Conclusion

In summary, we present here results about the viability of using MATLAB to simulate light propagation through an imaging pixel, as well as results as to the optimal placement of wires within such a pixel.  We have found the MATLAB script to be generally viable based on comparisons to OptiFDTD, especially for the on-axis case (incident light at 0 degrees).  For the off-axis case, the assumption in the current model of infinitely thin wires may prove problematic; more experimentation is required to determine the extent of the error introduced by this assumption.  In addition, a MATLAB script that takes into account wire thickness may be a useful future development.  In general we have seen that MATLAB provides a fast and simple way to optimize wire placement within pixels, whereas OptiFDTD is a robust engine useful for verification and visualization of these results.

Our optimizations within MATLAB have demonstrated that wires should be placed as far apart as engineering constraints will allow in order to maximize light collection at the photodiode.  For the on-axis case we recommend that the apertures be centered as one might expect, to allow the light a straight path to the pixel floor.  For the off-axis case we recommend a different shift in each metal layer depending on the angle of incident light and the depth of the metal layer.  The optimal shifts may not be intuitive, so using an optimization routine that accounts for as many factors as possible is indicated.  Lastly, we have seen that thorough optimization in the off-axis case can result in pixel configurations that rival and improve upon the trivial case of the empty pixel by better focusing the light and potentially reducing crosstalk.

These findings pave the way for future work in optimal pixel design.  Expansions on the current model could include optimization of multiple parameters simultaneously, a three dimensional pixel model rather than a cross section, or the use of different optimization routines and options.  This work is intended to be a starting point only, and we hope that future work along these lines can benefit from the background that we have provided.