This page provides some tips for optimizing the setup of your CMOS image sensor simulations.
Use a coarse mesh initially
We strongly recommend starting with a coarse mesh, using a mesh accuracy setting of 1 or 2. It is far easier to setup, test or optimize a simulation that takes a few seconds to minutes, compared to a simulation that takes several hours. Only once all other problems are resolved and you are getting good results should you try using a mesh accuracy setting of 3 or more by doing some convergence testing. The purpose of this convergence testing is to determine the minimum mesh accuracy setting that can be used while still obtaining results with acceptable accuracy. This testing can often be done on a single simulation and, once the mesh accuracy setting has been determined, you can rerun your parameter sweeps or optimizations with this setting.
The figures below, also shown at convergence testing, show the benefit and cost of using a higher mesh accuracy. While the simulated optical efficiency to the green pixel changes by less than 0.01 from a mesh accuracy of 1 to 8, the simulation time on a 4 processor, 8 core, AMD workstation, goes from 15 seconds to 2.5 hours and the memory goes from 60MB to 7GB.
X,Y override in Si
Due to the high index of Silicon (n>4), the automatic meshing algorithm will use a very small mesh everywhere in the Si region. This small mesh will make the simulation significantly slower that it would otherwise be.
From Snell’s law, we can show that the in-plane wave vector is conserved.
\(k_{x, glass} = k_{x, Si}\)
In other words, the in-plane wavevector (kx or ky) in the Silicon can never be larger than the in-plane wavevector in the glass. Therefore, it is possible to use a coarser mesh in the x and y directions without reducing the accuracy.
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Note: This technique is only valid if there are no scattering structures within the Si. Indeed, even scattering structure on or near the surface of the Si can generate light propagating at all angles in the Si, however, the above approximation is generally very good even if there are some scattering structures on the surface of the Si. We recommend testing the convergence if there are concerns about the amount of steep angle scattering that may be generated in the Si. |
To force a larger mesh size in the X and Y directions, add a mesh override region over the Si layer. Set the override region to treat this area as if it has an index of 1.5 (glass) in the X and Y directions. A small mesh is required in the Z direction, so the override should not be applied in the Z direction.
Use PEC for metal objects
In most image sensor simulations, metallic objects behave like perfect metals (100% reflection, no absorption). Rather than using a detailed material model for the metal (which will require a smaller mesh), simply use the Perfect Electrical Conductor (PEC) material model. The PEC material model does not require a small mesh, which makes your simulations faster.
Use conformal meshing (Conformal variant 1)
The conformal mesh can provide much more accurate results at larger mesh sizes and make it possible to run simulation much faster. If PEC is used for the metals, it is a good idea to switch to using the "Conformal variant 1" setting which will apply the conformal mesh algorithm to the PEC as well as the dielectric materials and the Si (please see Mesh refinement options for more details). The figure on the right shows that the Optical Efficiency to the green pixel is almost unchanged when going from a mesh accuracy of 1 (lambda/dx=6) to a mesh accuracy of 6 (lambda/dx=26). When using staircase meshing, the convergence is slower and a smaller mesh size is required for the same accuracy.
Please note that the conformal mesh can generate more numerical instability, especially if many highly dispersive materials are used that require large numbers of coefficients to fit. If these instabilities do occur, they can normally be controlled by making changes to the fit settings for certain materials. Please contact Lumerical support for advice if necessary.
Ignore polarization effects
For initial simulations, it can make sense to ignore polarization effects and choose only one polarization, S or P. Eventually, it makes sense to correctly calculate the incoherent response using both polarizations but a great deal of initial testing and optimization can be done with only one polarization.
Broadband simulations
Broadband simulations have the potential to give broadband results from a single simulation, but a number of complications exist. See the Broadband simulations page for more information.
Object display resolution
Setting up an image sensor structure tends to require a large number of primitives, especially when drawing multiple periods. This can start to overwhelm the graphics card of your computer, especially when using advanced primitives like the import object. You can reduce the drawing resolution of these objects by editing the Graphical rendering tab of the object properties.
A higher display resolution makes the surface look better in the CAD editor, but makes the drawing slower. The display resolution has no effect on the actual meshing of the structure or the simulation results.
Backside Illumination
See the reference below.
Related publications
- F. Hirigoyen, J. Vaillant, et al., "1.1μm Backside Imager vs. Frontside Imager: an optics-dedicated FDTD approach" IEEE 2009 International Image Sensor Workshop (IISW)