APPLIED PHYSICS LETTERS 96, 101111 共2010兲
Doping tunable resonance: Toward electrically tunable mid-infrared metamaterials Xiaoyu Miao,1,2,a兲 Brandon Passmore,1 Aaron Gin,1,2 William Langston,1 Shivashankar Vangala,3 William Goodhue,3 Eric Shaner,1 and Igal Brener1,2 1
Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185, USA Center for Integrated Nanotechnologies, Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185, USA 3 Department of Physics and Applied Physics, University of Massachusetts–Lowell, Lowell, Massachusetts 01854, USA 2
共Received 17 November 2009; accepted 17 January 2010; published online 10 March 2010兲 We demonstrate metamaterials at the mid-infrared 共mid-IR兲 wavelengths 共8 – 12 m兲 that can be widely tuned by doping in adjacent semiconductor epilayers. The metamaterials are based on metallic split ring resonators 共SRRs兲 fabricated on doped indium antimonide 共InSb兲. Finite integral time-domain simulation results and measured transmission data show that the resonance blueshifts when the semiconductor electron carrier concentration is increased while keeping the split ring geometry constant. A resonant wavelength shift of 1.15 m is achieved by varying the carrier concentration of underlying InSb epilayer from 1 ⫻ 1016 to 2 ⫻ 1018 cm−3. This work represents the first step toward active tunable metamaterials in the mid-IR where the resonance can be tuned in real time by applying an electric bias voltage to control the effective carrier density. © 2010 American Institute of Physics. 关doi:10.1063/1.3309707兴 The ability of metamaterials to create artificial electromagnetic properties absent in nature has initiated intense research efforts for applications in frequency selective surfaces,1 subdiffraction imaging,2 cloaking,3 etc. The development of tunable metamaterials, which allow for real-time tuning of the electromagnetic response, is emerging as an important subtopic in this field. Tunable metamaterials have the potential to become the building blocks of chip based active optical devices, such as switches, modulators, and phase shifters. A typical way to make such tunable metamaterials is to integrate a natural reconfigurable material in the metamaterial structure and apply an external stimulus to achieve tuning. For example, tunable metamaterials have been demonstrated using electrical reorientation in liquid crystals4 and thermally/electrically induced insulator-tometal phase transition in vanadium dioxide 共VO2兲.5,6 Recently, active terahertz metamaterials based on variants of SRRs on a doped gallium arsenide 共GaAs兲 substrate have been realized by dynamically changing the carrier concentration of the underlying semiconductor using an electric bias voltage, which effectively tunes the strength of the resonance,7 primarily producing an amplitude modulation effect. While gating the higher carrier densities required to impact the mid-IR frequencies 共8 – 12 m兲 is challenging, we use a structurally similar approach to explore the effects of semiconductor electrons to address the fundamental aspects of resonance tuning at this much higher frequency range 共⬃30 THz兲. As the first step toward dynamically tunable metamaterials in the mid-IR, we examine the response of mid-IR metamaterials consisting of SRRs fabricated on semiconductor substrates with different doping levels and demonstrate the first step required for electrical tuning through gating of mid-IR metamaterials. As shown in Fig. 1, the resonance of SRRs on a semiconductor substrate can be explained by an equivalent circuit a兲
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model, where the ring inductance is described by L, the split gap and fringing capacitance are denoted by C, the resistor R models the dissipation in the gold 共Au兲 split rings, and the resistor Rd models the dissipation due to the substrate free carrier absorption within the split gap 共and in the regions in close proximity to the metal lines兲.1,7 When the metal lines act as gates, the underlying carrier concentration, in principle, can be changed by the application of an electrical bias affecting thus both Rd and C. The resistance Rd is inversely proportional to the AC conductivity of the doped semiconductor material.8 The capacitance C is linearly related to the dielectric function of the semiconductor substrate due to the field lines fringing into the material.9,10 The resistance change in Rd influences the resonance strength while the capacitance change in C shifts the resonance frequency 共0 = 1 / 冑LC兲. In previous modulation work on doped GaAs,7 where the SRRs were designed to work at terahertz frequencies and the plasma frequency of the doped GaAs substrate matched this designed frequency, the resistance change of Rd was the dominant mechanism that modified the resonance. This is illustrated by the fact that mainly an amplitude modulation of the resonance was observed. In our devices we have a different situation where the built-in semiconductor plasma frequency p 共set by material properties and carrier density兲 lies (a)
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FIG. 1. 共Color online兲 共a兲 Schematic of a SRR on a semiconductor substrate 共top view兲. 共b兲 Side view of the metamaterial element. A voltage bias is applied between the metal resonator and doped semiconductor substrate to control the substrate carrier concentration. 共c兲 An equivalent circuit of the metamaterial element.
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FIG. 2. 共Color online兲 共a兲 Real component of complex dielectric function of InSb as a function of doping level at different wavelengths. 共b兲 Transmission spectra of SRRs on InSb substrate with different carrier concentration. The curves from right to left are the simulated transmission spectra of SRRs on InSb substrate at carrier concentrations of 1 ⫻ 1016, 1 ⫻ 1017, 5 ⫻ 1017, 1 ⫻ 1018, and 2 ⫻ 1018 cm−3, respectively. The inset shows the resonance wavelength of metamaterial vs carrier concentration in InSb substrate.
below the mid-IR metamaterial operating range. The AC conductivity of the doped semiconductor and thereby the resistance of Rd barely changes with the carrier concentration increases. The capacitance change 共through a change in the real part of the dielectric function兲 becomes the dominant mechanism and results in a resonance shift instead of an amplitude modulation when the carrier concentration of the semiconductor substrate varies. To enhance this tuning effect through a change in the dielectric function of the substrate, we choose InSb as it has a large dependence of dielectric function on doping levels. This effect has been used before for tunable subwavelength hole arrays,11 photonic crystals,12 etc. The real component of InSb’s dielectric function at mid-IR frequencies as a function of carrier concentrations is displayed in Fig. 2共a兲. This was calculated from published data using the Drude model, which includes scattering and measured values for carrier concentration dependent mobility13 and effective mass.14 As seen in this figure, the real part of InSb’s dielectric function decreases as the carrier concentration increases and such a trend becomes more significant at longer wavelengths. For instance, at the wavelength of 10 m, the real part of InSb’s dielectric function decreases from 15.6 to 11.0 as the doping level changes from 1 ⫻ 1016 to 2 ⫻ 1018 cm−3. According to the LC circuit model, a decrease in the real component of the substrate’s dielectric function will decrease the capacitance, and therefore shift the resonance to a higher frequency 共i.e., a shorter wavelength兲. To simulate the behavior of SRRs on InSb substrates with varying carrier concentrations, we use the frequency domain solver in CST Microwave Studio 共CST, Germany兲.15 The substrate consists of a 100-nm n-type doped layer grown on a semi-insulating InSb wafer. Gold SRRs were scaled from known designs such that the main resonance occurs at = 10 m 共arm length of 660 nm, arm width of 130 nm, gap of 100 nm, and thickness of 80 nm兲. The computed wavelength dependent dielectric functions of InSb at different doping levels were imported into the software and used for the simulation. For the dielectric function of Au, a fitted Drude model based on ellipsometric data measured in the mid-IR regime was used, with a plasma frequency of 1.27 ⫻ 1016 rad/ s and a collision frequency of 66 THz. A unit cell boundary condition was used to include the coupling effect between split ring resonators and the lattice constant between adjacent resonators was set as 1.34 m. Figure 2共b兲
shows the simulated transmission spectra of metamaterials at normal incidence when the polarization direction of the excitation light was parallel to the gap as shown in the inset and the carrier concentration of the doped InSb layer was varied. The simulated metamaterial resonances 共displayed as transmission minima兲 occur in the mid-IR range. More importantly, the resonances shift monotonically from 11.9 to 10.4 m when the carrier concentration increases from 1 ⫻ 1016 to 2 ⫻ 1018 cm−3 关inset of Fig. 2共b兲兴. Such resonance shifts are due to the differences in the dielectric functions of substrates when the carrier concentration in doped layer varies as discussed above. It should be noted that there is very little change in the Q-factor of these resonances as the doping is varied indicating that there is little effect of resistance shunting as observed at THz frequencies.8 Another way to look at the resonance shift is to study the transmission change at a specific wavelength; when the doping is varied from 2 ⫻ 1018 to 1 ⫻ 1016 cm−3, the metamaterial transmission at 10.4 m changes from 12% to 52%, which corresponds to a modulation depth of 62.5%. We also simulated the transmission spectra of metamaterials when the polarization direction of the excitation light is orthogonal to the gap and observed no resonance, as expected. For the experimental study, we fabricated metamaterial samples on four different InSb substrates. One of the substrates, a 共111兲 lightly doped InSb wafer without the doped epilayer, was chosen as a reference. The other three substrates consist of a thin n-type doped layer grown on the reference wafer by molecular beam epitaxy. The thicknesses of the doped layers in the three substrates are 150, 150, and 750 nm, respectively. The corresponding carrier concentrations of the doped layers are 2 ⫻ 1017 cm−3, 5 ⫻ 1017 cm−3, and 2 ⫻ 1018 cm−3. The carrier concentrations were determined from doped InSb layers grown on semi-insulating GaAs substrates by Hall measurements using the van der Pauw method at room temperature. The split ring resonators were patterned on InSb substrates using standard nanofabrication techniques including electron-beam lithography, metal deposition, and lift-off. The metamaterial elements were patterned with a period of 1.34 m to form a planar array of 2 ⫻ 2 mm2. The sample was spin coated with 495K C3 polymethylmethacrylate and baked at 170° for 30 min. The split ring structures were exposed using a JEOL JBX-6300FS electron beam lithography system operating at 100 kV and 1 nA beam current. The dose used for the small structures was around 1000 C / cm2. Electron beam evaporation was used to deposit 100 and 700 Å of Ti and Au, respectively. Lift-off was conducted in an acetone bath. A representative scanning electron microscope image of split ring resonators is shown in Fig. 3共a兲. To minimize the scattering from surface roughness during the transmission measurement, the backside of the samples was polished using a grinder-polisher. Transmission spectra of the fabricated metamaterials were measured using a Bruker IFS 125 Fourier-transform infrared spectrometer. Samples were analyzed at room temperature using a liquid-nitrogen cooled mercury cadmium telluride detector. A spectral resolution of 1 cm−1 was used and the data were averaged over 100 scans. An polarizer was placed in front of the sample so that polarization-dependent transmission could be recorded from = 0 ° – 90° in an increment of 15°, where is the angle between incident light polarization direction and the gap of the split ring resonator 共i.e., = 0° represents a polarization direction parallel to the
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FIG. 3. 共Color online兲 共a兲 Scanning electron microscopic image of the SRRs fabricated on InSb substrate. 共b兲 The resonance amplitude of SRRs fabricated on the InSb substrate at the doping level at 5 ⫻ 1017 cm−3 vs the angle between incident light polarization direction and the gap of the split ring resonator. The dots are the experimental measured values. The curve is a fit proportional to cos2 . 共c兲 The transmission spectra for the metamaterial with SRRs fabricated on the reference InSb wafer, and the other three doped substrate. The polarization direction of the incident light is parallel to the SRR gap. 共d兲 The resonance shift when the carrier concentration is increased from the intrinsic level. The curve shows the results from finite integral time-domain simulation. The dots are the experimentally measured values.
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gap; = 90° represents a polarization direction orthogonal to the gap兲. Figure 3共b兲 shows the amplitude of the resonance at different intersection angles 共measured on the sample with a carrier concentration of 5 ⫻ 1017 cm−3兲 and reveals that the amplitude of the resonance varies as cos2 , which represents the projection of the excited light intensity in the direction parallel to the gap. Such polarization dependence is consistent with the simulation results as discussed above and is indicative of excitation of the LC resonance of SRRs. The position of the LC resonance is found to be strongly dependent on the carrier concentration of the semiconductor substrate. Figure 3共c兲 shows the normalized transmission spectra of the four metamaterial samples used in this study. Each spectrum was taken with incident light polarization parallel to the gap. A clear blueshift of the transmission peak is seen as the doping level of the InSb substrate is increased. The experimentally observed trend of the metamaterial resonance as a function of substrate doping is consistent with both the LC circuit model analysis as well as the finite integral time-domain simulation. We plot this trend in Fig. 3共d兲 together with our simulation results. As shown, the experimentally observed shift is in very good agreement with the results from finite element simulations. The slight difference may be attributed to a number of factors, including the uncertainty in the measured carrier concentrations and the sizes of SRRs in different samples. Notice in our experiment the InSb substrate doped at 2 ⫻ 1018 cm−3 has a thickness as 750 nm, which is different from the other two. To examine the influence of doped layer thickness on the resonance shift, we simulated the SRRs on the InSb substrate with a doping level at 2 ⫻ 1018 cm−3 and different doped layer thickness. The simulation reveals that the resonance experiences a redshift only about 0.2 m when the doped layer thickness increases from 150 to 750 nm. By taking this into account, the general trend of resonance shift with doping level changes still holds. In conclusion, we have demonstrated the first step toward active tuning of metamaterials in the mid-IR using metallic metamaterials fabricated on InSb with various doping concentrations. The metametarials were designed to resonate at ⬃ 10 m and we showed a wavelength shift of the
metamaterial resonance of 1.15 m when the doping level is varied from 1 ⫻ 1016 to 2 ⫻ 1018 cm−3. Future activities will include the design and fabrication of electrically gated devices on in order to dynamically tune the metamaterial resonance in real time. We thank H.-T. Chen, A. J. Taylor, and M. Sinclair for useful discussions. This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a Lockheed-Martin Co., for the U. S. Department of Energy under Contract No. DE-AC0494AL85000. 1
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