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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 24, NO. 7, APRIL 1, 2012
Automated Design, Fabrication, and Characterization of Color Matching Plasmonic Filters Kirsty Walls, Qin Chen, Steve Collins, Member, IEEE, David R. S. Cumming, Senior Member, IEEE, and Tim D. Drysdale
Abstract— Plasmonic filters, with spectral responses matching the 1931 International Commission on Illumination (CIE) color matching functions, have been fabricated for use in digital imaging. The color matching filters are useful for effectively communicating color between color detection and output devices. A fully automated genetic algorithm that incorporated on-demand 3-D finite-difference time-domain simulations determined the dimensions for the red (600 nm), green (555 nm), and blue (445 nm) filters. The filters demonstrated resonances in the desired spectra with transmission of 25%–35%. These filters were simultaneously fabricated in a single electron beam lithography cycle using materials common to standard complementary metal–oxide–semiconductor production. Index Terms— Color, filters, finite difference methods, genetic algorithms, image sensors, plasmons.
I. I NTRODUCTION
F
ILTERS are essential components of colour digital imaging systems. Filters, typically centred at red, green and blue wavelengths, analyse the spectrum of the incoming light. The correct choice of filter properties enhances the accuracy of colour reproduction and must be appropriate for use with the sensing technology. The continuing advances of the complementary-metal oxide-semiconductor (CMOS) fabrication process technology results in ever smaller pixel sizes, yet filters in most commercial image sensors continue to be implemented by spin cast organic or pigment dye films fabricated in back-end of line (BEOL) processes. Multilayer dielectric stacks [1], [2] have been presented as an alternative. These deep structures require multiple process steps, with non uniform processing between pixels making them difficult and expensive to fabricate. Alternatively, plasmonic structures can be made in materials that are relatively straightforward to process and fully compatible with CMOS fabrication requirements. Further, no additional infra-red blocking filters are
Manuscript received October 3, 2011; revised December 6, 2011; accepted January 6, 2012. Date of publication January 16, 2012; date of current version March 16, 2012. This work was supported in part by the Engineering and Physical Sciences Research Council under Grant EP/G008329/1. K. Walls, Q. Chen, D. R. S. Cumming, and T. D. Drysdale are with the School of Engineering, University of Glasgow, Glasgow G12 8LT, U.K. (e-mail:
[email protected];
[email protected];
[email protected];
[email protected]). S. Collins is with the Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, U.K. (e-mail:
[email protected]). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LPT.2012.2184531
required because an array of holes in a metal sheet forms a high pass filter. Here we show how an advanced design process can be used to obtain arbitrary filter characteristic yet retain the same layer thickness in a thin metal-dielectric stack for all structures. Plasmonic colour filters have already been successfully integrated onto CMOS photo detectors [3]. The existing plasmonic colour filters are equivalent to the red, green and blue filters used in conventional cameras. However, with plasmonic filters it is possible to generate more sophisticated spectral responses. The arbitrary filter characteristics with which we demonstrate our approach are the 1931 International Commission on Illumination (CIE) 2° standard observer colour matching functions [4] (CMF) (x(λ), y(λ), z(λ)) that represent the response of the long, medium and short wavelength sensitive cones of the human visual system. The CMF serve to effectively communicate colour between colour capture and reproduction devices [5]. Implementing CMF filters reduces colour reproduction errors [6]. In order to implement the CMF we require to produce plasmonic filters with simultaneously optimised resonance central wavelength, full-width half-maximum (FWHM), transmissivity and in the case of one filter an additional resonance. The CMF cannot be obtained simply by scaling existing plasmonic filter designs. II. F ILTER D ESIGN Plasmonic filters exploit the excitation of surface plasmon resonances (SPR) by nanoscale surface structures in metal films [7]. As the SPR wave vector is larger than that of light for any given frequency, a momentum mismatch must be overcome. One method of achieving this is by the scattering of light from arrays of subwavelength holes. Resonant peaks in the transmission are achieved by localised SPR mode excitation at the hole edges. The centre wavelength and bandwidth are dependent on the material properties and the pattern geometry. The transmission peak λ0 , for a rhombic lattice array, is approximately εd 2π εεmm+ε d λ0 = 2π 2π 2 2π 2 (k|| cosφ + i ax + j ax ) + (k|| si nφ − i 2π ay + j ay ) (1) where εm and εd are the dielectric constants of the metal and dielectric respectively, k|| is the in-plane wave vector
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WALLS et al.: AUTOMATED DESIGN, FABRICATION, AND CHARACTERIZATION OF COLOR MATCHING PLASMONIC FILTERS
Fig. 1. Plasmonic filter structure. (a) Cross-section. (b) Scanning electron micrograph of a rhombic hole array of the fabricated green (555 nm) filter before oxide deposition.
magnitude and φ the azimuthal angle of incident light, ax and a y the lattice dimensions and i , j the scattering orders of the array [8]. Unfortunately no analytical solution is available that simultaneously predicts FWHM in addition to λ0 . The glass/Al/SiO2 filter structure [9] we use is shown in Fig. 1. Metals such as gold are often preferred due to their lower absorption [7], but we chose aluminium for its CMOS process compatibility and lower cost. Multiple design parameters influence performance [9] including the hole diameter (d), the lattice period (ax and a y ) and the layer thickness (t Si O2 and t Al ). An enhanced design and simulation procedure was applied to vary these parameters with the aim to identify filter designs to provide the spectral sensitivity curves, referred to as the red (600nm), green (555nm) and blue (445nm) filters. To optimise the parameters a genetic algorithm (GA) was used [10]. GA have been applied successfully to solve many electromagnetic design problems, for example the design of frequency selective surfaces [11]. For this application a steady state GA replacement strategy was implemented. A simple system of ranked population truncation was utilised; the proportion of the least fit solutions eliminated was determined by the pcross parameter. A random mutation process was implemented with a probability defined by the user ( pmut at ion ). The optimisation procedure is executed in Octave (an open source numerical computing environment) with the user specifying the algorithm variables as arguments. Initial testing indicated that pcross = 0.6 and pmut at ion = 0.05 gave a useful rate of change of population. Convergence was satisfactory at 100 iterations. In work not shown here, we extended the number of iterations to 200 without observing significant improvement in the filter performance. Fitness was evaluated by calculating the mean square error (MSE) between the solution response and the desired CMF. Since it is the relative response at the different wavelengths that is important the error was calculated after the spectra had been normalised to have the same maximum amplitude. Solutions with transmission ≤ 25% were rejected. To enable all the filters to be fabricated in a single step the metal and top layer thickness must be the same for all three designs. The red filter was designed first because it represented the most challenging optimisation problem due to the double peak and hence would benefit most from being
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Fig. 2. Simulated spectral responses of the GA optimised filters (dashed) compared to the CMF [4] (solid) normalized to the maximum transmission of the simulated filters. TABLE I F ILTER PARAMETERS (S EE F IG . 1) AS I DENTIFIED BY THE D ESIGN P ROCEDURE . t Si O2 = 220 nm AND t Al = 70 nm FOR A LL F ILTERS Filter Red Green Blue
d (nm) 160 140 100
ax (nm) 500 300 380
ay (nm) 420 620 260
MSE 2.47×10−3 0.91×10−3 1.33×10−3
able to treat the layer thicknesses as design variables. The layer thicknesses required by the red filter were set as constants in the subsequent designs of the green and blue filters. The filter set with the best overall performance is presented. The GA was combined with a finite-difference time-domain (FDTD) simulator based on TEMPEST [12], to form a fully automated optimisation process. Input files were generated from the design parameters selected by the GA. A single unit cell of the infinitely periodic structure was bounded above and below by perfectly matched layers and excited by a normally incident plane wave comprising of two orthogonal linear polarisations (equivalent to an unpolarised source) with a modulated Gaussian pulse waveform. The dispersive properties of the aluminium in the visible spectra were defined by the Drude + 2 Critical Points model [13]. The refractive index of the substrate and top layer was assumed constant (n = 1.462) with negligible loss. The cell size was x, y, z = 10nm. The optimisation of the three filters required approximately 15000 processor hours. Such simulations are routine even on modest high performance computing clusters. On our 256 core machine, the total simulation time is equivalent to three days, although slightly longer in practice due to scheduling constraints. The optimum parameters for the structure as identified by the design process are presented in Table I along with the MSE, and the resultant transmission spectra are shown in Fig. 2. The procedure successfully designed a red filter with two transmission peaks as desired (440, 600nm). It is difficult or impossible to achieve the ancillary peak in traditional dye based filters. The performance in Fig. 2 assumes unpolarised light. For linearly polarised incident radiation, the electric field vector should be orientated at 45° to the vectors ax and a y .
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depend on the material refractive index and absorption, which vary with deposition technique and equipment. These factors could be readily accounted for in the well-controlled conditions of a production foundry utilising dedicated equipment for each process step. IV. C ONCLUSION
Fig. 3. Measured (dashed) spectral responses of the GA optimized filters, compared to the CMF (solid).
III. FABRICATION AND R ESULTS The filters were fabricated simultaneously onto a glass slide. The procedure for device fabrication and measurement was identical to that used by Qin et al [9], with the exception of the structure parameters presented in Table I. An unpolarised halogen lamp and lens with a numerical aperture of 0.5 was used to measure the fabricated filters. The hole array of the green filter before oxide deposition is pictured in Fig. 1(b), with d = 139nm. The performance of the fabricated filters is plotted in Fig. 3. The MSE between the experimental results and the normalised CMF are 6.89 × 10−3 , 2.77 × 10−3 and 6.71 × 10−3 for the blue, green and red filters respectively. All the filters produced the desired bandpass response. The measured transmission was 25-35% for the three structures, slightly reduced compared to the simulated values of 35-46%. The minor difference in the relative peak transmission amplitudes of the three filters with respect to the standard CMF will be readily accommodated by the variable gain routinely applied to each colour channel within the camera, as part of the routine colour balancing step, that is used to compensate for changes in the spectrum of the light illuminating the scene. The FWHM were 100-150nm, or 40-75nm larger than predicted by simulation. Both effects are attributed to minor variations in the hole shape and non-zero line edge roughness. Simulations indicated that the secondary peak (at λ = 440nm) in the x(λ) CMF should be realisable in this structure however as a consequence of the broadening this peak was not separately resolved in the experimental results. The broadening effect would be minimised by using a smaller number of holes in each filter when integrated them into a CMOS imaging chip. The transmission maximum for the blue filter was shifted 10nm to 435nm. We conducted additional simulations, not shown here, that calculated such a shift could occur if 50% of the holes had a reduction of 10nm in the radius, also giving rise to a 13% reduction in transmission. This hole variation also resulted in shoulders on the resonances, similar to those observed in the measured filter spectra. The smaller structures of the blue and green filter are the most susceptible to the fabrication tolerances. Similarly variations in the top SiO2 layer have been shown to alter performance [9]. The transmission properties of the filters also
A fully automated design procedure using GA and a 3D FDTD simulator has been developed for the implementation of arbitrary characteristics in plasmonic filters. We demonstrated the utility of the approach by designing three CMF filters that can be fabricated in a single lithography step. The filter performance was in good agreement with simulations, yielding transmission of 25-35%. The designed filters represent a cost saving over conventional dye based filters due to a reduction in the number of processing steps and the use of inexpensive CMOS foundry compatible materials. Furthermore the implementation of CMF filters offers enhanced accuracy of colour reproduction in digital imaging systems. Further extension of the design process is possible to optimise additional parameters or to compensate for the spectral response of the sensing element. R EFERENCES [1] Y. Inaba, M. Kasano, K. Tanaka, and T. Yamaguchi, “Degradation-free MOS image sensor with photonic crystal color filter,” IEEE Electron Device Lett., vol. 27, no. 6, pp. 457–459, Jun. 2006. [2] K. Engelhardt and P. Seitz, “Optimum color filters for CCD digital cameras,” Appl. Opt., vol. 32, no. 16, pp. 3015–3023, Jun. 1993. [3] Q. Chen, D. Chitnis, K. Walls, T. D. Drysdale, S. Collins, and D. R. S. Cumming, “CMOS photo detectors integrated with plasmonic color filters,” IEEE Photon. Technol. Lett., vol. 24, no. 3, pp. 197–199, Feb. 1, 2012. [4] CIE 1931 Standard Colorimetric Observer Data [Online]. Available: http://www.cie.co.at/main/freepubs.html [5] G. Sharma and H. J. Trussell, “Digital color imaging,” IEEE Trans. Image Process., vol. 6, no. 7, pp. 901–931, Jul. 1997. [6] R. Hunt, The Reproduction of Color, 6th ed. Chichester, U.K.: Wiley, 2004. [7] C. Genet and T. W. Ebbensen, “Light in tiny holes,” Nature, vol. 445, pp. 39–46, Jan. 2007. [8] W. Zhou, H. Gao, and T. W. Odom, “Toward broadband plasmonics: Tuning dispersion in rhombic plasmonic crystals,” ACS Nano, vol. 4, no. 2, pp. 1241–1247, Jan. 2010. [9] Q. Chen and D. R. S. Cumming, “High transmission and low color cross-talk plasmonic color filters using triangular-lattice hole arrays in aluminium films,” Opt. Express, vol. 18, no. 13, pp. 14056–14062, Jun. 2010. [10] J. M. Johnson and Y. Rahmat-Samii, “Genetic algorithms in engineering electromagnetics,” IEEE Antennas Propag. Mag., vol. 39, no. 4, pp. 7– 21, Aug. 1997. [11] M. Ohira, H. Deguchi, M. Tsuji, and H. Shigesawa, “Multiband single-layer frequency selective surface designed by combination of genetic algorithm and geometry-refinement technique,” IEEE Trans. Antennas Propag., vol. 52, no. 11, pp. 2925–2931, Nov. 2004. [12] A. Wong and A. Neureuther, “Rigorous 3-D time-domain finitedifference electromagnetic simulation for photolithographic applications,” IEEE Trans. Semicond. Manuf., vol. 8, no. 4, pp. 419–431, Nov. 1995. [13] A. Vial and T. Laroche, “Description of the dispersion properties of metals by means of the critical points model and the application to the study of resonant structures using the FDTD method,” J. Phys D, Appl. Phys., vol. 40, pp. 7152–7158, Nov. 2007.
