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Adding patterning to the layers in an OLED can increase the light extraction efficiency. This example uses 2D FDTD simulations to measure the light extraction enhancement.

Minimum product version: 2019a r1

### Contents

Overview

Run and results

Updating the model with your parameters

Taking the model further

Convergence

Appendix: OLED simulation methodology

## Overview

Understand the simulation workflow and key results

OLEDs are challenging devices to simulate as a large number of time-consuming simulations are required and the post processing is complex. Additional information on the simulation methodology can be found in the appendix.

Starting with 2D simulations is strongly recommended as these simulations run much faster. Once you learn the methodology and gain confidence in the results, it is relatively straightforward to apply the same methodology to 3D simulations.

In step 1, we characterize the emission of a 1D stack (without patterning). In the subsequent steps, we characterize the enhancement provided by adding a pattern to some of the layers in the device.

Step 1: Characterize the 1D stack using FDTD simulations.

The incoherent, unpolarized emission from the active layer of the OLED is obtained by running a series of simulations using a dipole source in various positions and orientations. See the appendix for more information on this approach.

Step 2: Use same approach as step 2, but with the patterned OLED.

Step 3: Through post-processing determine the performance enhancement provided by the patterning.

The light extraction efficiency (LEE) is defined as the fraction of optical power generated in the active material that escapes into the air above the device, within a desired range of angles.

The extraction efficiency enhancement is then the ratio of the LEE obtained for 2 designs, without and with pattern.

In this example, we only consider the electromagnetic decay rate (due to radiation and absorption). Electrical effects, edge effects and packaging are not taken into consideration.

The FDTD simulation do not take into account the actual emission spectrum of the active material. However, this can be added as a post processing step.

Note: this workflow could, in theory, also be applied to LEDs, but the large thickness of the substrate makes it unrealistic due to the large memory and simulation time that would be required.

## Run and results

Instructions for running the model and discussion of key results

### Step 1: Characterize stack (FDTD)

1.Open the file "OLED_2D.fsp".

2.Open the script file "OLED_2D_nopattern.lsf".

3.Click the run script button.

4.The results are automatically plotted or can be explored in the script workspace.

As discussed in the appendix, we use the parameter sweep “nopattern_dipole_orientation” to run 3 simulations and incoherently average their results.

The “far_field_change_index” analysis group is used to calculate the farfield projection and fraction of power transmitted in the glass substrate as well as in air, accounting for Fresnel reflections that occur at the interface.

Fraction of emitted power

The fraction of emitter power is obtained from the analysis group and normalized to the emitter power:

In this device, less than 30% of the light is actually extracted, the rest being lost in the various layers.

Farfield profile in air

The "far_field_change_index" analysis group uses FDTD Solutions' far field projection functions to calculate the far field angular distribution. This analysis object also accounts for reflection and refraction that would occur at a far field glass/air interface.

Decay rate enhancement (relative to homogeneous emitter)

As discussed in the appendix, the radiative decay rate enhancement is given by the Purcell factor:

$$\frac{\gamma_{em}}{\gamma_{em}^0} = \frac{dipolepwer}{sourcepower} = Purcell factor$$

The "dipole_power" analysis group calculates the power emitted using 2 different methods:

Using a box of monitors around the dipole source.

Using the "dipolepower" function.

Both methods give very similar results. However, the "dipolepower" script function should not be used when the dipole is located in a dispersive medium. For example, if the active layer "alq3" object is changed from being a simple dielectric to using a dispersive material, the "dipolepower" function and box of monitor technique will give very difference results. In such case, the box of monitor technique is more reliable.

### Step 2: Characterize stack with pattern (FDTD)

1.Open the file "OLED_2D.fsp".

2.Open the script file "OLED_2D_pattern.lsf".

3.Click the run script button.

4.The results are automatically plotted or can be explored in the script workspace.

As discussed in the appendix, we use the nested parameter sweep “pattern_dipole_position” to run 6 simulations (2 position and 3 orientations for each position) and incoherently average their results.

Similar to step 1, the “far_field_change_index” analysis group is used to calculate the farfield projection and fraction of power transmitted in the glass substrate as well as in air, accounting for Fresnel reflections that occur at the interface.

Fraction of emitted power

The fraction of emitter power, cumulative in different layers, is obtained from the analysis group and normalized to the emitter power:

About 60% of the emitted light is absorbed in the OLED layers, about 10-15% is trapped in glass, and only 20-25% is able to reach air.

Farfield profile in air

The “far_field_change_index” analysis group uses FDTD Solutions' Far field projection functions to calculate the far field angular distribution. This analysis object also accounts for reflection and refraction that would occur at a far field Glass-Air interface.

Adding the pattern has a strong impact on the radiation pattern and its wavelength dependency.

Decay rate enhancement (relative to homogeneous emitter)

Similar to step 1, we get the decay rate enhancement (relative to homogeneous emitter) from the Purcell factor calculated using the 2 methods (“dipolepower” and box of monitors).

The dipole power has a much more complicated shape when the pattern is present.

### Step 3: Enhancement due to pattern

1.Open the file "OLED_2D.fsp".

2.Open the script file "OLED_2D_enhancement.lsf".

3.Click the run script button.

4.The results are automatically plotted or can be explored in the script workspace.

Extraction efficiency enhancement

As discussed in the appendix, the extraction efficiency enhancement is calculated from the extraction efficiency with and without patterning:

$$LEE_{enhancement} = \frac{LEE_{pattern}}{LEE_{no pattern}}$$

The script “OLED_2D_enhancement.lsf” calculated the extraction efficiency of light escaping into the air within a 5-degree cone, from the farfield profiles in air calculated with and without pattern.

The above plots show that extraction efficiency is highly wavelength dependent, and one can achieve significant enhancement at particular wavelengths with the use of PC patterning. Therefore, by setting the operating wavelengths of the OLED at these wavelengths, one can potentially achieve extraction efficiencies much higher than that of the conventional OLED. To analyze the OLED for different operating wavelengths, one can simply integrate the results over the desired emission spectrum (see “Taking the model further”).

Note: the simulation file already contains the results from the parameter sweeps. You can simply run the script file to extract the results.

Decay rate enhancement (pattern/no pattern)

Similarly, the decay rate enhancement due to the pattern can be calculated from the results obtained with and without pattern:

$$\gamma_{em}^{enhancement} = \frac{\gamma_{em}^{pattern}}{\gamma_{em}^{no pattern}}$$

We can see on the plot above the decay rate enhancement has a complicated shape and is very wavelength dependent.

## Important model settings

Description of important objects and settings used in this model

### Simulation region width

The simulation span must be large enough such that light propagating upwards is able to pass through the far field monitor before it is absorbed in the PML on the side of the simulation region.  Light propagating at steep angles requires the simulation span to be large. It is worthwhile to understand that some light is permanently trapped within the high index layers.  It is ok if this light is absorbed in the PML on the sides of the simulation region.

The movie monitor is a helpful way to visualize these fields.   The movie monitor is disabled by default, since it increases the overall simulation time.

### Mesh override region over cathode

We use a mesh override region over the metal cathode to force a coarser mesh which reduces simulation times significantly. By default, the automatic meshing algorithm generates a mesh far smaller than is required for this simulation.

### Mesh override region over the emitter

In FDTD simulations, we use a dipole source to emulate the emitter. In principle, dipole sources are injected by exciting the electric and magnetic fields at only one point on the mesh. In order to allow injection at arbitrary spatial positions and dipole orientations, several mesh points are actually excited with appropriate weighting's. This means that the total injected power changes when you move the dipole by amounts smaller than the mesh size, dx.

By using a mesh override region over the dipole, we ensure the position of the source with respect to the mesh stays the same when moving the source.

### Box monitor vs dipolepower

In the FDTD simulations, the power emitted by the dipole source is calculated using 2 different methods:

Using a box of monitors

Using the “dipolepower” script function.

In principle, both methods give the same result. However, if the dipole is located within a dispersive medium (with a non-zero imaginary part of the refractive index), then the results of this function are not reliable. In such situations, using a box of monitors around the dipole is recommended.

Additionally, numerical errors in “dipolepower” calculation may become noticeable when very small simulation mesh sizes are used. If the mesh step is the order of, or smaller than, $$\lambda/1000$$, verifying the “dipolepower” results by measuring the radiated power with a small box of monitors surrounding the dipole is recommended.

That said, “dipolepower” is simpler, and generally recommended when the mesh size is large and the material is non dispersive.

### “far_field_change_index”

The ‘top’ material in the simulation is glass.  Due to the thickness of the glass, it is not practical to directly include the glass-air interface in the simulation.  The far_field_change_index analysis object takes the near fields measured in the glass and calculates the resulting far field emission pattern in glass or air (taking into account Fresnel reflection at the interface).  Since farfield projections can be time consuming, you can reduce the projection resolution (by default, 1001 points) in the analysis variables, and/or the number of frequency points (by default, 300 points) in the monitors’ global properties.

## Updating the model with your parameters

Instructions for updating the model based on your device parameters

The OLED 2D simulation file is parametrized to allow easy modification of the common properties:

Presence of pattern

Period and height of the pattern

Index for farfield reflection

Frequency/wavelength range of interest

Material stack (materials and layer thicknesses)

## Taking the model further

Information and tips for users that want to further customize the model

### How to use a custom spectrum

By default, FDTD Solutions will normalize the fields recorded by frequency monitors to the source spectrum, so these monitors will return the impulse response of the device. It is then easy to calculate the response to an arbitrary power spectrum. We simply multiply the impulse response of the system by the new power spectrum:

$$f_{spectrum}(\lambda) = Power_{density} (\lambda) \cdot f_{impulse} (\lambda)$$

Where $$f_{impulse}$$ is the impulse response, $$Power_{density}$$, the new power spectrum.

This can be performed as a post-processing step. Therefore, you can calculate the response to any spectrum without having to re-run the FDTD simulation.

### Export farfield data to ray tracing

Designing OLED/LED devices requires a combination of nanoscale and macroscale optics. The individual pixels often have sub-wavelength features such as thin dispersive layers scattering structures that require electromagnetic field solvers, while the emission from the macroscopic device requires a ray-based tool.

For these applications, one can calculate the angular distribution of a pixel with the Stack Optical Solver or FDTD Solutions, and then load the result into a ray tracing tool in the form of ray sets.

FDTD Solutions supports the export the angular distribution to ray sets for Breault Research ASAP and ZEMAX OpticStudio (requires an additional license).

## Convergence

Tips for ensuring that your model is giving accurate results

Many parameters can affect the accuracy of a FDTD simulation. It is generally advised to perform some careful convergence testing to make sure you are using the optimum settings for the desired accuracy. The methodology is described in the “Convergence testing for the FDTD Solver" page.

In this section, we will focus on settings specific to this application. As a starting point, you can compare the results obtained at step 1 and step 2. If the agreement between the 2 is not good enough, you can adjust the following parameters.

### Simulation width

As mentioned previously, the simulation region should be wide enough so the light propagating upwards will pass through the monitor before being absorbed by the PML on the edge of the simulation region. This can be visually checked by using a movie monitor to record the propagation of the fields in time.

A movie monitor is included in the simulation file. By default, the monitor is deactivated as it generally increases the simulation time.

If you increase the simulation region width, make sure the structure and “far_field_change_index” analysis group still extend beyond the limit of the simulation, so you will not clip the fields or add an air interface.

### Number of dipole positions

In this example, with the pattern, we consider only 2 dipole positions:

aligned with a hole (x=0)

between 2 holes (x=a/2, where a is the period of the pattern)

In most cases, this should be enough but advised to validate this by increasing the number of positions and check the results are not affected.

This can be achieved by modifying the “pattern_dipole_position” parameter sweep.

### Dipole power vs box of monitors

As mentioned in “Important model settings”, in most cases, both methods will give similar results and the difference will decrease with the mesh size.

However, the “dipolepower” script function should not be used when the dipole is located in a dispersive media. For example, if the active layer is changed from being a simple dielectric with index 1.68 to a dispersive material model in the material database, the “dipolepower” script function and box of monitor technique will give very different results, as shown below:

In such cases, the box of monitor technique is more reliable.

The simulation and script files provided in this example will automatically use both methods, so you will be able to compare the results and use the appropriate one when needed.

### Mesh size in active layer

In the example, we use a mesh override region to set a coarser mesh in the x direction, than the mesh automatically generated by the algorithm. This allows to reduce the simulation time significantly, but you need to make sure it will not affect the results too much.

This can be checked by disabling the mesh override object and comparing the results.

Additional documentation, examples and training material

Related KB pages:

Lumerical University courses:

## Appendix: OLED simulation methodology

### Simulating incoherent, isotropic emitters

Light is generated in the active layer of an OLED as the electrons and holes recombine to create photons. The photons are created by a process called spontaneous emission and each photon has a random direction, phase and polarization. While in principle, the exact treatment of this process must be described quantum mechanically in terms of photons, in practice, it is possible to treat the generated light classically using electromagnetic point dipole sources. Therefore, the average electromagnetic field intensity of an ensemble of incoherent, isotropic dipole emitters in a small spatial volume can be calculated by:

$$\langle \vert \vec E \vert ^2 \rangle = \frac{ \vert p_0 \vert ^2}{ 3 } \left[ \vert E_a \vert ^2 + \vert E_b \vert ^2 + \vert E_c \vert ^2 \right]$$

Where $$E_a$$, $$E_b$$ and $$E_c$$ are the electromagnetic fields generated by single dipole along the x, y and z axes. Since FDTD is a coherent method, this means we have to run 3 separate simulations of the same dipole oriented along the x, y, z axes and sum up the results incoherently.

### Decay rates

FDTD based simulations of OLED devices often involve measuring enhancements to the radiative decay rate of the emitter. The following definitions will be helpful to understand the results that can be obtained from FDTD based OLED simulations.

Radiative decay rate $$\gamma_{rad}$$:

The decay rate of excitations to photons that can be collected and used in the device. For an OLED structure, this would be the decay rate of excitations to photons that propagate from the OLED structure into the air within a useful range of angles. Calculations involving the radiative decay rate are within the scope of an FDTD simulation.

Loss decat rate $$\gamma_{loss}$$:

The decay rate of excitations to photons that are absorbed or otherwise lost in the device. Photons absorbed in lossy material, trapped by TIR in high index layers, or radiate outside a desired range of angles are included in this category. Calculations involving the loss decay rate are within the scope of an FDTD simulation.

Total electromagnetic decay rate $$\gamma_{em} = \gamma_{rad} + \gamma_{loss}$$:

The total electromangetic decay rate. This is simply the sum of $$\gamma_{rad}$$ and $$\gamma_{loss}$$. This is within the scope of an FDTD simulation.

Non-radiative decay rate $$\gamma_{nr}$$:

The decay rate of excitations to non-radiative processes. Excitations that decay into phonons (heat) are included in this category. Calculations involving the non-radiative decay rate of an emitter are beyond the scope of an FDTD simulation.

Excitation decay rate $$\gamma_{excitation}$$:

The excitation rate of the emitter. The emitter is typically excited electrically. Calculations involving the excitation rate are generally beyond the scope of an FDTD simulation. In cases where the system is pumped optically, then enhancements to this quantity can be calculated by FDTD. For simulations involving optical pumping, the 4-level 2-electron laser model may be a helpful starting point.

### Light extraction efficiency (LEE)

The light extraction efficiency of an OLED is defined as the fraction of optical power generated in the active layer of the OLED that escapes into the air above the OLED within a desired range of angles.

$$LEE = \frac{ \gamma_{rad} }{ \gamma_{rad} + \gamma_{loss} }$$

We can also define the light extraction efficiency enhancement as the ratio of the light extraction efficiency for two different designs, such as a patterned vs un-patterned OLED structure as in this example.

$$LEE_{enhancement} = \frac{ LEE_{pattern} }{ LEE_{no pattern} }$$

When calculating the light extraction efficiency, we measure the fraction of useful power emitted from the OLED device relative to the total power emitted from the active layer. We may consider the fraction of useful power to be the light that escapes to the glass substrate, or we may consider the light escaping to the glass substrate within a particular solid angle (eg. bounded by the TIR critical angle). It is important to remember that the glass substrate is usually quite thick, which means the glass-air interface cannot be directly modeled in the FDTD simulation. Instead, the far field projection functions are used to include any reflection and refraction effects that occur at this interface.

The following are the steps for analyzing the extraction efficiency, once the simulations have completed:

1.Use a far field projection to calculate the angular distribution of light into the glass (or eventually into air)

2.Integrate the far field distribution to calculate the fraction of light that escapes into the air. Note that if we are only interested in the total amount of light that escapes into the glass, then a near field transmission calculation will be sufficient. The more time-consuming far field projections are only required when it is necessary to calculate the power within some range of angles, or when including effects from the glass-air interface.

3.Steps 1 & 2 must be repeated for each simulation (dipole orientation and position). Finally, the results must be averaged to obtain the response (light extraction efficiency or enhancement) of the device to a more realistic incoherent isotropic source.

In the example file in this topic, we use the "far field change index" analysis group to obtain the power transmission and far field projection data into both the glass and air regions.

$$\frac{ \gamma_{em}}{ \gamma_{em}^0 } = \frac{ dipolepower }{ sourcepower } = Purcell factor$$
where $$\gamma_{em}$$ is the total radiative decay rate with patterning, $$\gamma_{em}^0$$ is the total radiative decay rate without patterning. It then allows us to calculate the decay rate enhancement between those designs.