered by ultrafast amplifiers at typical pulse repetition rates of 1kHz [7].

Yet these approaches face two major hurdles on the path to potential industrial applications. First, using semiconductor bulk wafers inherently induces etalon effects due to reflections from the front and back surface of the substrate and thus leads to distinct wavelength-periodic THz transmission spectra that superimpose and interfere with the desired spectroscopic data [15]. Hereby, the free spectral range of the etalon is determined by $\mathrm{\Delta }v=\frac{c}{2nd}$, where c is the speed of light, n the substrate’s refractive index and d its thickness. Assuming e.g. a refractive index of sapphire of 3.07 at 1THz [29] and a sapphire thickness of 530εm, we obtain a free spectral range of 93GHz. Considering THz time-domain spectroscopy in the range between 0.1 and 2THz, we observe that the spectrum of interest is clearly superimposed by the etalon effect which readily complicates the retrieval of the plain spectroscopic data. Since ∆ν is inversely proportional to the substrate thickness, it is advisable to shift the free spectral range out of the spectroscopic range of interest by significantly decreasing the thickness of the embedded semiconductor. The fabrication and incorporation of thin semiconductors in metamaterial structures is non-trivial. Recently, Fan et al. reported a fabrication method based on specifically grown GaAs [28]. In this paper, we demonstrate a simple fabrication method for the embedding of ultra-thin silicon that does not require specific growing and makes use of standard industrial silicon wafers.

2. Challenges and benefit of thin layer Silicon

Before explaining this fabrication method, we would like to point out the basic challenges when working with ultra-thin substrates. A crucial parameter for efficient optical tuning of metamaterials is the recombination life-time of the photo-excited carriers. Furthermore, we require high energies to excite a sufficiently high carrier volume density in the semiconductor layer which can be usually only obtained by ultrashort, high power laser pulses from ultrafast amplifiers. In commercial systems, the pulse duration of about 100fs is typically much shorter than the time between consecutive pulses of about t_rep = 1ms, corresponding to a pulse repetition rate of f_rep = 1/t_rep = 1kHz. Upon photo-excitation by a laser pulse the excited carriers decay within the 1/e recombination carrier lifetime τ_r, which is a material characteristic, depending especially on the semiconductor impurity density [16] and surface preparation [17]. In standard non-radiation-damaged SOS τ_r lies in the nanosecond range [18], and in the ps to fs-range for radiation-damaged SOS [19]. As a natural condition for stationary tuning the condition τ_r > t_rep must be fulfilled.

The process of photoexcited carrier accumulation by pulsed laser illumination can be approximated by an approach that assumes a constant quantum efficiency over time. In such a model, the charge carrier density decays exponentially within the carrier recombination lifetime τ_r between consecutive pulses. That way we obtain an accumulation of the photoexcited carrier density ∆n with time t that can be formally described by

Hereby, ∆n₀ denotes the charge carrier density excited by a single pulse, Θ is the Heavyside function and k describes the pulse number.

For this consideration it is assumed that the pulse duration t_pulse is negligible compared to the repetition rate t_rep, which is true for typical pulsed laser system used for these experiments, where t_rep ≃ 10⁻⁷s − 10⁻³s and t_pulse ≃10⁻¹²s. After a certain number of excitation pulses, the charge carrier density enters a quasi-steady-state regime, where the carrier density added by a new pulse is compensated by the decay of the previously generated carrier density.

In order to realize a high quasi-steady-state carrier density, we need to combine a laser system with a high repetition rate and a semiconductor layer with a high carrier lifetime, which then allows a quasi-continuous device operation. For a laser system with f_rep = 80MHz, eq. 1 tells us that carrier lifetimes greater than 1ms would cause a charge pile-up to carrier densities in the range of 10¹⁸ cm⁻³, which would be comparable to the induced carrier density following a single pulse excitation of a f_rep = 1kHz system, provided that both systems deliver equal average pump power. Choosing silicon as the semiconductor offers the possibility for large scale fabrication at low cost, which renders it an ideal choice for semiconductor based metamaterial devices. Yet, such high carrier lifetimes are typically not obtained in the SOS fabrication procedure and also not in most other thin film deposition techniques. One main reason for reduced carrier lifetimes in thin semiconductors is the effect of surface/interface recombination [16], which becomes even more dominant with decreasing thickness of the semiconductor and can be mitigated by passivating the silicon surface [17], e.g. with SiO₂ [20]. For passivated Czochralski-grown silicon wafers, carrier recombination lifetimes in the range of 60εs are reported [21]. The purer float zone silicon can yield even higher carrier recombination lifetimes in excess of 1ms, even without additional surface passivation [22].

3. Sample fabrication

In the following we demonstrate a fabrication method for the implementation of ultra-thin, flexible and optically tunable metamaterial membranes with stable tuning characteristics for the example of a bandpass filter. The basic scheme and the unit cell of the filter are shown in Figs. 1(a) and 1(b). At the core of this approach stands the embedding procedure of a thin film silicon layer that exhibits sufficiently high carrier lifetimes. We oriented our basic approach on the fabrication technique for thin passive metamaterial films reported by Paul et al. [23], in which a (non-tunable) metallic metamaterial structure is sandwiched between two thin layers of BCB (Cyclotene 3022-63 resin from The Dow Chemical Company) and thus constitutes a flexible membrane, which can be bend by more than 180°. In order to obtain an active, optically tunable metamaterial film with mechanical flexibility, we had to deal with the problem to embed an ultra-thin silicon layer of a thickness of about 4εm underneath the plasmonic metamaterial structure. As a first step, we thinned a commercially available 525εm thick silicon wafer of sufficiently low impurity density by means of etching processes. In the experiments performed here, we used standard double-side-polished float zone silicon wafers with a surface resistivity in excess of 10kΩcm. First, we performed a wet chemical etching process in 30wt% potassium hydroxide (KOH) mixed 5:1 with isopropanol (IPA) at 60°C. During the electrochemical reaction of the Si with the OH⁻ ions of the aqueous KOH solution, hydrogen evolved [24] and the hydrogen bubbles locally blocked the transport of reactants to the surface [25] which lead to a masking of the reaction sites [26] and an increase of the surface roughness. Adding IPA improved the morphology of the surface, especially at lower concentrations [27]. This technique resulted in a high etching rate of ≈ 25 εm/_h, proving itself as a fast and reliable way for thinning wafers. We used double-side-polished silicon wafers because single-side-polished wafers exhibit a surface roughness in the εm-range, causing a large variation in the resulting layer thickness. We then positioned the thin silicon layer on a 10εm thick layer of BCB, which had been spin-coated on a 525εm thick handling substrate and soft-baked by heating it from 60°C to 90°C in 30min and keeping at 90°C for 30min. Afterward, we bonded the two layers, silicon and BCB, during the BCB hardcure procedure at 220°C for 12h in a vacuum oven, yielding an easy to handle and robust layer system consisting of 20 εm silicon on 10 εm BCB. In the following we further thinned the silicon by Reactive Ion Etching (RIE) (Roth&Rau MicroSys 350) in a plasma at a pressure of 10⁻³ mbar and gas flow of 30sccm SF₆, 5sccm O₂, 5sccm CHF₆ and 5sccm He for cooling purposes. With these parameters, we realized an isotropic etching rate of 0.18^εm/_min. The samples discussed here displayed a final silicon layer thickness of about 4εm.

 

Fig. 1 (a) Schematic of a thin-film optically tunable metamaterial bandpass filter, (b) Optical microscope image of the unit cell with the dimensions: a = 25εm, b = 19εm, c = 61εm, d = 54εm, unit cell size 78εm

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After thinning the silicon, we evaporated a 0.2εm thick copper layer on the silicon, patterned it by conventional photolithography and spin coated another 10εm thick protection layer of BCB on the plasmonic structure. We finally detached the BCB/Si/Cu/BCB layer system from the substrate used to handle the samples, and obtained a flexible, optically tunable metamaterial membrane with a total thickness of about 25εm. The silicon thinning and transfer procedure outlined here exhibits the advantageous option to choose silicon of any desired composition, especially silicon with a suitably low impurity density and thus high charge carrier recombination lifetime. Further, by altering the etching parameters, the silicon layer thickness can be adjusted by less than 1 εm, which allows to design the THz absorption characteristics of the final device.

4. Experimental results compared to simulation

We characterized the fabricated metamaterial membranes in two different THz time-domain spectroscopy (TDS) setups with different laser sources for photo-excitation, one with f_rep = 1kHz at a pulse energy of up to 415 εJ and the other with f_rep = 80MHz at an approximately 7 · 10⁴ times lower pulse energy of up to 6.2 nJ. Figure 2(a) shows the measured spectrally resolved amplitude transmission through the bandpass filter for increasing pump power of the photo-excitation using the 1 kHz system. By tuning the charge carrier density in the silicon, we obtained a modulation depth of 98% for tuning the pulse energy from 0εJ to 415εJ. In addition to a decrease in transmission, the resonance frequency shifted by 100GHz towards higher frequencies for an increase of the pulse energy from 0εJ to 41.5εJ. We also numerically calculated the transmission spectrum using the software package CST Microwave Studio (MWS) as shown in Fig. 2(b). We modelled copper as a lossy metal with a conductivity of σ = 5.8 · 10⁷ Sm⁻¹. The permittivity of BCB was ε_r = 2.67 and we used experimental data for the frequency-dependent loss tangent $\tan \delta =\frac{\kappa }{n_r}$, resulting in a loss tangent of tan δ = 0.00944 at 0.75THz [23].

 

Fig. 2 a) Measured amplitude transmission spectra of the band-pass filter for different photoexcitation energies at 800nm and f_rep = 1kHz. The layer system of the filter was BCB/Si/Cu/BCB with thicknesses 10εm/4εm/0.2εm/10εm. b) Corresponding numerical calculation of the amplitude transmission spectra of the filter.

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We described the dielectric response of silicon by a Drude model [30]:

with ε_∞ = 11.9 describing the material response for high frequencies ω or low plasma frequencies ω_p. Hereby, we accounted for scattering of the excited charge carriers by use of an effective damping constant Γ.

For the non-tuned state we found good agreement between the numerical and experimental data when choosing a plasma frequency of $\frac{{\omega }_p}{2\pi }=2.5\text{THz}$. THz. This frequency corresponds to a free carrier density of approximately 5 · 10¹⁴ cm⁻³ which is slightly higher than the expected value for n-Si with a resistivity of 10 kΩcm. Yet, an increase of the plasma frequency seems justified since we expect an additional doping of silicon during the fabrication process. To take the photoexicited charge carrier density n into account, we increased the plasma frequency ω_P stepwise to $\frac{{\omega }_p}{2\pi }=39\text{THz}$ in accordance with the relation ${\omega }_P\propto \sqrt{n}$.

We observed an excellent agreement between the measured and simulated data. The increase in the plasma frequency perfectly reproduces the measured decrease in amplitude transmission as well as the blue shift of the center frequency for an increasing average photoexcitation power. Without photo-excitation, the FWHM bandwidth of 0.27THz of the fabricated bandpass filter has been slightly broader than the numerically calculated bandwidth of 0.20THz. In this respect, it should be noted that we conducted the experiments in a standard air environment where the water vapour introduces distinct absorption lines in the THz spectrum. This explains the discrepancies between experiment and simulation at 0.9THz and 1.0THz. Also the water absorption lines at 0.56THz and 0.75THz might contribute to a broadening of the slope of the band-pass and thus to an increased spectral bandwidth.

We further examined the filter in a second THz-TDS setup with a repetition rate of 80 MHz to evaluate its applicability when approaching a quasi-continuous wave regime. In this experiment, we used a f_rep = 80MHz laser for the photoexcitation of carriers in the silicon. Figure 3(a) shows the amplitude transmission through the filter for different pulse energies of the photoexcitation, revealing a maximal modulation depth of 10 % at 6.2 nJ excitation pulse energy. As discussed above, the pulse energy was about 7 · 10⁴ times smaller than in the 1 kHz system which results in a reduced modulation depth. From the numerically calculated spectra we can determine a maximal photo-excited conductivity of 18Sm⁻¹ (Fig. 3(b)) which corresponds to an averaged carrier density of about 1 · 10¹⁵ cm⁻³. By aid of Eq. 1 we can estimate the carrier lifetime in the silicon layer to be about 70ns. In comparison with float zone silicon, the carrier lifetime in our silicon layer is rather low. This can be explained by the direct contact between the silicon layer and the copper layer. Due to a continuous energy spectrum of electrons in metals, the non-radiative recombination at the metal-semiconductor interface is strongly enhanced which results in a decrease of carrier lifetimes [20]. In principle, this effect could be reduced by applying a thin passivation layer to the silicon, e.g. silicon nitride or silicon oxide, which would not impair the performance of the metamaterial device.

 

Fig. 3 a) Measured amplitude transmission spectra through the band-pass filter for different photoexcitation energies at 780nm and f_rep = 80MHz. The layer system of the filter was BCB/Si/Cu/BCB with thicknesses 10εm/4εm/0.2εm/10εm. b) Corresponding numerical calculation of the amplitude transmission spectra of the filter.

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5. Conclusion

In conclusion, we demonstrated a novel fabrication procedure for optically tunable, ultra-thin and flexible terahertz metamaterial membranes with an embedded semiconductor thin film. The main advantage of the methodology lies in the usability of commercially available silicon wafers that are thinned to a thickness of a few εm and fully embedded in the metamaterial membrane. Based on this technology, we fabricated an optically tunable, ultra-thin terahertz bandpass filter of 25εm thickness with a peak transmission of 85 % at an operating frequency of 0.65THz. Using a tuning laser with a repetition rate of 1 kHz, we demonstrated a maximal amplitude modulation depth of 98 %. We further discussed the impact of the carrier lifetime on the tuning characteristics of the device. The demonstrated fabrication technique can be adapted to semiconductors other than silicon, but is especially suited for the implementation of ultra-thin optically tunable metamaterial membranes based on low-cost commercially available silicon wafers without the need for sophisticated growing processes.