Spectral Selectivity of Photonic Crystal Infrared Photodetectors Li Chen, Weidong Zhou *, Zexuan Qiang Department of Electrical Engineering University of Texas at Arlington, TX 769-72 Gail J. Brown Air Force Research Laboratory, Materials & Manufacturing Directorate Wright Patterson AFB, OH 45433-777 ABSTRACT In this paper, we present the simulation results on the absorption modification in photonic crystal (PC) structures. For one-dimensional (D) PC, using transfer matrix method (TMM), we obtained enhanced absorption in both defectfree and defect based PC structures. High absorption (>6%) and small bandwidth (<. λ ) at defect level were observed with optimal absorption layers of -5 for structures with single defect. We also present the modified infrared absorption in two-dimensional photonic crystal slabs (2D PCS), based on the three-dimensional finitedifference time-domain method (3D FDTD). The normalized absorption power spectral density in single defect based 2D PCS structures increased by a factor of 8 at the PC defect mode level. This enhancement factor is largely dependent upon the spectral overlap between the absorption material and the defect mode cavity. Complete absorption suppression within the photonic bandgap region was also observed in defect-free cavities, and in single defect cavities when the absorption spectral band has no overlap with the photonic bandgap. Keywords: Infrared absorption, Photonic crystals, Photonic crystal slabs, Defect mode, Infrared photodetectors.. INTRODUCTION Infrared (IR) photodetectors with wide spectral coverage and controllable spectral resolution are highly desirable for absorption spectroscopy gas sensing and hyper-spectral imaging applications []. Significant progresses have been made in quantum well and quantum dot based IR photodetectors (QWIPs, QDIPs) [2]. The incorporation of photonic crystals (PCs) [6] can lead to engineered spectral resolution with multi-spectral coverage in IR photodetectors. Simultaneous enhancement and suppression of absorption at different spectral locations is feasible via lithographically controlled photonic bandgap (PBG) and defect mode cavity. Theoretical investigation has been carried out on the spectrally selective absorption properties in one- and twodimensional (D, 2D) PC structures with and without defect. The work is based on transfer-matrix method (TMM) [9] and three-dimensional (3D) finite-difference time-domain (FDTD) [] technique. For defect-free D PC structures, enhanced absorption was observed at either lower or higher frequency bandedges, depending on the relative refractive index of absorptive layers. Wavelength selectivity as high as 4 was observed. For 2D symmetric air hole triangular lattice PC structures [], enhanced absorption at defect level was obtained, with the enhancement factor largely dependent upon the spectral overlap between the absorption material and the defect mode cavity. Complete absorption suppression within photonic bandgap region was observed in defect-free cavities, and in single defect cavities when the absorption spectral band has no overlap with the photonic bandgap. In what follows, the simulation setup and results will be discussed for D and 2D PC structures, with the conclusion given in the end. * wzhou@uta.edu; Tel: 877227. Nanomaterial Synthesis and Integration for Sensors, Electronics, Photonics, and Electro-Optics, edited by Nibir K. Dhar, Achyut K. Dutta, M. Saif Islam, Proceedings of SPIE Vol. 637, 637I, (26) 277-786X/6/$5 doi:.7/2.686565 Proc. of SPIE Vol. 637 637I-
2. MODELING AND COMPUTATIONAL RESULTS 2.. Absorption analysis of D PC using TMM As shown in Figure a. one-dimensional photonic crystals (D PC) consists of absorptive and non-absorptive layers arranged alternately, with refractive index and layer thickness of, d, and, d 2, respectively. The bulk material with equivalent absorptive thickness is also used as the reference (Figure b), with refractive index and thickness d. For N period D PC, the equivalent absorptive bulk material thickness d equals to Nd. D PC with absorptive layers Bulk absorptive material (reference) d d 2 d=n x d Absorptive layer Non-absorptive layer N Periods Figure Structures under simulation: D PC structure with absorptive layers; Reference bulk absorptive material with equivalent absorption layer thickness. n B Reflected A Incident B' B B'2 B2 B'2N B2N B'2N- B2N-. A' A A'2 A2 A'2N A2N A'2N- A2N- d d 2 n A2N Transmitted Figure 2 Schematic of the transfer matrix method (TMM) theory. From Transfer Martrix Method (TMM) theory (Figure 2), the whole structure was divided into unit cells each of which contains two transfer matrixes: P n and Q n, The former was applied on the field propagation in a uniform medium and the later was used for the interface between two media, i.e. A' A A A' = Q = P B' B B B' The overall transfer matrix M is expressed as the following equation, where,2,3 indicate the number of the unit cell counting from the incident direction: A2N A = M where M = Q2 N + PlQl B l= 2N The total transmissivity T and reflectivity R can be obtained from the elements of the transfer matrix as: T= M -M 2 M 2 /M 22 2 R= M 2 /M 22 2. Therefore, absorption A can be calculated from A=-T-R [2], assuming other losses are negligible. The simulation results for the absorptance are shown in Figure 3, for two different structures. Significant suppression in absorption, as compared to the bulk, is evident for the frequencies within the photonic bandgap (PBG). On the other hand, enhanced absorption occurs at either higher or lower bandedges of the PBG, depending on the relative refractive index differences for these two structures. Due to the energy concentration in the high-index region [3], the enhancement occurs at the lower frequency bandedge when the absorptive layer refractive index is higher. As shown in Figure 4, the normalized absorptance for the structure in Figure 3b is plotted for a small frequency (wavelength) range near the lower frequency bandedge. The spectral selectivity increases with the increase of the period. Additionally we found the ratio of the absorption enhancement and the absorption suppression was more than 4 for the case with periods. Proc. of SPIE Vol. 637 637I
To tune the absorption peak position, single defect and resonant cavity were introduced into the otherwise defectfree PC. Due to the existence of the strong localized mode, much stronger enhancement in the absorption was observed in the defect level, with close to % absorption (Figure 5). On the other hand, absorption saturation was observed in the conventional resonant cavity, as shown in Figure 5. Compared to the bulk structure with the same absorption layer thickness, an enhancement factor greater tha is evident for the single-defect D PC cavity. =.5+.5i =5+.3i D PC.8 =2.5.8 =3.5 Bulk (ref) N= periods.6.6 Absorptance.4 Absorptance.2 D PC.2 Bulk (ref) 2 4 6 8 2 4 6 ω/ ω ω/ ω 8 Figure 3 Simulated absorptance for D PCs, with the refractive index of the absorptive layer to be either lower or higher than that of the non-absorptive layer. The absorptance for the reference bulk material is also shown as the reference. 5 4 N= N=5.4 absorptance 3 2 PbSe =5. Silicon ( =3.5) xn.2.4.6.8 λ/λ Figure 4 Enhanced absorption spectra at bandedge with periods N=5,. n GaAs substrate n s n d N t =4 Defect N b =4,9,4 N t =4 Defect nd Absorption Absorption N b = 5.8 5.6.4.2.8.6.4.8.9..2 λ/λ N b = 5 5 N.2 n b =4,9,4 2.2 2 4 6 8 2 GaAs substrate n s Total Periods.8.9..2 λ/λ (c) Figure 5 PC with defect: distributed absorption at defect level with =3.6+.28i, =3., n s =3.5. Resonant cavity: cavity absorption at defect level with =3.5, =3. n s =3.5, and n d =5+.3i (c) Absorption comparison of, and bulk with periods from to 2. Absorption.8.6.4 PC with defect Bulk Resonant cavity Proc. of SPIE Vol. 637 637I-3
Frequency (ωa/2πc=a/λ) 2.2. 3D FDTD modeling on absorption property modulation Simultaneous inhibition and redistribution of spontaneous emission in PC has been demonstrated theoretically and experimentally in a lossless PCS structure [4]. Following a similar approach, 3D FDTD simulation was carried out in an air-slab-air PC cavity, with an absorptive layer in the center of the slab, as shown in Figure 6. Perfectly matched layers (PMLs) were incorporated at the boundaries of the computational domain to avoid unnecessary reflections of light at the boundaries. A dipole source was introduced in the center of the cavity, with power monitors placed at the boundaries to collect the transmitted spectral power density after Fourier-transformation from the average of the Poynting vectors. r/a=.4.6 Pn T/a=.8 nh=3.5.4 Pw a.2 Dipole Source M K 2r Pe Γ. Γ M T z PML: MatchedLayers Layers PML:Perfectly Perfect Matched 5-Layer Slab Air n = n=3.5 n = 3.6+ikα n = 3.5 Air n = Ps Γ K h = 2a h =.3a h =.2a h =.3a h = 2a Air x Pt y Pb Air x Absorption Power Spectral Density Figure 6 Photonic dispersion plot for the symmetric air-slab-air photonic crystal slab, with the thin absorptive layer inserted in the center of the slab; 3D FDTD simulation setup with dipole and monitor locations schematically shown. H defect-free Slab kα=.59 H single-defect - 2 H - M PBG Slab (no PC) - H D Monopole kα=.59 Dipole 2.5 3 3.5 4 4.5 5 - - 5.5 2 2.5 3 3.5 4 4.5 5 5.5 Figure 7 linear- and log-scale plots of absorption spectral power density for single-defect (H), defect-free (H) and slab without PC structures. The same approach was performed for the slab waveguide without PC as reference with one example shown in Figure 7, with the imaginary part of the refractive index ka=.6 (corresponding to absorption coefficient of 5x3cm- at λ=4µm). It is worth noting that two different defect modes exit in this simple single-defect (H) cavity, as confirmed by the mode property plots shown in the inset of Figure 7a. Based on the transmission spectral power density calculations, simultaneous enhancement and suppression of absorption were also found. As shown in Figure 8, the normalized absorption power spectral density is plotted for single defect (H) and defect-free (H) PC cavities. Note Proc. of SPIE Vol. 637 637I
that the dominant absorption occurs in the vertical (surface normal) direction, as compared to the in-plane absorption. While absorption suppression is evident inside the PBG region, the enhanced absorption is seen at the defect level, with the peak absorption enhancement factor of 8. Normalized Absorption 2 Top In plane H PC R (Top) H Defect-free k a =.6 2 2.5 3 3.5 4 4.5 5 5.5 wavelength (µm) Figure 8 Normalized absorption in single defect (H) and defect free (H) PC cavities for k a =.6. Further design optimization can lead to the shift in defect levels for desired absorption spectral selectivity with different absorption coefficients in single defect PC cavities. Normalized absorption power spectral density was derived from the results above together with the reference sample (slab without PC) with each absorption coefficient shown in Figure 9. 2 H Cavity Normalized Absorption Power k a =.6.5.3.6 3 3.2 3.4 3.6 3.8 4 2 3 4 5 Figure 9 linear- and log-scale plots of normalized absorption power with different imaginary part of the refractive index k a for single-defect (H), defect-free (H) and slab without PC structures. The absorption enhancement factor, defined as the relative absorption power spectral density compared to that obtained from the reference slab (without PC) with the same absorption coefficient, can be derived from the normalized absorption power spectral density. The absorption change (absorption enhancement factor) due to the presence of the PC cavity is shown in Figure, at the defect-level wavelength (4 µ m), for different absorption coefficients. Enhanced absorption can be obtained with the enhancement factor greater tha8. The high enhancement factor can be obtained for a large range of absorption coefficients. High spectral selectivity is enabled due to the spectrally selective enhancement and suppression of absorption (R v >). The dominant absorption occurred at the surface normal vertical direction (R ), due to the high in-plane cavity Q. With same absorption coefficients (5cm - ), more peaks appeared in multiple-defect cavities as compared to single-defect case, as shown in Figure a, as a result of multi-mode behavior in multi-defect cavities. However, the total integrated absorption power remains the same, which results in smaller absorption power for each defect mode Normalized Absorption Power k a =.6.5.3.6 Proc. of SPIE Vol. 637 637I-5
level in multi-defect cases. For coupled-cavities (Figure b), the absorption peaks occur at the same wavelengths, compared to the single defect H cavity. However, broadened peak is evident in H-C3 cavity due to reduced cavitiy Q. Absorption Enhancement and Suppression Factor 2 Top H In Plane λ=4µm (defect) H Top In Plane 2 47 94 5 Absorption Coefficient (cm - ) Figure Absorption enhancement factor for H and H cavity for different absorption coefficients. Note the dominant absorption occurs along the vertical direction (top). Normalized Absorption Power - H H 2 H 3 H H H H3 H3 2µm H H -C 3 H-C3 H H 2 H 3 H -C 3-2 3 4 5 Figure Normalized absorption in multiple-defect cavities coupled-defect cavities H 2µm 3.2 3.4 3.6 3.8 4 4.2 4.4 3. CONCLUSIONS In conclusion, theoretical investigation has been carried out on the spectrally selective absorption properties id and 2D PC structures with and without defect. The work is based on TMM and 3D FDTD techniques. For defect-free D PC structures, enhanced absorption was observed at either lower or higher frequency bandedges, depending on the relative refractive index of absorptive layers. Wavelength selectivity as high as 4 was observed. For 2D symmetric air Proc. of SPIE Vol. 637 637I
hole triangular lattice PC structures, enhanced absorption at defect level was obtained, with the enhancement factor largely dependent upon the spectral overlap between the absorption material and the defect mode cavity. Complete absorption suppression within photonic bandgap region was observed in defect-free cavities, and in single defect cavities when the absorption spectral band has no overlap with the photonic bandgap. The findings here can aid the cavity design in the infrared (IR) photodetectors with the incorporation of PC cavities. The incorporation of PC into IR photodetectors (e.g. quantum well and quantum dot infrared photodetectors) can potentially lead to IR photodetectors with higher operation temperature due to enhanced spectrally selective absorption. The spectral resolution and tunability can be accomplished through PC defect engineering. ACKNOWLEDGEMENTS This work was supported by Air Force Office of Scientific Research (AFOSR) under SPRING and Nano programs. REFERENCES [] A. Krier, Mid-infrared semiconductor optoelectronics. London: Springer, 26. [2] S. Y. Lin, J. G. Fleming, Z. Y. Li, I. El-Kady, R. Biswas, and K. M. Ho, "Origin of absorption enhancement in a tungsten, three-dimensional photonic crystal," Journal of Optical Society America B, vol. 2, pp. 538, 23. [3] Y.-G. Xi, X. Wang, X.-H. Hu, X.-H. Liu, and J. Zi, "Modification of absorption of a bulk material by photonic crystals," Chinese Physics Letters, vol. 9, pp. 89, 22. [4] G. Freymann, S. John, M. Schulz-Dobrick, E. Vekris, N. Tetreault, S. Wong, V. Kitaev, and G. A. Ozin, "Tungsten inverse opals: the influence of absorption on the photonic band structure in the visible spectral region," Applied Physcis Letters, vol. 84, pp. 224, 24. [5] M. Artoni, G. L. Rocca, and F. Bassani, "Resonantly absorbing one-dimensional photonic crystals," Physical Review E, vol. 72, pp. 4664, 25. [6] K. T. Posani, V. Tripathi, S. Annamalai, N. R. Weisse-Bernstein, S. Krishna, R. Perahia, O. Crisafulli, and O. J. Painter, "Nanoscale quantum dot infrared sensors with photonic crystal cavity," Applied Physcis Letters, vol. 88, pp. 54, 26. [7] E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Physical Review Letters, vol. 58, pp. 25962, 987. [8] S. Noda and T. Baba, Roadmap on Photonic Crystals ed: Springer, 23. [9] J. B. Pendry, A. MacKinnon, "Calculation of photon dispersion relations," Physical Review Letters, vol. 69, pp. 2772775, 992. [] A. Taflove, Computational Electrodynamics: the Finite-Difference Time-Domain method. Boston: Artech House, 995. [] S. G. Johnson, F. Shanhui, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Physical Review B (Condensed Matter), vol. 6, pp. 575-5758, 999. [2] P. Yeh, Optical Waves in Layered Media. New York: Wiley, 988. [3] J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals. Princeton: Princeton University Press, 995. [4] M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, "Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals," Science, vol. 38, pp. 29698, 25. Proc. of SPIE Vol. 637 637I-7