Here we consider the waveguide modes in a conventional OLED structure. Some of these waveguide modes trap and absorb much of the light generated in the emission layer. Our goal is to determine the propagation loss of the various waveguide modes due to the material losses and absorption by the metal cathode. Even though MODE's FDE solver is more efficient for carrying out this slab mode analysis, this calculation is also possible in FDTD via the integrated mode source.
Waveguide mode analysis
The following screenshot of MODE shows the structure without PC patterning defined by Kitamura . These results can be recalculated with the file slab_interface.lms.
At 500 nm, there are 3 bound modes shown below with and without the layer structure overlaid. These are calculated on a 0.5 nm mesh.
For the above modes, mode 1 and mode 3 have both Ey (normal to the layers) and Ez (direction of propagation) components. Mode 2 has an Ex (tangential to the layers) component only. The losses are as follows
- mode 1: 3.7 dB/micron (essentially an SPR mode)
- mode 2: 0.18 dB/micron (waveguide mode with some loss)
- mode 3: 1.7 dB/micron (combined dielectric/SPR mode)
In an LED structure, dipoles oriented in the slab plane have a reasonable efficiency for coupling out of the device because much of the radiation is directed upwards (or downwards and then reflected upwards) anyway. These in-plane dipoles weakly couple to mode 2 and do contribute to some of the trapping of the light in the device.
For the dipoles normal to the slab, the light is primarily radiated in-plane and is mostly trapped. Some of this trapped light couples to modes 1 and 3 and is absorbed after propagating at most a few microns. Even mode 2 will only allow light to propagate 55 microns before it is down 10 dB.
With FDE, it is easy to look at the variations in loss and effective index of these guided modes with wavelength (via Frequency analysis). At short wavelengths, a fourth mode is supported that cuts off near 480 nm. The blue, green, red and pink lines represent mode 1, 2, 3 and 4 respectively.
In the figures below, the mode loss of the four modes is plotted vs wavelength. The right hand figure is an expanded view of the lowest loss modes in the left hand view.
We can ignore the loss fourth mode above the cutoff wavelength. The bound modes never have losses below about 0.15 dB/mm, but the modes that will be excited by the vertical dipole have losses on the order of dB/micron over the whole wavelength range.
In FDTD, the same analysis can be carried out via the integrated mode source. The same structure discussed above has been set up in slab_interface.fsp. Here, a mode source is set up across the OLED layers, and we can use the script mode_source_sweep.lsf to obtain the change in the effective index with respect to wavelength. This process is made possible with the use of the updatesourcemode script command, which updates the selected mode source for each wavelength. If a mode is already stored, it selects mode that has the best overlap with the original mode, allowing the same mode to be tracked as one sweeps the wavelength. Unlike in MODE (where one can sweep all 4 modes at the same time), with the integrated mode solver, one can only track one mode at a time.
The basic idea of adding a micro-structure pattern (such as a photonic crystal pattern) is to help scatter out some of this light trapped as waveguide modes and surface plasmon modes in the LED (OLED) structure. It is clear that for this pattern to be effective at increasing the light extraction efficiency for vertical dipoles, the pattern will have to be able to extract most of the light from the SPR modes in less than a few microns distance. Thus reasonably strong scattering is needed.
Finally, it is also clear that simulation methods that ignore these waveguide modes and the actual material losses in the layers comprising the LED will not correctly calculate the light extraction efficiency. Fortunately, FDTD inherently treats all these effects without approximation.
- M. Kitamura et al., "Enhanced Luminance Efficiency of Organic Light-Emitting Diodes with Two-Dimensional Photonic Crystals", Japanese Journal of Applied Physics, 44, 2844-2848, (2005)
We gratefully acknowledge the collaboration of Horst Greiner of Philips Research in the development of this application example.