Image Sensor Lenslet Analysis : Image Sensor Lenslet Analysis

Requires: S-Pisces/Luminous
Minimum Versions: Atlas 5.28.1.R

This example shows how finite difference time domain (FDTD) analysis can be applied to optimization of lenslet design for an microlens image sensor.

In this example we will use the built-in analytic lens specification defined on the LENS statement. This allows us to define lenslets considered during FDTD analysis but does not impact the drift diffusion analysis. The advantage of lenslets is that extra mesh points are not added into the device analysis part of the simulation.

There are several different lens forms supported by FDTD in Luminous2D and Luminous3D. These include spherical, elliptical, pyramidal, composite and aspheric types. The composite lenslet is formed by a planar face with cylindrical and spherical roll off at the edges. The aspheric lenslet is defined by a 10th order polynomial fitted to measured h-sag data using a Levenberg-Marquardt non-linear least squares algorithm.

The device in this example is defined simply by a buried N well under the lens and light blocking structures. In this case we are less concerned with the electrical operation of the device than the light collection capability.

In this example we compare six lens designs in six simulations. In all six cases the geometry is the same with the exception of the lens height. The lenslet width is fixed at 8 microns and the height is varried from 0.5 to 3.5 microns in half micron steps. Simple geometrical calculations give six lens radii and associated lens centers for the cases.

We will characterize the lenslet light gathering capability based on the integrated photogeneration rate in the N well region. This is done using the PROBE statement.

Each of the six simulations begins with a description of the device structure and mesh using the MESH , X.M , Y.M , REGION , ELEC , and DOPING statements.

Next, we specify some material models and parameter defaults. Of significance is the specification of the complex index of refraction of aluminum using the REAL.INDEX and IMAG.INDEX parameters of the MATERIAL statement. In this case we set the imaginary index to a very high value. This makes the aluminum blocking regions highly reflective/absorptive to light.

Next we specify the optical source on the BEAM statement. We specify the light with normal incidence from above with a wavelength of 0.415 microns. This is only a nominal wavelength and is never used since we will define the analysis wavelengths explicitly on the subsequent SOLVE statments. We also define the sampling in the FDTD mesh. This sampling should typically be a small fraction of the incident wavelength. The TD.WAVES parameter specifies how many source wavelengths are propogated in this simulation. Finally, we specify a file for capture of the structure as represented in the final FDTD mesh solution. This is useful to examine the interference and diffraction patterns that might not be otherwise discernable in the standard finite-difference structure file.

Next, we specify the lenslet. The six cases will be differentiated by the location of the center along the y axis, Y.LOC and the radius, RADIUS .

We add perfectly matched layers (PMLs) at the top and bottom of the FDTD domain to absorb reflected and transmitted light. This is specified on the PML statements.

After obtaining the initial solution, we define a probe using the PROBE statement to allow us to measure the integrated photogeneration rate as a function of wavelength for each lens design. It is important to notice that we specified the FDTD parameter on the PROBE statement. This indicates that the integration of the generation rate will take place in the FDTD analysis domain. The FDTD domain presents a more accurate estimate since some loss is expected during interpolation to the finite-difference domain.

Finally, we capture the solutions for various wavelengths over the visible spectrum.

At the end of the simulations we will have two data sets to consider. First, we will produce optical intensity plots of the six lenslet designs under green illumination. In comparing these plots we can see that focusing is better under the taller lenslets.

Second, we can overlay the integrated generation rate curves versus optical wavelength. This verifies that the 3.5 micron lens height produces the best light collection.

To load and run this example, select the Load button in DeckBuild > Examples. This will copy the input file and any support files to your current working directory. Select the Run button in DeckBuild to execute the example.