This section shows how a 3D multi-layer OLED structure with square PC patterning can be simulated efficiently with FDTD.
This example assumes that the user has read and understood the contents in Simulation methodology, Simple 2D OLED, and Using symmetry to reduce the number of simulations in detail.
We will start with the same simulation setup as 3D OLED with no symmetry. Here, we will follow a modified process to sweep through the different dipole locations and orientations in order to take advantage of this lattice symmetry.
1.Open OLED_3D_square.fsp and verify that the parallel settings are correct for your computer system. Take a look at the Setup->Variables tab in the model analysis group. Here, px/py are the locations of each dipole source (as a fraction of the unit cell). Weight is used to keep track of the area contribution from each dipole as we unwrap the results, defined in OLED_params_3D_square.lsf. For example, if there are 16 dipole locations (4x4) in a unit cell, then each dipole location occupies 1/16 of the unit cell area. If the sqaure lattice symmetry applies, an on-diagonal dipole location only occupies 1/32 unit area (0.5*1/16).
2.The script file OLED_params_3D_square.lsf can be used to generate the values for the parameters listed under Setup->Variables. This is based on the technique described in the previous section for "PC with square symmetry". This file will generate the values for px/py/orientation/weight for the patterned PC. These values can then be entered directly into the parameter sweep project:
Note that the last two columns (Value_8 and Value_9) correspond to the 2 simulations for the non-patterned case (the px/py/orientation/weight values are irrelevant here, and are set to 0 by default). The default settings correspond to 4x4 dipole locations in a full unit cell, which should work well for most OLEDs with square PC patterning. These values have already been entered into the parameter sweep project in this example (shown above).
3.Before proceeding to run the parameter sweep project, one can use the Animate feature to "watch" the sweep without running the simulations.
The process of calculating the internal quantum efficiency is similar to the approach used in Simple 2D OLED. Here, we use the script OLED_internal_QE_analysis_3D_square.lsf to calculate the power emitted by the dipole. Note that we cannot use the Mean Operation in the parameter sweep project to calculate the average power in this case, since using symmetry means that the contribution from each dipole orientation and location may be not the same, and we need to multiply the results for each simulation by different weight factors as we unwrap the results.
The result for the power emitted by the dipole source (normalized to the power emitted in a homogeneous medium) is shown below. Note that there is not much difference between the case with and without the PC structure, which tells us that the excitation lifetimes will not be modified by more than a few percent by the periodic patterning. We calculated the results by 2 different methods and both give similar results to within a few percent. Better agreement could be achieved by using a smaller mesh.
Again, we should no rely on only using the parameter sweeping tool to average the far field results over different dipole orientations and locations (unfolding the unit cell requires taking the transpose and applying different weight factors to the results for the simulated dipoles). In this case, we rely on FDTD' scripting environment to carry out this analysis. The script OLED_total_QE_analysis.lsf will load all the individual simulations and calculate the angular distribution of the light in either the substrate (glass) or the air. The projection in the air accounts for the reflection and refraction that will eventually occur at a glass/air interface. This script uses the results of the small number of simulations and, through symmetry operations, reconstructs the angular distribution from the incoherent superposition of all the dipole locations in the unit cell. (Note that this process can take up to several hours depending on the size of the simulation used). The final results are stored in OLED_farfield_results.ldf and this file contains all the information necessary to characterize your OLED. You will likely want to make a backup copy of this file because it can be useful even if the simulation files are deleted.
We calculate the emission enhancement as a function of wavelength. The result is shown below. For this structure, the enhancement is quite modest, but could be improved with some design modifications. Note that these results show the enhancement in emission to air.
We calculate the actual angular emission pattern that would be observed for different operating wavelengths of an actual OLED. For this, we choose 3 different center wavelengths and a FWHM bandwidth for our OLED. In this case, we have chosen to evaluate operation at 460nm, 510nm and 620nm with a FWHM of 15nm. The emission spectra are plotted below.
We calculate the angular emission by doing a weighted average of the previous results over the above spectrum. The resulting angular distributions are shown below.
Color filtered angular emissions
The color filters tend to smooth some of the features observed with the unfiltered angular distribution. To plot the unfiltered angular distribution for all wavelengths (51 in this case), set the variable plot_all_wavelengths to 1 in OLED_total_QE_analysis_3D_square.lsf. An example of three of the figures produced are shown below.
Raw angular emissions
In order to make these simulation run quickly, a simulation span of only 8x8 microns2 was used. This is almost certainly not large enough to obtain accurate angular emission spectra. In general, spans of 12x12 microns2, 15x15 microns2 and even sometimes 30x30 microns2 may be necessary. The simulations can take some time to run, although the entire set of simulations and analysis for a 12x12 microns2 can be achieved in approximately 7 hours on a single Intel Xeon X5550 workstation.
It may also be necessary to reduce the size of the mesh, particularly dz, to accurately resolve the effects of thin emission layers.
Testing of higher numbers of dipole locations has shown very little change in results for most structures. In general, we do not recommend using more than the 16 dipole locations described here which requires only 7 simulations.