Fano Resonance Enhanced Infrared Absorption for Infrared Photodetectors

Transcription

1 Fano esonance Enhanced Infrared Absorption for Infrared Photodetectors Zexuan Qiang, Weidong Zhou *, Mingyu Lu, and Gail J. Brown 2 Department of Electrical Engineering, NanoFAB Center, University of exas at Arlington, X 769, USA 2 Air Force esearch Laboratory, Materials & Manufaturing Directorate, Wright Patterson AFB, OH 45433, USA ABSAC We report spectrally selective I absorption enhancement in the defect-free photonic crystal cavities, via Fano resonances. For a symmetric slab structure (air-slab-air membrane) with an absorptive layer in the center of the slab, enhanced absorption can be observed with enhancement factor ~8 for certain range of r/a values at wavelength of 4 µm. Similar results can also be achieved in an asymmetric slab structure (air-slab-semiconductor substrate), where higher index substrate is feasible for the proposed I detectors, with optimized design. his important feature ensures flexible design for infrared photodetectors incorporating photonic crystal cavities. Detailed simulations were carried out to understand the design trade-offs on the key parameters, such as the substrate index, the absorption layer thickness, and the air hole radius. Keywords: Photonic crystals, Fano resonances, Infrared photodetectors.. INODUCION Infrared (I) photodetectors with wide spectral coverage ( to 2 µm) and controllable spectral resolution are highly desirable for absorption spectroscopy gas sensing and hyper-spectral imaging applications. Owing to the lightmatter interaction modifications, spectrally selective absorption can be achieved in photonic crystal cavities. We reported earlier enhanced spectrally selective I absorption in photonic crystal slab (PCS) defect cavities, due to the coupling of the vertical/out of the plane radiation mode with the in-plane defect mode []. ecently, great attention has been paid to guided resonances, a class of leaky modes in PCS. hese guided resonances are standing electromagnetic waves that are guided with the electric field distribution confined within PCSs, but are also strongly coupled to out-of-the-plane radiation modes due to phase matching provided by the periodic lattice structure. herefore, guided resonances can provide an efficient way to channel light from within the slab to the external environment, and vise versa. he interaction between the discrete guided resonances and the continuum incident radiation manifests itself in the form of very sharp peaks in the transmission spectrum, called Fano resonances [2, 3], or guided mode resonance (GM) in D grating structures [4, 5]. Unlike PCS structures with a complete photonic bandgap, the effects of guided resonance phenomena do not require exceptionally high index contrast. he substrate index requirement is also substantially relaxed [6]. his Fano resonance effect has been investigated, both theoretically and experimentally, in photonic crystal structures for filters [7-], modulators[2, 3], sensors [4, 5], thermalradiation spectral and spatial control [6], broadband reflectors[7, 8], surface emitting lasers [9], bistable and other nonlinear optical devices [2, 2]. Here, we report spectrally selective I absorption enhancement in the defect-free photonic crystal cavities, via Fano resonances. he spectral location of Fano resonances can be controlled with several design parameters, such as the ratio of the air hole radius to the lattice constant (r/a), the refractive index and slab thickness, and the absorption layer properties. For a symmetric slab structure (air-slab-air) with an absorptive layer in the center of the slab, enhanced absorption can be observed with enhancement factor ~8 for certain range of r/a values, where a typical absorption coefficient of 4 cm - at wavelength of 4 µm was used. he impact of design parameters have been investigated in terms of the spectral tunability and absorption enhancement factor. Most importantly, we achieved similar results for an asymmetric slab structure (air-slab-substrate), with enhancement factor with enhancement factor ~6 to 7, depending on the r/a value and the substrate index. his important feature ensures flexible design for infrared photodetectors incorporating photonic crystal cavities. * wzhou@uta.edu. Photonic Crystal Materials and Devices VII, edited by Ali Adibi, Shawn-Yu Lin, Axel Scherer, Proc. of SPIE Vol. 69, 69F, (28) X/8/$8 doi:.7/ Proc. of SPIE Vol F-

2 In what follows, the proposed photodetector structure and the simulation setup will be discussed in Sec. I, where the spectrally dependent absorption was derived and the absorption enhancement factor was computed, based on the ratio of the absorption in PC cavities to that in slabs without PC cavities. he effect of parameters on a symmetric slab structure (air-slab-air) with an absorptive layer in the center of the slab will be then discussed in Sec. II, followed by the similar discusses in an asymmetric slab structure with high index substrate. he conclusions are given in the end. 2. FANO I PHOODEECO AND HE SIMULAION SEUP he Fano I photodetector structure is shown schematically in Figure (a), where a square lattice air hole structure is used in the design and simulation reported in this paper. A unit cell has size a by a; and r denotes the radius of the air holes. he cross-sectional view of the layered structure is shown in Figure (b), for either symmetric structure (air-slabair) or asymmetric structure (air-slab-substrate). he thin film semiconductor slab consists of an absorptive/dispersive layer in the center with refractive index of n 2. his absorption layer extinction coefficient k 2, i.e., the imaginary part of the refractive index, was tuned for different absorption coefficient α ( k 2 = αλ /(4π ) ), where λ is the wavelength. In our simulation, we assumed this layer to be epitaxially grown InAs quantum dot layers, commonly used in the quantum dot infrared photodetectors (QDIPs), with n 2 and k 2 dispersion curves shown in Figure 2, for wavelengths from 3 to 7 µm. he Lorentz model is used for the frequency dependent dispersion property modeling for the quantum dot absorption layer [22, 23]. he indices and the thicknesses for the top and bottom layer of the slab are assumed to be the same, with n of 3.43, and t =.4a, unless otherwise noted. a r (i) Symmetric air-slab-air t, n t 2, n 2,, k 2 t, n (ii) Asymmetric air-slab-substrate Planewave source Monitor P t, n Monitor P B a a ~ Substrate n s ~ PML (a) (b) (c) Figure (a) Fano I photonic detector structure (top) and the square lattice air hole lattice configurations (bottom); (b) Cross-sectional views of (i) symmetric air-slab-air structures and (ii) asymmetric air-slabsubstrate structures; and (c) Cross-sectional view of the computational setup for the calculations of transmission/reflection/absorption in Fano PC structures. A single unit cell of photonic crystals (shown in the dash line enclosed area of (a)) is incorporated in the simulation domain enclosed with the periodic bounding conditions in the lateral directions and perfectly matched layers on the vertical direction. Frequency-dependent three-dimensional (3D) finite-difference time-domain [2, 24] simulation technique was used here. he computational domain, which only contains the region of a unit cell, is shown in Figure (c). A planewave source is placed above the slab with incident direction perpendicular to the slab (surface normal direction). wo power monitors are placed above and below the slab region, to record the top and bottom spectral power density (P, P B ), respectively.. Perfectly matched layer (PML) boundary conditions are used to truncate the computational domain along vertical direction. For the remaining four lateral boundaries, periodic boundary condition (PBC) are applied [6]. he same simulation was performed for the slab waveguide without photonic crystals as the reference. he absorption results were normalized to the one obtained from the reference sample (slab without PC). he monitor power values (transmitted spectral densities) were shown in Figure 3(a) for a symmetric slab suspended in air, with photonic crystal patterns, and without (as a reference, shown in grey colored curves). Note there are two dominant Fano resonances with asymmetric lineshapes observed from the coupling between the vertical continuum of radiation modes, and the in-plane discrete resonant modes, as shown in Figure 4, where the top view and t, n t 2, n 2,, k 2 PBC:Periodic boundary condition PML: Perfectly matched layer PBC Proc. of SPIE Vol F-2

3 cross-sectional view of the mode field profiles are shown for both resonant and non-resonant modes. For the Fano resonant modes I (λ = 3.6 µm) and II (λ = 4.7 µm) shown in Figure 3, the modes are strongly confined to the photonic crystal slab region. By contrast, non-resonant modes have a field intensity distribution that quickly radiates away from the slab and into the surrounding medium (e.g., λ = 5. µm). efractive index n, k n k Figure 2 eal and imaginary parts of the absorptive layer refractive index n 2, k 2, used in this work. Monitor Values (a.u.) Normalized / op P Bottom P B (a).2 (b) Normalized Absorption Enhancement factor Mode I Mode II Figure 3 Simulation results for the symmetric structure shown in Fig. with the following parameters: a = µm, r/a =.5, t 2 =.2a, n s =. (a) Power monitor values (top P and bottom P B ) for the slab with PC patterns. he monitor values from the reference slab without PC are also plotted as the virtually overlapped grey colored lines. (b) he transmission and reflection from the PC slabs; (c) Normalized absorption plots; and (d) Absorption enhancement factors. he transmission, defined as the ratio of the transmitted power with slab (P Slab B ) to the power without slab (air only, (P Air Slab Air B ), i.e., = P B / PB. Similarly, the reflection, can be derived based on the following equation: Air Slab Air = ( P P ) / P. he absorption A can then be obtained with A =. o be able to compare the different absorptions, we introduce an enhancement factor F, as a figure of merit, to quantify the absorption enhancement, by comparing the absorption with and without PC slabs. F can be calculated with the equation: F = A PCS / A Slab. Based on the monitor values shown in Figure 3(a), the transmission and reflection curves are (c) (d) Proc. of SPIE Vol F-3

4 plotted in Figure 3(b). he normalized absorption and the absorption enhancement factors are shown in Figure 3(c), and Figure 3(d), respectively. An absorption enhancement factor of was obtained at one of the Fano resonances (Mode I in Figure 3), with a quality factor Q of 58. (a) Fano esonance Mode I, λ=3.6 µm (b) Fano esonance Mode II, λ=4.7 µm (c) Non-esonant Mode λ=5. µm Figure 4 op view (top) and cross-sectional view (bottom) of simulated field profiles for two resonant modes ((a) Mode I and (b) Mode II) identified in Figure 3. he cross-sectional views show the in-plane confinement of these resonant modes. Also shown is in (c) is the non-resonant mode, where the field intensity distribution quickly radiates away from the slab and into the surrounding medium. 3. ABSOPION IN FEE SANDING MEMBANES 3. Effect of Absorption Layer hickness he symmetric air-slab-air structure was first investigated to understand the impact of various design parameters, including the absorption layer thickness and the air hole sizes. As discussed earlier ( Figure 3 and Figure 4), the absorption enhancement factor can be greater than at Fano resonant mode locations, as compared to the case where the slab does not have PC patterns on it. However, we do see multiple Fano resonant modes appear. In general, a thicker absorption layer is preferred wherever possible, for maximum absorption, especially under operation conditions where the material absorption coefficient is relatively low (e.g. QDs in the mid-wave and long-wave I regions). However, further increase in the absorption layer thickness can lead to increased numbers of Fano resonant modes and reduced mode spacing. As shown in Figure 5. the absorption, along with transmission and reflection, were plotted for different absorption layer thicknesses (t 2 varies from.2a to.42a), while all other parameters were kept the same, i.e., a =2.772 µm, r/a =.5. his finding agrees well with the slab waveguide theory. With the increase in the slab thickness (due to the increase in the absorption layer thickness), more and more guided resonances with closer mode spacings appear. Based on this, we set the absorption layer thickness to be.2a for the following simulations. 3.2 Effect of Air Hole Size he impact of the air hole size was subsequently investigated with fixed absorption layer thickness t 2 of.2a. As shown in Figure 6 (a) to (c), with the increase of air hole size or r/a ratio, the Fano resonances will shift towards the short wavelength, consistent with the photonic crystal theory. On the other hand, the absorption enhancement factor changes differently, depending on the mode spectral location and quality factors. For two different modes (denoted as Mode I and Mode II ), we see the optimal enhancement factor appears at different r/a values. Generally, we can argue that smaller r/a value is favorable for larger enhancement factors. he argument can be further validated with Figure 6 (d), where the enhancement factors were plotted from a different set of structural parameters, where n =n 3 =3.463, t =.a, t 2 =.a, t 3 =.a. Intuitively it is reasonable. he absorption enhancement factor is determined by two major factors: (i) increased absorption at resonances due to Fano resonance effect; (ii) reduced absorption due to the reduction in the actual absorption areas with the presence of etched air holes through the absorption layer. Smaller r/a values mean large effective absorption areas for the air hole based PC slabs, which can lead to effectively large absorptions, assuming the impact due to the Fano resonance itself remains largely similar, to the first order. Based on these findings, we will set the absorption layer thickness to be relatively thin (t 2 of.2a), and the air hole radius to be relatively small (r/a =.5). Proc. of SPIE Vol F-4

5 Normalized Absorption.8 (a) t 2 =.2a (b) t 2 =.22a (c) t 2 =.32a (d) t 2 =.42a Normalized ransmission () and eflection () Figure 6 he impact of air hole size on Fano resonant modes Figure 5 he impact of absorption layer thickness on Fano resonant modes..6 2 Mode I Mode II.5a.5.8a Mode II.2a a.27a.3 6 Normalized absorption Absorption peak (µm) (a) Mode II Mode I elative hole radius r/a (b) Absorption Enhanced factor Absorption Enhanced factor Mode I elative air hole radius r/a (c) 8 Mode c Mode b 3 Mode a elative hole radius r/a (d) Proc. of SPIE Vol F-5

6 4. ABSOPION IN ASYMMEIC MEMBANES WIH SUBSAES For most practical device applications, the presence of substrate is beneficial for the desired electrical, mechanical and thermal properties. Often, such substrate can be either a relative low index glass substrate, or higher index semiconductor substrate, such as AlGaAs or GaAs, InP, etc. Our objective here is to find out the limitation of high index substrate on the device performance, mostly the resonance peaks and the absorption. he simulation results are shown in Figure 7, where cases were simulated with different substrate indices. Based on Figure 7 (a) to (c), for the same slab structural parameters shown in Figure 3, it is concluded that in addition to the Fano resonant modes, more and more substrate modes appear with the increase of the substrate index, shown as multiple spikes on the shorter wavelength side. his sets an upper limit on the substrate index. On the other hand, single Fano resonant peak in the spectral regime of interest is feasible with the optimized design, as shown in Figure 7 (d), where a =.5 µm, r/a=.2, t =.5a, t 2 =.2a, and n s = 2.5. It is expected that even high substrate index is feasible with further optimization of the slab design. his flexibility of Fano resonance based device design offers significant advances for practical design applications. he absorption enhancement factor was also calculated and plotted in Figure 8, where the enhancement factor F varies from 6 to 7, depending on the substrate index and the Fano resonant modes. his result is similar to the values discussed earlier for the symmetric slab structures, which indicates that the enhancement factor is largely independent to the substrate index. his found is also very critical for the practical design of Fano I detectors with substrates. Normalized Absorption.8 (a) n s =,a=2.772µm (b) n s =.5,a=2.772µm (c) n s =2,a=2.772µm (d) n s =2.5,a=.5µm Normalized ransmission () and eflection () Figure 7 he impact of substrate index on Fano resonant modes, where substrate index varies from (a) n s = to (d) n s =2.5. Note other design parameters are the same for (a) to (c) with r/a=.5, t =.4a,t 2 =.2a, and a = µm. he simulation parameters for (d) are r/a=.2, t =.5a,t 2 =. 2a, and a =.5 µm. Proc. of SPIE Vol F-6

7 Enhancement factor (F) n s = n s = n s =2 n s = Figure 8 he absorption enhancement factor for Fano I detectors with sustrates. All the parameters are the same as the ones shown in Fig CONCLUSIONS In conclusion, we reported here spectrally selective I absorption enhancement in the defect-free photonic crystal cavities, via Fano resonances. For the symmetric slab structure (air-slab-air membrane) with an absorptive layer in the center of the slab, enhanced absorption can be observed with enhancement factor ~8 for certain range of r/a values at wavelength of 4 µm was obtained, where smaller r/a values and thinner absorption layers are preferred for high performance I detectors. Similar results can also be achieved in an asymmetric slab structure (air-slab-semiconductor substrate), where the presence of the substrate modes sets an upper limit on the substrate index to be used. Higher index substrate is feasible with optimized slab structures. his important feature ensures flexible design for infrared photodetectors incorporating photonic crystal cavities. 6. ACKNOWDGEMENS his work was supported in part by the U.S. Air Force Office of Scientific esearch, and in part by the exas Space Grant Consortium. eferences [] W. Zhou, L. Chen, Z. Qiang, and G. J. Brown, "Spectrally selective infrared absorption in a single-defect photonic crystal slab," Journal of Nanophotonics, vol., p. 355, 27. [2] S. Fan and J. D. Joannopoulos, "Analysis of guided resonances in photonic crystal slabs," Phys. ev. B, vol. 65, p. 2352, 22. [3] U. Fano, "Effects of Configuration Interaction on Intensities and Phase Shifts," Phys. ev., vol. 24, p. 866, 96. [4]. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett., vol. 6, p. 22, 992. [5] S.. hurman and G. M. Morris, "Controlling the spectral response in guided-mode resonance filter design," Appl. Opt, vol. 42, pp , 23. [6] A. osenberg, M. Carter, J. Casey, M. Kim,. Holm,. Henry, C. Eddy, V. Shamamian, K. Bussmann, S. Shi, and D. W. Prather, "Guided resonances in asymmetrical GaN photonic crystal slabs observed in the visible spectrum," Opt. Express, vol. 3, pp , 25. Proc. of SPIE Vol F-7

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