Tunable narrow-band infrared emitters from hexagonal lattices

Tunable narrow-band infrared emitters from hexagonal lattices

Photonics and Nanostructures – Fundamentals and Applications 1 (2003) 69–77 Tunable narrow-band infrared emitters from hexagonal lattices I. El-Kady ...

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Photonics and Nanostructures – Fundamentals and Applications 1 (2003) 69–77

Tunable narrow-band infrared emitters from hexagonal lattices I. El-Kady a,b,∗ , R. Biswas a , Y. Ye a , M.F. Su a , I. Puscasu c , Martin Pralle c , E.A. Johnson c , J. Daly c , A. Greenwald c a

Department of Physics and Astronomy, Ames Laboratory and Microelectronics Research Center, Iowa State University, Ames, IA 50011, USA b Sandia National Laboratories, Photonic Microsystems Technologies, P.O. Box 5800, MS 0603, Albuquerque, NM 87185, USA c Ion Optics, Inc., Waltham, MA 02452, USA Received 27 August 2003; received in revised form 24 September 2003; accepted 9 October 2003

Abstract In this work, we present both the theoretical basis as well as supporting experimental measurements for development of a novel mid-infrared thermally stimulated narrow band emitter with a spectral bandwidth of less than 10%. To achieve this, we utilize a metallized-surface 2D photonic crystal of air voids in a silicon background with hexagonal structure symmetry. Our results are based on the generation of discrete surface plasmon (SP) modes in the thin metallized layer residing on the top surface. This yields a series of adequately spaced discrete peaks in the reflection spectrum, dominated by a single sharp feature corresponding to the lowest plasmon order, in an otherwise uniform highly reflective spectrum (>90%) over most of the IR spectrum. This, in turn, gives rise to a sharp absorption feature with a correspondingly narrow thermal emission peak in the emission spectrum. Transfer matrix calculations simulate well both the position and strengths of the absorption peaks. By altering the period of the surface photonic lattice, the SP peak and emissive band can be tuned to the desired wavelength. These devices promise a new class of tunable infrared emitters with high power in a narrow spectral bandwidth. Such narrow band sources are critical to achieving high efficiency gas sensors. © 2003 Elsevier B.V. All rights reserved. Keywords: Infrared emitters; Spectral bandwidth; Surface plasmon modes; Infrared gas sensors

1. Introduction Sensors of trace toxic gases are of great importance to diverse fields such as meteorology, environmental protection, household safety, bio-hazardous material identification, and industrial environments. Home environments need to detect minute concentrations of ∗ Corresponding author. Tel.: +1-5052844308; fax: +1-5058448985. E-mail address: [email protected] (I. El-Kady).

CO, whereas early detection of a host of other toxic effluents such as SO2 , CH4 , NO are needed in various manufacturing environments. The underlying principle of infrared (IR) gas sensing relies on the unique IR absorption signatures of most gases due to IR-active vibrational modes in the 2–14 ␮m region. This enables conclusive identification and quantification of molecular species in liquid and gas phase mixtures with little interference from other gases. However, this requires the use of extremely narrow band emitters and detectors for resolving the

1569-4410/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.photonics.2003.10.002

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different signatures. For example, to spectroscopically detect carbon monoxide by detecting its absorption at 4.65 ␮m, its signal needs to be distinguished from the 4.26 ␮m absorption of CO2 , thus requiring a narrow band source (≤9% width) to prevent a spurious signal from the tails. In this paper we design such a narrow band emitter utilizing the narrow absorption profile of surface plasmon (SP) modes in a metal-coated periodic lattice. Our results are further reinforced by actual experimental measurements from such a fabricated emitter. For the first time, we calculate and observe SP modes in a hexagonal surface lattice far sharper than the previously reported square lattice structures [1].

2. Theoretical development The theoretically modeled and fabricated lattice (Fig. 1) consists of a gold-coated silicon wafer in which circular or square perforations (of diameter d) have been made to a depth, t. The thickness of the metal film (tm ) is much smaller than t (typically 5–8 ␮m). The perforations are arranged in a hexagonal lattice of lattice constant a. The corresponding reciprocal lattice vectors are   2π 1 G1 = 1, − √ a 3

Fig. 1. (a) Experimentally fabricated hexagonal lattice of circular metal trenches on a metal-coated silicon wafer, with a lattice constant (nearest-neighbor separation) of a = 3 ␮m. The scale bar is 4 ␮m. (b) Schematic cross-section of hexagonal structure showing patterning in silicon wafer and metal coating. (c) Schematic of the actual numerically modeled structure.

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  2π 2 G2 = 0, √ a 3 Such periodic metal films have longitudinal SP modes propagating along the surface (with an E field and charge oscillation along the propagation direction) and an exponentially decaying amplitude perpendicular to the interface. The SP dispersion relation [2] is given by   ω ε1 ε2 1/2 ksp = (1) c ε1 + ε 2 ε2 is the real part of the metallic dielectric function, which is negative and large in magnitude for IR frequencies. ε1 describes the response of the dielectric media. Since the SP dispersion lies below the incoming light line for any angle of incidence (θ), incoming light cannot directly generate SPs on a smooth surface. When an incident light beam of frequency ω impinges on the patterned surface at an angle θ, it can couple to an SP at the air–metal interface through a surface reciprocal lattice vector: [3,4] ω (2) sin θ nˆ + G = k sp , c where nˆ is a unit vector lying in the plane of incidence and θ is the angle of incidence with respect to the

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normal to the surface of the crystal, assumed here to be the xy-plane. By combining the dispersion relation (1) with this momentum conservation condition (2), we obtain the following eigenvalue equation for the SP frequencies:    ε 1 ε2 ν0 2 = sin θ cos φ ± i ε1 + ε 2 ν   1 ν0 2 ν0 2 ¯ + sin θ sin φ+i √ ± j√ 3 ν 3 ν (3) Here, ν is the SP frequency, i and j are integers, φ is the azimuthal angle, and ν0 = c/a. The fundamental SP mode (i = 1, j = 0 or i = 0, j = 1, corresponding to the√first shell of G vectors) occurs at a wavelength of 3a/2. The wavelengths (Fig. 2) decrease with increasing shells of G vectors. The strength of higher-order SP modes is expected to decrease rapidly beyond the fundamental mode. In addition to the upper gold–air interface, there is the lower gold–silicon interface, where SPs with the same symmetry also propagate. The calculated wavelengths of the SP modes for the gold–air (ε1 = 1), gold–Si (ε1 = 12), and a metal–oxide (ε1 = 2) interface, obtained from Eq. (3), are shown in Fig. 2. The wavelength of the gold–silicon SPs is about a factor of

Fig. 2. Surface plasmon mode wavelengths obtained from a solution of the simple SP theory (Eq. (3)) as a function of the magnitude of the G vectors used in Eq. (3). Results are shown for gold–air (ε = 1), gold–silicon oxide (ε = 2), and gold–silicon (ε = 12) interfaces.

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ε1 (∼3.5) longer than the corresponding gold–air SP modes. The simple plasmon theory predicts well the location of the SP modes, but to calculate the reflection/ absorption of the metal surface, we utilize the wellestablished transfer matrix method (TMM). In the TMM electromagnetic (EM) waves of fixed frequency impinge on a structure that is periodic in two dimensions but finite in the third direction. Calculations were performed for the structure in Fig. 1, where the patterned hexagonal lattice of trenches is etched in a thick metal-coated silicon wafer. We developed a new technique to eliminate unphysical reflections from the back surface of the thick silicon wafer from occurring in the calculations. We use a virtual silicon substrate in the TMM where the real component of complex dielectric function is gradually graded from the silicon value to that of air. At the same time, the imaginary component is gradually stepped up to maintain an overall fixed magnitude of the dielectric function equal to that of silicon. This method prevents reflection at any interface in the graded structure

and the substrate absorbs all radiation incident on it, similar to the experimental measurements with thick substrates. Computations with the virtual silicon substrate have been very successful in comparing with the measured SP modes on square lattices [1]. TMM simulations utilized the frequency-dependent real and imaginary components of the dielectric function of gold [5] for two lattices (a = 3 ␮m, d = 1.5 ␮m; a = 4 ␮m, d = 2 ␮m). The gold layer thickness (tm ) was taken to be 0.5 ␮m. For a normally incident wave, we find (Fig. 3) exceedingly sharp reflectivity √ dips at the fundamental SP mode wavelength (λ= 3a/2), as expected from the simple SP theory (3). The reflectivity falls to almost 0.25 from a long-wavelength value of 0.85–0.9, exhibiting an exceedingly narrow full-width half-maximum (FWHM) of 0.13 ␮m, where the incident wave is absorbed by the sharp SP resonance on the gold substrate. The narrow FWHM corresponds to ∆λ/λ0 = 0.05. We repeated calculations for a square trench with the same width and depth as the circular feature as in Fig. 3, and found virtually identical results for the reflectivity

Fig. 3. Calculated reflectivity from the transfer matrix method (TMM) as a function of wavelength for two hexagonal lattices with a = 3, d = 1.5 ␮m and a = 4, d = 2 ␮m. d is the hole diameter.

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Fig. 4. (a) Measured reflectivity of a hexagonal lattice of air trenches (structure of Fig. 1) as a function of wavelength. The lattice constant is 4.2 ␮m. (b) Measured emissivity as a function of wavelength for experimentally fabricated hexagonal lattice (inset) with a = 4.2 ␮m. An oxide layer is in between the gold film and silicon substrate.

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and position of SP resonance, with a slight increase of line width to ∆λ/λ0 = 0.06. The calculated central reflectivity dip is degenerate for both polarizations. However, the p-polarization also produces a weak dip at 2.6 ␮m (3.4 ␮m) for the a = 3 ␮m (4 ␮m) lattices, at a slightly smaller wavelength than the principal SP resonance. The wavelength of the absorption feature scales simply with the lattice constant a (Fig. 3). These are the first theoretical calculations to calculate the sharp SP of a hexagonal lattice ideally suited for a narrow emission source. The next higher SP mode (i = 2, j = 1) at λ = 0.52a is visible as a very weak dip at 2 ␮m in the TMM calculation for the a = 4 ␮m lattice. Due to computational constraints on finite-size computational grids, we model the gold coating to 0.5 ␮m thickness. This is somewhat thicker than the experimental value, 0.12 ␮m. We have, however, verified that a decreased thickness of 0.19 ␮m generates very similar results. The important point to realize, however, is that both the numerical and the actual experimental metallic coating thicknesses are larger than the metallic skin depth (0.025 ␮m) [6]. The width and depth of the SP resonance strongly depend on the size of the air pores relative to the period, d/a, which determines the filling ratio. Both calculations and measurements indicate that d/a ∼0.5 is near the optimum value for the SP resonance. According to energy conservation, the absorption is A = 1 − R − T ∼ = 1 − R, since the transmission through the substrate is eliminated in the calculations. Experimentally, A ∼ = 1 − R since negligible transmission is observed through the thick gold-coated Si wafer. The absorption spectrum is thus characterized by a sharp peak complementary to the reflectivity calculation (Fig. 3). By Kirchoff’s law, the emission of the structure is equal to the absorption (A) weighted by the blackbody emissivity (K(ν, T)) at the temperature T of the measurement. E(ν, T) = A(ν)K(ν, T),

K(ν, T) =

8πhν3 /c3 ehν/kT − 1 (4)

Finally, an enlarged view of the calculated reflectivity displays very weak reflectivity dips (<1%) corresponding to SP modes of the gold/silicon substrate at 3.33 ␮m (4.43 ␮m) for the two lattices, correspond-

ing to the (3, 0) SP modes in Eq. (3). As the metal’s thickness is made thinner, the coupling to the back SP modes increases and their features become larger.

3. Experimental measurements Experimentally, a thermal-oxide-coated silicon wafer was coated with a multilayer of Ti/Au with thickness values of 0.02/0.12 ␮m and patterned with a hexagonal array of circular perforations (diameter d = 2.1 ␮m, trench depth t = 4.5 ␮m, lattice constant a = 4.2 ␮m), using photolithography and deep reactive ion-beam etching. A thick silicon substrate lies below the patterned region. Structures with trench depths varying between 0.5 and 8 ␮m were fabricated. The near-normal reflectance (incident angle θ ∼ 10◦ ) was measured with an FTIR (Fig. 4a). For a trench depth of 4.5 ␮m, the reflectivity shows a pronounced narrow dip at a wavelength λ ∼ a (a = 4.2 ␮m), with reflectivity as low as 0.1. The reflectivity rises to 0.7–0.8 in the long-wavelength regime, consistent with a patterned metal layer. The recovery of the reflectivity at short wavelengths is much weaker. The entire patterned wafer was heated to 325 ◦ C. The emission from the wafer was collected in a cone of angular half-width 10–11◦ about the normal. The measured emission (Fig. 4) consists of a narrow peak centered at 4.2 ␮m with a small half-width of ∼0.5 ␮m. The position of the emission peak agrees well with the fundamental SP-mode wavelength expected for this structure at an angle of incidence equal to the measurement cone apex angle (Figs. 2 and 3).

4. Discussion We develop a quantitative model to understand the measured reflectivity and emission. Since reciprocity of emission and absorption holds, it is sufficient to start with the absorption of the incident wave by the structure. The incident wave generates the top surface gold–air plasmon. There are two regimes. If the lifetime, τ, of this SP is long (compared to its period), the width of the absorption or emission feature is controlled by the envelope of the absorption profile around the normal direction. The shift in frequency of the absorption profile from an incident angle of 0◦ to an

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0.9

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Fig. 5. Calculated reflectivity as a function of wavelength, from the TMM simulations for off-normal incidence. The incident angle is 10.5◦ and the azimuthal angle varies from 0◦ to 30◦ . (a) s polarization (b) p polarization.

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experimental measured cone of width θ determines the emission width. In the second regime, the lifetime of the SP, τ, is short due to either: (i) the decay of the SP into the SPs of the lower gold–dielectric interface or (ii) the scattering of SPs at imperfections in the top surface. The scattering of SPs by defects is expected to be small since experimental structures have a high degree of perfection. The emission/absorption width ∆ν is thus controlled by the lifetime τ with ∆ν = 1/τ. Since the experimentally fabricated structures have excellent periodicity and high perfection, the major decay mechanism is expected to be the decay of the top SP into the lower-interface SPs. The frequency of the top SP, ν1 , should be equal to the frequency of one or a combination of two gold–dielectric lower-interface SPs: ν1 =ν2 ; or ν1 =ν2 + ν3 . However, the Au–air SP frequency ν1 of 114.7 THz is sufficiently mismatched from the lowest SPs of gold–oxide, where ν2 = 81.3 THz ((1, 0) mode) and ν3 = 140.4 THz ((1, 1) mode). Hence, the top SP decays only weakly to the lower-interface SP modes. We then expect the angular variation of the absorption profile to be the primary contributor to the emission width. Consequently, we calculate the shift of the absorption wavelength of the air–gold SPs with TMM calculations for off-normal incident beams, as a function of polar angle θ and azimuthal φ. Experimental measurements (Fig. 4) were confined to a narrow emission cone of θ of 10–11◦ about the normal for a hexagonal lattice and show a narrow emission band centered about λ ∼ a, (a = 4.2 ␮m). To model the measurements, we performed TMM calculations (Fig. 5) for off-normal incidence. As the angle of incidence is changed to θ = 10.5◦ (and φ = 0◦ ), the degeneracy is lifted and the s and p polarizations split into two reflectivity peaks with shorter and longer wavelengths of λ ∼ 0.7a–0.83a and λ ∼ a, respectively √ (Fig. 5). Notably, from a single peak at λ ∼ λ ∼ 3a/2 (for θ = 0◦ ), we see a new peak emerge at λ ∼ a (θ = 10.5◦ ). This angular dependence of the plasmon modes also emerges from Eq. (3). As the azimuthal angle is increased, the reflectivity dips become weaker and there is a weak shift of the reflectivity minima towards longer wavelengths (Fig. 5). In the simplest scheme, we linearly superpose the absorption profiles for different φ for θ = 10 − 11◦ to obtain the integrated reflectivity profiles (Fig. 5) for the two polarizations. The average of the p polariza-

tion (Fig. 5b) generates a deep reflectivity dip at near λ ∼ a, and a weaker feature near λ ∼ 0.8a–0.83a. The primary peak, in the measured reflection (Fig. 4a) at λ ∼ a can be identified with the longer-wavelength SP feature, evident in the p polarization. The observed shoulder in reflectivity near λ ∼0.88a is consistent with the position of the calculated shorter-wavelength feature. The azimuthal average of the multiple peaks in the s polarization (Fig. 5a) is more complex and is likely to contribute to the overall width of the reflectivity peak. The expected emission can be obtained by linearly superposing the absorption profiles for different θ and φ within the experimental width of ∆θ = 10–11◦ to obtain the integrated absorption profile (Fig. 5) for the two polarizations. The larger θ angles contribute a greater weight to the solid angle of the emission and lead to a peak near the wavelength λ ∼ a, similar to that of the averaged reflectivity (at θ = 10.5◦ , Fig. 5). Within this scheme the emission width is related to the angular averaged absorption profile. More detailed analysis incorporating the radiative strengths of the different SP modes and their coupling to photon modes of the silicon lattice are needed to quantitatively calculate the emission from this structure. Finally, the stronger recovery of the reflection spectrum in the shorter-wavelength regime observed in the calculations and not in the experimental measurements can be attributed to the numerical reflectivity of the virtual silicon substrate.

5. Conclusions In conclusion, we have presented a prescription for the design of a narrow IR band emitter with a spectral bandwidth of 9–10% ideal for use in gas-sensing applications. The sharp emission and accompanying sharp reflectivity from the hexagonal lattice are found to be dominated by the SPs at the top surface. Our theoretical predictions were further reinforced and supported by experimental measurements. Hence, the sharp absorption of an SP can be converted into a narrow-band thermal emitter and detector. Deviations between the ideal extremely sharp numerically modeled SP modes and the relatively wider experimental signatures were attributed to and successfully accounted for the angular roll-off in the measurements.

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In addition to possible applications in gas sensing, the emitter described here can be further tuned to produce an emission/absorption band in the optical wavelength regime. When stimulated, such a source would emit radiation exclusively in the visible, suppressing all the unwanted IR and thermal losses—thus allowing us to achieve directional narrow-band emission. This effect distinctly differs from the previously reported three-dimensional metallic tungsten photonic crystal of Fleming et al. [7], where the narrow allowed transmission and absorption band are a result of wave propagation in the three-dimensional metallic crystal. Using two-dimensional geometries, like the one at hand, it is thus possible to achieve directional narrow-band emission in the forward direction away from the metallic interface. The SPs in the present work resemble those in thin metallic films with sub-wavelength apertures [3]. The generation of SPs at the top surface of a thin metal film decays into SPs at the lower interface and is responsible for the anomalous transmission through sub-wavelength arrays.

Acknowledgements This work was partly supported by the NIST ATP program and the National Science Foundation. Ames

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Laboratory is operated by Iowa State University for the US Department of Energy under contract W-7405-Eng-82. The work at Sandia Laboratories is supported through the DOE. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin company, for the US Department of Energy under contract DE-AC04-94-AL 8500.

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