This page discusses issues related to running broadband CMOS image sensor simulations. Typical users will follow these steps as they move from single wavelength simulations to broadband simulations:
- Initially, run simulations at 3 different wavelengths to collect data for red, green and blue illumination.
- Increase the bandwidth of the 3 simulations to collect light over a range of wavelengths associated with red, green and blue.
- Eventually, it may be possible to simulate the entire spectrum in a single simulation.
The example simulations described in the previous pages used the initial approach and collected data at only one wavelength. Collecting results at more than a few wavelengths in this manner would be slow, since the entire set of simulations must be re-run at each frequency of interest. A better approach is to collect broadband (multiple frequencies) results from a single simulation, and this capability is a key advantage of using a time domain simulation method like FDTD. However, there are some complications related to broadband simulations that must be considered and this section explains how to address them.
Source injection angles
Broad band simulations using plane wave sources at non-normal incidence suffer from a problem that the source angle of incidence changes as a function of frequency. For example, suppose the source wavelength range is 400-700nm, with a nominal injection angle of 20 degrees. The actual injection angle will be 15.5 degrees at 400nm, 20 degrees at 510nm, and 28 degrees at 700nm.
For small frequency ranges or angles near normal incidence, it is usually safe to ignore this problem. However, for large frequency ranges or angles, this issue must be considered. For more information, see the Broadband injection angles section of the User Guide. For this particular application, this issue is generally straightforward to solve: when plotting an angular response curve, the angle vector must be corrected for each wavelength considered. The actual angles for a given wavelength can be calculated by the script command getsourceangle.
Finally, if you are integrating results from incident plane waves over a range of angles, please remember that the integral should be over the in-plane wave vector (kx and ky) and not the source angle. The in-plane wave vectors are constant over all wavelengths which means that no correction is required when calculating this integral. However, the total integration range does change as a function of wavelength.
The idealized color filters we used in the examples of this section create difficulties in broad band simulations because they are highly dispersive with sharp features. The following three figures show the imaginary index of a set of idealized Red - Green - Blue color filters.
If you are running broadband simulations, you should try to use real data for your different materials, particularly the color filters. Examples of fits to more realistic color filter materials are shown below.
Real and imaginary permittivity for Red filter
Real and imaginary permittivity for Blue filter
Controlling the material fits is very important. Highly dispersive material fits can lead to increased numerical instability, particularly when conformal meshing is used. One aspect that is quite important for this application can be to lock the material fits to a particular wavelength range. For example, if you are interested in studying your design from 300nm to 1000nm but are constantly changing the source wavelength and bandwidth within that range, you can force your material to always use a unique fit. For example, the figure below shows how you can fit silicon data over 300nm to 1000nm regardless of the wavelength range of your source. This helps give much more consistent, stable results and avoids any discontinuities if you are combining results from different, smaller wavelength ranges.
For more information about controlling material fits, see Modify material fits.
Force a constant simulation mesh
As you change the wavelength range of your sources, the simulation mesh will change. This is because, for a desired mesh accuracy setting, we can use a larger mesh size for longer wavelengths and must use a smaller mesh size for shorter wavelengths. The automatic meshing algorithm also takes into account the changes in refractive index properties of your materials over the simulation bandwidth. Like the material fits, this can lead to some problems such as apparent discontinuities in results when you are studying a design over a large wavelength range, such as 400nm to 700nm, but are constantly changing the source wavelength range for different simulations, for example to study narrow bands around red, green or blue wavelengths. To force the mesh generation algorithm to always use your entire wavelength range of interest, rather than the current source settings, set the properties shown below in the Advanced Options tab of the FDTD simulation region.
Changes of beam profiles with wavelength
If you are using a beam as a source, you should be aware that the beam profile is calculated at the center frequency of your source bandwidth. The beam profiles are therefore incorrect away from the center frequency of your source. This issue can often be ignored, but for large enough bandwidths it can become a problem. Please verify how much the beam profile changes to see if this problem can be ignored. To see how the beam profile changes, set the source wavelength span to 0, set the source wavelength to the minimum of your range, and plot the beam profile. You can do this again at the maximum of your range and again plot the beam profile. For example, the figures below show the beams (real(Ex)) for an NA=0.2 lens system at 400nm, 700nm, 525nm and 545nm. You can see that if you are trying to use a source range of 400nm to 700nm, you should not ignore the changes in beam profile with wavelength. However, if your source covers a range of 525nm to 545nm, this change is negligible.
Fortunately, there is an option for the beam source that allows you to inject a broadband beam with a consistent spatial profile. See this page for more information.
Crocherie et al., “Three-dimensional broadband FDTD optical simulations of CMOS image sensor”, Optical Design and Engineering III, Proc. of SPIE, 7100, 71002J (2008)