Featured Webinar: How to Simulate and Optimize CMOS Image Sensors Lumerical Solutions, Inc. http://www.lumerical.com For More Information More information on simulation CMOS image sensors on our Knowledge Base: http://docs.lumerical.com/en/fdtd/cmos.html Dr. James Pond CTO [email protected] Dr. Guilin Sun Senior R&D Scientist [email protected] Chris Kopetski Director of Technical Services [email protected] Dr. Mitsunori Kawano Technical Sales Engineer [email protected] Check out other webinars: http://www.lumerical.com/support/webinar_schedule.html http://www.lumerical.com Outline Introduction Trends in image sensor design Impact on simulation General simulation considerations Simulation steps Parameterization of your design FDTD Simulation Analysis of results Optimization Broadband simulations Questions and Answers http://www.lumerical.com Introduction We simulate light interacting with wavelength scale structures MODE Solutions FDTD Solutions 12 mm 20 mm 6 mm http://www.lumerical.com CMOS image sensor simulation What are the components of a pixel? Micro-lens Color filters Vias and interconnects Silicon Transistors and collection electronics http://www.lumerical.com CMOS image sensor simulation Why simulate? Simulation gives the opportunity to cheaply and quickly test ideas, optimize designs and solve problems Expensive and time-consuming to build prototypes Design optimization is challenging and results are not always intuitive http://www.lumerical.com CMOS image sensor simulation What do we want to calculate? The quantum efficiency, QE The ratio of collected electrons to incoming photons The optical efficiency, OE The ratio of generated electrons to incoming photons Equal to the absorbed optical power in the Si over the incident power, assuming that absorption in the Si can only come from exciting an electron-hole More advanced Spectral cross talk • Color matrix coefficients Point spread functions (spatial cross talk) And more... http://www.lumerical.com CMOS image sensor trends Pixel Size (mm) Pixel sizes continue to decrease Pixel size stays about 20x the current technology node Year Source: Advanced Image Sensor Technology, Dr. Albert Theuwissen http://www.lumerical.com Impact on simulation Ray tracing works well at 5 mm pixels sizes (visible light) Starts to break down around 3 mm (visible light) Source: Hirigoyen et al., “FDTD-based optical simulations methodology for CMOS image sensor pixels architecture and process optimization”, PROCEEDINGS- SPIE THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING, 6816, 2008, [6816 08] http://www.lumerical.com Impact on simulation At 1.75 mm, visible light Angular response Spot at Si surface for (1) ray tracing and (2) FDTD Solutions Source: Hirigoyen et al., “FDTD-based optical simulations methodology for CMOS image sensor pixels architecture and process optimization”, PROCEEDINGS- SPIE THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING, 6816, 2008, [6816 08] http://www.lumerical.com General simulation considerations Wave optics vs ray optics Simulation methodology Using focussed beams Using plane waves How to obtain unpolarized results http://www.lumerical.com Wave optics At the wavelength scale, some intuitive questions may not make sense Example: “Which lens did the photon pass through before creating an electron-hole?” http://www.lumerical.com Wave optics An electron-hole created here is a result of the interference pattern created by the photon (a wave) passing through all lenses at once Ray optics does not take these effects into account and is one reason for the breakdown at small pixel sizes In this example, the incident light is green, and is blocked by the red and blue filters http://www.lumerical.com Simulation methodology We want to calculate the Optical Efficiency, OE We need to consider the entire optical system and illumination conditions http://www.lumerical.com Simulation methodology N 2 Euniform Ei i 1 1 OEuniform N Lens or lens system 2 Point source N OEi Microlen s array i 1 Incoherent sum Uniform illumination = 1 2 3 … N http://www.lumerical.com Simulation methodology The direct approach Model a large number of gaussian beams • The parameters are determined by the lens system Shift the position of the beam across the image sensor Sum |E|2 or the OE incoherently Perfect for looking at spatial PSF http://www.lumerical.com Point spread function There is not an obvious definition of a PSF in a digital system Here is one way Fully illuminate one pixel http://www.lumerical.com Point spread function 32 simulations 16 beam positions 2 polarizations per position Could use these results to reconstruct other illumination conditions Structure is locally periodic http://www.lumerical.com Point spread function Incident light is green Can see cross talk to other green pixels Also spectral cross talk to red and blue pixels http://www.lumerical.com Simulation methodology Another approach for uniform illumination An incoherent sum of focussed beams for uniform illumination is mathematically equivalent to an incoherent sum of all plane waves supported by the lens system This is the most commonly used approach to optimize the OE and determine optimal micro-lens shifts See Jérôme Vaillant, Axel Crocherie, Flavien Hirigoyen, Adam Cadien, and James Pond, "Uniform illumination and rigorous electromagnetic simulations applied to CMOS image sensors," Opt. Express 15, 5494-5503 (2007) http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-9-5494 http://www.lumerical.com Simulation methodology Uniform illumination z Objective lens y 2 2 2 Euniform dk x dk y W (k ) E (k ) 2 OEuniform dk x dk y W (k ) OE(k ) k x W is a property of the lens system and pixel location A reasonable approximation for the central pixel is 1, k k0 NA W 0, k k0 NA http://www.lumerical.com Simulation methodology Uniform illumination z y For an edge pixel, W is different. Again at low NA, a reasonable approximation can be made from the NA and geometry of the system kCRA k Objective lens x 1, k k CRA k0 NA W CRA 0, k k k0 NA http://www.lumerical.com Simulation methodology Optimizing OE for uniform illumination means optimizing the integral under the curve kxCRA NA http://www.lumerical.com Simulation methodology We often plot the angular response but the integral is really over k http://www.lumerical.com Simulation methodology Several options to optimize the optical efficiency Simulate only the chief ray angle (CRA) and try to make the peak efficiency appear at the center of the integration window Simulate the CRA and some points near the edges of the integration window Simulate enough angles to get an accurate integral • Excellent agreement with experimental results Source: Hirigoyen et al., “FDTD-based optical simulations methodology for CMOS image sensor pixels architecture and process optimization”, PROCEEDINGS- SPIE THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING, 6816, 2008, [6816 08] http://www.lumerical.com Unpolarized results FDTD simulations have well defined polarization Unpolarized results are obtained by averaging the results of 2 orthogonal polarization simulations incoherently 2 E unpolarized 1 2 2 1 2 2 2 d E ( ) 0 2 d E1 cos( ) E2 sin( ) 0 1 2 2 E1 E2 2 http://www.lumerical.com Simulation steps Parameterization of design FDTD simulation Analysis of results Optimization Parameter sweeps Optimization algorithms http://www.lumerical.com Parameterization of your design Parameterized is essential for optimization CMOS image sensors are complex 3D structures Import from GDSII, AFM data Use script to reproducibly draw the structure http://www.lumerical.com Parameterization of your design Create your own properties http://www.lumerical.com Parameterization of your design Construct image sensor http://www.lumerical.com Parameterization of your design Parameterization can include position of sources and monitors Any group can set properties of the children http://www.lumerical.com Parameterization of your design Essential for Reproducibility Easy parameter sweeps Optimization Lumerical’s hierarchical group layout and script based parameterization makes almost anything possible It is worth the initial investment! http://www.lumerical.com Angular response curve How to obtain the angular response curve and spectral cross talk How to optimize the microlens shift and other layer shifts Optimization of different parameters, such as lens radius of curvature http://www.lumerical.com Angular response curve Plane wave source Bloch boundary conditions One unit cell Arbitrary lens shift or layer shift is OK Structure is still periodic http://www.lumerical.com Angular response curve Calculate response of each pixel by integrating the power into each region at the surface of the Si We will consider 3D optical generation effects later! Saves considerable simulation time because we don’t need to simulate the Si volume http://www.lumerical.com Angular response curve Note that by integrating over a particular region of Si, we are making a first effort at calculating the QE (photons to collected electrons) of the device We still often refer to this as the Optical Efficiency http://www.lumerical.com Tip Use a coarse mesh for simulations Memory scales as dx3 Simulation time scales as dx4 http://www.lumerical.com Tip Use Lumerical’s conformal mesh technology to get submesh accuracy http://www.lumerical.com Tip You don’t need a small dx and dy in the Si, just dz The in-plane wavector is the same in Si as in the upper layers (Snell’s law) Not strictly true when scattering structures are on the Si surface But in practice is an excellent approximation Do some convergence testing to confirm http://www.lumerical.com Tip Simulation times at mesh accuracy 1 6 points per wavelength Machine Year Approximate cost (US$) Parallel processing time (all cores) Lenovo laptop, 2 cores 2009 $1500 3:20 minutes Intel Core i7, 8 cores 2010 $1000 56 seconds Intel X5550 Worsktation, 2 processors, 16 cores 2009 $3700 43 seconds AMD Opteron, 4 processors, 32 cores 2010 $3500 15 seconds http://www.lumerical.com Angular response curve Make an analysis group perform the integral http://www.lumerical.com Angular response curve Create a nested sweep Polarization (for unpolarized result) Source angle http://www.lumerical.com Angular response curve Demonstration Use all the computers in your office Save, run and load files if you have a cluster Ideal shape is cosine Ideal peak efficiency is 50% for green light http://www.lumerical.com Concurrent computing Optimization and parameter sweep require many simulations Send them to many different workstations Each workstation can run in distributed computing mode, using all cores N computers means you can get your optimization or parameter sweep results N times faster! http://www.lumerical.com Optimization How to optimize the microlens shift and other layer shifts Calculate a map of shift vs optical efficiency for all possible CRAs http://www.lumerical.com Optimization Optimization of different parameters Example: lens radius of curvature http://www.lumerical.com Optimization For lens radius of curvature (ROC), assume spherical lens Set up a nested parameter sweep Use only 2 angles: 0 and 15 degrees Plot average OE as a function of ROC http://www.lumerical.com Optimization There is a maximum near 1.3 microns. The normal incidence light has 2 maxima, one near 1.1 microns http://www.lumerical.com Optimization Setup an optimization task Actual optimal result is about 1.29 microns http://www.lumerical.com Loss per unit volume in silicon Insert a “Power absorbed” object in the Si Absorbed power, log scale http://www.lumerical.com Advanced 3D efficiency analysis We can calculate the optical generation rate, G The number of generated electrons per unit time per unit volume Assume that all photons are absorbed by exciting an electron-hole FDTD Pabs (r , ) Psource( ) Pabs (r , ) G (r , ) FDTD Psource ( ) http://www.lumerical.com Advanced 3D efficiency analysis We can make a better effort at calculating the quantum efficiency of the device The number of collected electrons over the number of incident photons We assume that all electrons in a given spatial volume are collected We simply integrate G over that volume Example integration volume http://www.lumerical.com Use in subsequent electrical modeling Once we can calculate the generation rate, we can use it as an input to electrical modeling http://www.lumerical.com Electrical modeling STMicroelectronics and CMOS image sensors Three steps to modeling 1. Process modeling 2. Optical modeling (FDTD Solutions) 3. Electrical device modeling Comparison with experiment 550nm Source: A. Crocherie et al., “From photons to electrons: a complete 3D simulation flow for CMOS image sensor”, IEEE 2009 International Image Sensor Workshop (IISW) http://www.lumerical.com Broadband simulation First time users 3 simulations for red, green, blue wavelengths Can calculate spectral cross talk • Can make initial calculation of the color matrix More advanced users Will want to try and include more spectral information • Initially, in small wavelength bands near red, green and blue • Eventually can try full bandwidth in one simulation http://www.lumerical.com Broadband challenge FDTD is appealing because we can obtain the entire spectrum from 1 simulation Challenges Dispersive material models Incident angle changes with wavelength Incident beam profile changes with wavelength http://www.lumerical.com Broadband challenge Dispersive materials Well-known frequency domain relationship D( ) ( ) E ( ) FDTD is a time domain technique: relationship? t D(t ) (t ) E (t ) E (t ) (t t )dt 0 http://www.lumerical.com Broadband challenge Common solutions are Lorentz or Drude models Often insufficient for real materials Lumerical’s Multi-Coefficient Model (MCM) can solve for materials with arbitrary dispersion such as Si, GaAs, or color filters Silicon GaAs Red filter http://www.lumerical.com Blue filter Broadband simulation Tips The angle of incidence changes with wavelength • Can easily be corrected in angular response curve You may want to lock the simulation mesh as you vary the source bandwidth You will likely want to lock material fits to a particular wavelength range Many fits with large numbers of coefficients will reduce numerical stability • Most issues can be resolved by carefully controlling the fit http://www.lumerical.com Broadband simulation Broadband simulation can give excellent agreement with experimental results Source: Crocherie et al., “Three-dimensional broadband FDTD optical simulations of CMOS image sensor”, Optical Design and Engineering III, Proc. of SPIE, 7100, 2008, [71002J] http://www.lumerical.com Challenges and solutions Challenge Solutions and best practices Wavelength scale devices Full vectorial 3D Maxwell solver Simulation methodology “Think before you simulate” •Setup simulation methodology to calculate the same results you can obtain experimentally •Understand how to deal with effects like incoherent and unpolarized light •Reduce unnecessary computational requirements •Store only necessary field data Complex 3D geometries Parameterize designs Simulation time •Use coarse mesh size where possible •Always for initial simulations •Do convergence testing of mesh size last! •Make reasonable approximations •Example, treat metal as PEC •Advanced meshing •Use non-uniform meshing •Use conformal meshing •Use distributed parallel computation to take advantage of modern hardware Broadband simulation •Time domain gives broadband results •Highly dispersive materials require multi-pole material models •Carefully control your models •Keep material fits constant as you change simulation bandwidths •Use a fixed mesh as you change simulation bandwidths Optimization and parameter sweeps •Using a global search algorithm that significantly reduces the number of simulations required •Use concurrent computing to use all your available computer resources optimally http://www.lumerical.com For More Information Dr. James Pond CTO [email protected] Dr. Guilin Sun Senior R&D Scientist [email protected] Chris Kopetski Director of Technical Services [email protected] Dr. Mitsunori Kawano Technical Sales Engineer [email protected] Sales inquiries [email protected] Sales representatives (other regions) http://www.lumerical.com/company/representatives.html Free, 30 day trial at www.lumerical.com http://www.lumerical.com
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