CMOS image sensor pixel optical efficiency and optical crosstalk optimization using FDTD Solutions
The cost of CMOS image sensor digital camera systems is being reduced through the use of smaller pixel sizes. Ideally, the reduction in size of CMOS image sensor pixels can be achieved with an improvement in image resolution and without a significant decrease in signal to noise. As image sensor pixel sizes continue to decrease, there is the risk of a reduction in optical efficiency, as well as an increase in optical crosstalk between adjacent image sensor pixels. These effects can be mitigated through suitable pixel design and placement of microlenses above each photodiode to redirect and focus the light onto the active detector regions.
“The optimization function available in Lumerical’s FDTD Solutions is useful to quickly find the best operating point for parameters like the radius of curvature of the microlenses or the best antireflective layers in order to optimize the quantum efficiency of CMOS images sensors.”
- Dr. Axel Crocherie, STMicroeletronics
We gratefully acknowledge our collaboration with, and the assistance of, Axel Crocherie, Flavien Hirigoyen, Jérôme Vaillant and Yvon Cazaux of STMicroelectronics, France.
Step 1. Construct the FDTD Solutions model of the CMOS image sensor pixel microlens array
The layout editor shows the 3D layout of the CMOS image sensor microlens array. Each image sensor pixel model includes color filters, parametrized microlenses, metallic interconnects and sometimes light shields above the silicon active regions and substrate. Each individual pixel is composed of four sub-pixels as can be seen in the figure below: two green, a red and a blue.
Comparisons between the simulated performance of the idealized device relative to the device as it would be manufactured – here, incorporating surface roughness as measured via AFM measurements – can help pinpoint where design and process improvements can benefit overall device performance.
Screenshot of full three-dimensional CMOS image sensor pixel microlens model, including color filters and microlenses, in FDTD Solutions.
More sophisticated pixel models can incorporate effects like surface roughness as measured via AFM measurements and imported into FDTD Solutions via the custom surface simulation primitive.
Step 2. Improve your understanding of CMOS image sensor pixel performance and design challenges by studying how it operates
To gain insight into the sources of scattered light in the CMOS image sensor, use the built-in movie monitor in FDTD Solutions to capture the field dynamics of the simulation. A properly designed image sensor pixel microlens focuses light between the metallic interconnects, avoiding unwanted scattering and crosstalk while maximizing detector efficiency. The ability to visualize device performance helps designers understand the origins of light scattering that undermine device performance.
Movies showing the light incident at an angle of 15 degrees focusing through the light shield. In the top movie, without microlens shift there is strong scattering from light hitting the interconnect layer, while in the bottom image with microlens shift this scattering is decreased dramatically. Scattering from interconnects at non-normal incidence leads to optical crosstalk between pixels.
Step 3. Optimizing the angular response of CMOS image sensors and measuring the chief ray angle: increasing optical efficiency and reducing spectral optical crosstalk
To measure spectral optical crosstalk, the downward power flow in adjacent sub-pixels can be calculated by integrating the Poynting vector. Spectral optical crosstalk is generally minimized when optical efficiency is maximized, but at steep angles of incidence elevated levels of crosstalk are observed and are, to a certain extent, unavoidable. More sophisticated device designs, in which other sub-pixel elements (e.g. interconnects) are also shifted, may provide a means by which overall crosstalk levels can be reduced.
By examining cross sections of the above data, it is straightforward to determine what shift is required to optimize the optical efficiency. The measured optical efficiency (i.e. transmission) into the active region underlying the green sub-pixel shows that for a 10 degree incident angle, a shift of about 350nm is required, and that as the angle of incidence increases to 30 degrees, shifts approaching 1 micron are required. Initially, a good design could be achieved by assuming that the CRA is equivalent to the angle of incidence used in this analysis. A more complete analysis of this data could incorporate effects due to the incident light cone without requiring one to run more simulations.
Optical efficiency of the green sub-pixels at a wavelength of 550nm as a function of incident angle and microlens shift from the center of the pixel. The larger the angle of incidence, the larger the microlens shift required to maximize pixel response.
Spectral optical crosstalk measured – here, under the red sub-pixel – at a wavelength of 550nm as a function of incident angle and microlens shift from the center of the sub-pixel.
Optical efficiency versus microlens shift at incident angles of 0, 10, 20, and 30 degrees.
Step 4. Point spread function calculation via FDTD Solutions for CMOS image sensors
Spatial optical crosstalk can be characterized via the point spread function – which quantifies how much an incoming signal is blurred through the CMOS imaging system. In these simulations, we illuminate a central pixel (composed of four sub-pixels – two green, one red, and one blue) with green light at a wavelength of 550nm through a lens system with a numerical aperture of 0.25.
Owing to imperfect color filters, the finite-sized incident beam, and the scattering, refraction and diffraction taking place within the image sensor pixel, incoming green light illuminates the silicon surface above the photodiodes of the illuminated pixel, and adjacent pixels. The figure below shows the downward power flux into the silicon substrate over the pixels as indicated. While the incoming signal is brightest over the two central green sub-pixels, residual signal is observed over the illuminated red and blue sub-pixels, and on nearby green sub-pixels.
Integrating over the active region underneath each sub-pixel region, it is straightforward to calculate the device response. The figure to the left shows that, as expected, the two central green sub-pixels indicate a large amount of incident light. The next largest signal is recorded on the adjacent green sub-pixels. Finally, there is a very slight signal recorded on the nearby red and blue sub-pixels owing to the extra absorption that takes place in the red and blue color filters for the incident green light. The underlying asymmetry of the sub-pixel structure leads to an asymmetric point spread function.
Each pixel is composed of four sub-pixels: two green, one red, and one blue.
Spatial distribution of power flux recorded at the silicon surface shown on a logarithmic scale. While most of the flux is observed under the two green sub-pixels, residual signals is observed at adjacent pixels.
Relative photocurrent generated within each photodiode.