Buss, IJ

Craddock, IJ

Cryan, MJ

Haigh, MK

Ho, Y-LD

Nash, G R

Railton, CJ

Rarity, JG

English

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3D Modelling of Enhanced Surface Emission using Surface Roughening

3D FDTD is used to study the effect of surface roughening on the emission of a point source embedded in GaAs with a mirror behind the dipole. Enhancement factors of 10 : 1 are observed. © 2006 Optical Society of America.3D FDTD is used to study the effect of surface roughening on the emission of a point source embedded in GaAs with a mirror behind the dipole. Enhancement factors of 10 : 1 are observed. © 2006 Optical Society of America

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3D modelling of enhanced surface emission using surface roughening

I.J. Buss

M.J. Cryan

D. Ho

G. Nash

M.K. Haigh

I.J. Craddock

C.J. Railton

J.G. Rarity

A 3D FDTD modelling is used to study the effect of surface roughening on the vertical emission of a point source emitting at lambda0=0.94 mum embedded in GaAs with a mirror behind the dipole. Enhancement of emission is seen at lambda0=1.95 mum for a rough-surface device with a perfect metal mirror placed 150 nm below the sourc

Nash, GR

Haigh, Mary

                          Buss, I. J., Cryan, M. J., Nash, G. R., Haigh, M., Craddock, I. J., Railton, C.J., & Rarity, J. G. (2006). 3D modelling of enhanced surface emission usingsurface roughening. In International Conference on Transparent OpticalNetworks, Nottingham, UK. (Vol. 4, pp. 150 - 153). Institute of Electricaland Electronics Engineers (IEEE). 10.1109/ICTON.2006.248523Link to published version (if available):10.1109/ICTON.2006.248523Link to publication record in Explore Bristol ResearchPDF-documentUniversity of Bristol - Explore Bristol ResearchGeneral rightsThis document is made available in accordance with publisher policies. Please cite only the publishedversion using the reference above. Full terms of use are available:http://www.bristol.ac.uk/pure/about/ebr-terms.htmlTake down policyExplore Bristol Research is a digital archive and the intention is that deposited content should not beremoved. However, if you believe that this version of the work breaches copyright law please contactopen-access@bristol.ac.uk and include the following information in your message:• Your contact details• Bibliographic details for the item, including a URL• An outline of the nature of the complaintOn receipt of your message the Open Access Team will immediately investigate your claim, make aninitial judgement of the validity of the claim and, where appropriate, withdraw the item in questionfrom public view.Tu.P.18 150 ICTON 2006 1-4244-0236-0/06/$20.00 ©2006 IEEE 3D Modelling of Enhanced Surface Emission using Surface Roughening Ian Buss, Martin Cryan, Geoff Nash*, Mary Haigh*, Ian Craddock, Chris Railton and  John Rarity Centre for Communications Research, Department of Electrical Engineering, University of Bristol, UK * QinetiQ, Malvern, UK,  e-mail: ian.buss@bristol.ac.uk ABSTRACT 3D FDTD modelling is used to study the effect of surface roughening on the vertical emission of a point source emitting at λ0 = 0.94 µm embedded in GaAs with a mirror behind the dipole.  Enhancement of emission is seen at λ0 = 1.95 µm for a rough-surface device with a perfect metal mirror placed 150 nm below the source. Keywords: light-emitting diodes, surface roughness, FDTD modelling. 1. INTRODUCTION Increasing the extraction efficiency of light-emitting diodes (LEDs) has been of intense interest for all spectral regions of emission.  The limiting factor in the external quantum efficiency of the LED is the poor external coupling efficiency of photons out of the bulk semiconductor.  This is a result of the high difference in refractive indices between the bulk semiconductor, typically n ≈ 3.5, and the external coupling medium, often air (n ≈ 1).  Following the ~1/(4n2) [1] rule of thumb the external coupling efficiency in a smooth planar LED is ~2% for most semiconductor materials.  Using the escape cone concept we can calculate a photon escape efficiency (discounting Fresnel reflection at the interface) via the ratio of the solid angle of the escape cone and the surface area of a sphere, see Equation (1).    ( ) ( )222 1 cos 1 cos24c cconeescsphererAA rπ θ θηπ− −= = =  (1) For GaAs the critical angle θc = 16.5o; this gives an approximate escape efficiency ηesc = 2.07%. Several approaches have been identified in the attempt to increase the external efficiency of the LED.  These include adding a highly reflective surface to the substrate side of the device [2, 3], applying surface roughening to the emission surface [4, 5], using novel chip geometries such as the truncated inverted pyramid (TIP) [6], the resonant cavity LED [7] and most recently using 2D photonic crystal patterns [8, 9]. This paper will concentrate on roughening as a method to increase efficiency. Most roughness models use analytical techniques [4]; however, here we adopt a 3D numerical approach using the Finite Difference Time Domain (FDTD) method. This will enable detailed study of the effects of different types of roughness and will enable accurate comparisons between different methods for increasing emission, such as those based on photonic crystals. It is also envisaged that this type of model will be ideally suited to devices that use pre-patterned roughness that is not completely random but is derived from a masking process or even direct etching using techniques such as Focused Ion Beam (FIB) etching [10]. 2. FDTD MODEL This paper will use an in-house 3D FDTD code which has been developed over a number of years and has been used extensively in the design and modelling of optical devices, in particular photonic crystal based structures [11]. In this paper an infinitesimal dipole is placed in a block of GaAs (n = 3.48 [12]) in the centre of a simulation space measuring 5 × 5 × 5 µm. Figure 1 shows a 3D view of the block with the roughened top surface. The block measures 5 × 5 µm in x-z plane and is 4µm thick in the y direction. A perfect metal layer is placed 150nm below the dipole in order to recycle the light scattered from the rough surface [4]. This distance is chosen to ensure constructive superposition of the electromagnetic fields from the point dipole and the virtual dipole (created by the presence of the mirror) at the surface at λ0 = 1.5µm. Figure 2 shows a top view of the roughness pattern being used. In this case it is made up of a pseudo-random grid of 625  100 nm square air holes. The depth of the air holes is varied from 0 nm to 200 nm pseudo-randomly, while their width is roughly half an internal wavelength [4].  This type of pattern could be easily created using FIB etching. Figure 3 shows a cross section through the model at z = 2.5 µm.  Initially the structure is meshed with ~ 2million FDTD cells, using non-uniform meshing of 25 nm (~ λg/11 for λ0 = 0.94 µm) near the dipole and 50 nm further away from the source to reduce run-time requirements. A typical run time for this structure is around 10 hours on a Pentium 4 processor. A Gaussian modulated sinewave excitation, centred at 0.94 µm is imposed on the dipole which is oriented parallel to the x-axis. The simulation is bounded on the sides and the top by 1st order absorbing boundaries after Mur [13].  Authorized licensed use limited to: UNIVERSITY OF BRISTOL. Downloaded on January 7, 2009 at 04:54 from IEEE Xplore.  Restrictions apply.ICTON 2006 151 Tu.P.18    Figure 1. 3D view of FDTD model. Figure 2. Top-down view of surface roughness in FDTD model (x-z plane).  Figure 3. x-y section through FDTD model. 3. RESULTS Models with both smooth surfaces and roughened surfaces are studied in order to be able to assess the effect of roughening the surface.  These simulations are also performed with and without the mirror to show its contribution to vertical emission through the surface.  Typical distributions of |Ex| in the y-z plane at x = 2.5µm are shown in Fig. 4a and Fig. 4b for a smooth surface with mirror and a roughened surface with a mirror respectively.  The rough surface in this case consists of 100nm square holes of random depth between 0 and 200 nm.  It is difficult from these data to assess which structure is giving the strongest emission and full vertical Poynting vector calculations across the whole simulation plane at y = 4.2 µm for a range of wavelengths are now underway.  However it is clear to see the perturbation introduced by the roughened surface. In order to assess the wavelength dependence of the emission, single probes have been placed at regular points on the x-z plane above the structure at a height y = 4.2µm.  These monitor all six field components at each time step. Thus these can be used to calculate the emission as a function wavelength using discrete Fourier transforms (FFT).  Figure 5 shows the ratio in dB of |Ex|2 at the centre of the block, 200 nm above the surface of the block to that for a flat block with no mirror for three different cases. Firstly, Fig. 5a is the case of a roughened surface with no mirror and only very slight improvement over the flat surface is seen; this to be expected, since without a mirror there is no chance to recycle the randomly reflected light into the light cone. In Fig. 5b data for a flat surface with a mirror added 150nm behind the dipole is shown and two features are noticeable. Firstly there is a large suppression of emission when the dipole is ~ λg / 2 from the dipole around 1050 nm and much stronger emission when the distance from dipole to mirror is in the region of λg / 4 (2100 nm) as might be expected, remembering that there is a π phase shift introduced by the mirror. In the case of Fig. 5c the roughened surface with mirror, similar behaviour is observed to that in Fig. 5b with suppression around Authorized licensed use limited to: UNIVERSITY OF BRISTOL. Downloaded on January 7, 2009 at 04:54 from IEEE Xplore.  Restrictions apply.Tu.P.18  152 ICTON 2006 ~λg / 2 and enhancement around ~ λg / 4. However, now a small region of strong enhancement exists around 1950 nm and this is most likely due to a combination of mirror and roughness recycling working together.  Further investigation is required.   In order to confirm the role played by the mirror, its location is moved to 220 nm away from the source which is expected to produce strong suppression of the field at λ0 = 1.5 µm.  Figure 6 confirms that this is indeed the case. (a) (b) Figure 4. |Ex| at λ0 = 940nm  for (a) smooth surface with mirror; (b) roughened surface with mirror. -30-25-20-15-10-505101520950 1150 1350 1550 1750 1950 2150Wavelength (nm)20*Log(Mag(Ex))(a) Rough no mirror(b) Flat mirror(c) Rough mirror-30-25-20-15-10-5051015950 1150 1350 1550 1750 1950 2150Wavelength (nm)20 log Mag(Ex)Mirror 150nmMirror 220nmFigure 5. Ratio of (a) rough surface with no mirror, (b) flat surface with mirror, (c) rough surface with mirror to flat surface without mirror. Figure 6. Data as in Fig. 6 compared for mirror locations of 150nm below source and 220nm          below source. 4. CONCLUSIONS This paper has presented results for 3D numerical modelling of emission from an infinitesimal dipole in the centre of a block of GaAs with a mirror placed 150 nm behind the dipole with and without a roughened surface. The results show that suppression and enhancement of emission is observed as expected for constructive and destructive interference caused by the mirror. A region of strong enhancement is also observed for the roughened surface where the mirror and the roughened surface work together to emit light into the escape cone. These preliminary results are for a single observation point 200 nm above the surface and detailed calculations to evaluate the total vertical radiated power and far field radiation pattern are now underway. Models investigating the effect of differing roughness depth and width and multiple sources are also planned. REFERENCES [1] E.F. Schubert, "Light-Emitting Diodes," Cambridge, Cambridge University Press, 2003. [2] D.G. Deppe, J.C. Campbell, R. Kuchibhotla, T.J. Rogers, and B.G. Streetman, "Optically-coupled mirror-quantum well InGaAs-GaAs light emitting diode," Iee Electronics Letters, vol. 26, 1990. [3] T. Kato, H. Susawa, M. Hirotani, T. Saka, Y. Ohashi, E. Shichi, and S. Shibata, "GaAs/GaAlAs surface emitting IR LED with Bragg reflector grown by MOCVD," Journal of Crystal Growth, vol. 107, pp. 832, 1991. [4] I. Schnitzer, E. Yablonovitch, C. Caneau, T.J. Gmitter, and A. Scherer, "30-Percent External Quantum Efficiency from Surface Textured, Thin-Film Light-Emitting-Diodes," Appl. Phys. Lett., vol. 63, pp. 2174-2176, 1993. Authorized licensed use limited to: UNIVERSITY OF BRISTOL. Downloaded on January 7, 2009 at 04:54 from IEEE Xplore.  Restrictions apply.ICTON 2006 153 Tu.P.18 [5] Y. J. Lee, H. C. Kuo, S. C. Wang, T. C. Hsu, M. H. Hsieh, M. J. Jou, and B. J. Lee, "Increasing the Extraction Efficiency of AlGaInP LEDs via n-Side Surface Roughening," IEEE Photon. Technol. Lett., vol. 17, pp. 2289-2291, 2005. [6] M.R. Krames, M. Ochiai-Holcomb, G.E. Hofler, C. Carter-Coman, E.I. Chen, I.H. Tan, P. Grillot, N.F. Gardner, H.C. Chui, J.W. Huang, S.A. Stockman, F.A. Kish, M.G. Craford, T.S. Tan, C.P. Kocot, M. Hueschen, J. Posselt, B. Loh, G. Sasser, and D. Collins, "High-power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P/GaP light-emitting diodes exhibiting >50% external quantum efficiency," Appl. Phys. Lett., vol. 75, pp. 2365-2367, 1999. [7] E.F. Schubert, Y.H. Wang, A.Y. Cho, L.W. Tu, and G.J. Zydzik, "Resonant cavity light-emitting diode," Appl. Phys. Lett., vol. 60, pp. 921-923, 1991. [8] M. Boroditsky, R. Vrijen, T.F. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, "Spontaneous emission extraction and Purcell enhancement from thin-film 2-D photonic crystals," Journal of Lightwave Technology, vol. 17, pp. 2096-2112, 1999. [9] D.H. Kim, C.O. Cho, Y.G. Roh, H. Jeon, and Y. Soo Park, "Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns," Appl. Phys. Lett., vol. 87, 2005. [10] M.J. Cryan, M. Hill, D.C. Sanz, P.S. Ivanov, P.J. Heard, L. Tian, S.Y. Yu, and J.M. Rorison, "Focused ion beam-based fabrication of nanostructured photonic devices," IEEE J. Sel. Topics Quantum Electron., vol. 11, pp. 1266-1277, 2005. [11] M.J. Cryan, D.C.L. Wong, I.J. Craddock, S.Y.J. Rorison, and C.J. Railton, "Calculation of losses in 2-D photonic crystal membrane waveguides using the 3-D FDTD method," IEEE Photon. Technol. Lett., vol. 17, pp. 58-60, 2005. [12] E.D. Palik, "Handbook of optical constants of solids II," London Academic Press, 1991. [13] G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations," IEEE Trans. Electromagn. Compat., vol. EMC-23, pp. 377-382, 1981. Authorized licensed use limited to: UNIVERSITY OF BRISTOL. Downloaded on January 7, 2009 at 04:54 from IEEE Xplore.  Restrictions apply.

30-Percent External Quantum Efficiency from Surface Textured, Thin-Film Light-Emitting-Diodes,&quot;

Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,&quot;

Calculation of losses in 2-D photonic crystal membrane waveguides using the 3-D FDTD method,&quot;

Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,&quot;

Focused ion beam-based fabrication of nanostructured photonic devices,&quot;

GaAs/GaAlAs surface emitting IR LED with Bragg reflector grown by MOCVD,&quot;

Handbook of optical constants of solids II,&quot;

High-power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P/GaP light-emitting diodes exhibiting >50% external quantum efficiency,&quot;

Increasing the Extraction Efficiency of AlGaInP LEDs via n-Side Surface Roughening,&quot;

Light-Emitting Diodes,&quot; Cambridge,

Optically-coupled mirrorquantum well InGaAs-GaAs light emitting diode,&quot;

Resonant cavity light-emitting diode,&quot;

Spontaneous emission extraction and Purcell enhancement from thin-film 2-D photonic crystals,&quot;

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3D modelling of enhanced surface emission using surface roughening

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