# Application Gallery

 Navigation: OLEDs > Planar OLEDs Optimizing far field emission of multilayer stack

In this topic, we will demonstrate how to use the Stack Optical Solver to optimize the position of a dipole inside a multilayer OLED structure to improve the farfield emission. To do this, we first use the stackfield command to calculate the field profile inside the OLED. Then, using the stackpurcell command, we will calculate the far-field emitted power density as a function of dipole positions.

FDTD

### Associated files

simpleOLED_fdtd.fsp

simpleOLED_stackfield.lsf

simpleOLED_stackPurcell.lsf

Calculating radiated power from incoherent, isotropic point dipole sources

stackdipole

stackpurcell

stackfield ### Related publications

 Seung Hwan Ko, "Organic Light Emitting Diode - Material, Process and Devices", (2011), DOI: 10.5772/19292. see chapter 10,  "Micro-cavity in organic light-emitting diode" by Young-Gu Ju.

## Simulation setup

While some OLED designs use scattering structures to improve the extraction efficiency, optimizing such devices are computationally expensive and not recommended as the initial step. A more efficient approach is to start with the multilayer stack using the Stack optical solver. Once the optimal stack geometry is determined, one can further optimize the device by introducing scattering structures like gratings and performing FDTD simulations. The recommended workflow for optimizing an OLED/LED device can be described as below:

Use stackfield to study the field intensity pattern within stack

Determine where to y place the active layer

Use stackdipole or stackpurcell to verify OLED design

If nano/microstructures are required, proceed to direct simulations of Maxwell's equations (ex. FDTD simulations)

The dielectric stack geometry in  consists of six layers with n = 1.5 : 2.13 : 1.87 : 1.94 : 1.75 : 0.644+5.28i. While both FDTD simulations and the stackfield command can be used to calculate the electric field distribution inside this geometry, stackfield is much more efficient for multilayer geometries, especially when a large number of simulations are required.

To calculate electric field distribution using the stackfield command, the refractive index and thickness of these layers as well as source wavelength and injection angles are given as input to stackfield. This is equivalent to running a 1D simulation (with one mesh cell along the x- and z-axis) with a plane wave source traveling along y-axis.

The figure below shows the electric field profile inside the stack layer when a plane wave is injected at 500nm and 700nm wavelengths. For illustration purposes we show the results for all layers. This plot compares the results from FDTD with the results from stackfield and shows good agreement between the two. To create this plot, open fdtd_simpleOLED_Field.fsp and run the simpleOLED_stackfield.lsf script: As can be seen in the plot, the electric field is at its maximum near the center of the active layer. This is ideal because the rate of spontaneous emission is enhanced near locations of high field intensity (ie. high local density of states) and suppressed near locations of low field intensity.

Now that location of the active layer is determined, we can proceed to study the farfield emission of the dipole inside the active layer.

## Results

To obtain the farfield emission, run 1D_OLED_purcell.lsf. The script calls the stackpurcell command for a range of dipole positions within the active layer, and outputs the power density  (Frad(θ) from stackpurcell) as a function of emission angle. This is equivalent to sweeping the dipole position for 301 different values in FDTD. While each FDTD simulation for every dipole location can take several minutes to run, stackpurcell can calculate the result for all dipole positions in a fraction of a second. The figures below shows the farfield power density as a function of polar angle for different dipole locations inside the active layer:

NOTE: FDTD results

A comparison of the FDTD simulation and Stack optical solver results is provided in stackfield and FDTD simulations. One of the main challenges for using FDTD for OLED simulations is that FDTD simulations often require a large simulation region and can be very time consuming compared to stackpurcell, which is based on analytical methods and often require a fraction of a second to run. However, for structures that require scattering geometries, direct simulations of Maxwell's equations like FDTD will eventually become necessary.

## Quantum efficiency and extraction efficiency

The Purcell factor is defined as the ratio of dipole power to source power, as is a measure of the quantum efficiency of an OLED/LED. As discussed earlier in the Simulation methodology of OLEDs section, this parameter measures the decay rate enhancement in the presence of the multilayer stack. This parameter can be calculated using the stackpurcell command.

The plots below shows both the quantum and extraction efficiency as a function of dipole position in the active layer. While the Quantum efficiency approaches infinity near the metal boundary, the extraction efficiency approaches negative infinity, as most of the photons generated are absorbed by the metal layer.

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