# Application Gallery

 Navigation: OLEDs > Patterned OLED Simulation Methodology

This section describes the recommended methodology required to simulate the effect of patterning on a conventional OLED.

FDTD

### See also

Dipole sources

Incoherent unpolarized dipoles

### Related publications

A. Chutinan et al., Organic Electronics, 6, 3-9 (2005)

M. K. Callens, H. Marsman, L. Penninck, P. Peeters, H. de Groot, J. M. ter Meulen, and K. Neyts, “RCWA and FDTD modeling of light emission from internally structured OLEDs,” Opt. Express 22, A589–A600 (2014)

We gratefully acknowledge the collaboration of Horst Greiner of Philips Research in the development of this application example.

## Simulation setup

### Structure

The conventional OLED layers can be constructed using rectangle objects. The OLED patterning can be parameterized using a structure group, which allows one to sweep the design parameters to achieve optimal efficiency. Creating a parameterized model of your OLED will require some initial effort, but it is a worthwhile investment.

### Simulation region

PML (absorbing) boundaries should be used on all sides except possibly below the metallic cathode layer, where we can use Metal boundary conditions where light is supposed to be minimal when reaching the Metal boundary conditions. The simulation span should be large enough to include multiple periods of the patterning. The span of the simulation region needs to be large enough such that there is enough propagation distance for the light to be fully extracted from the emission layer.

We do not recommend using periodic boundaries, even though the structure is periodic, because periodic BC's would imply the dipole sources are periodic and radiate in a coherent manner. In reality, the dipole sources radiate incoherently, which requires a number of simulations with a single dipole source per simulation, as explained in the next paragraph.

In the example simulations, we have used a mesh override region over the cathode to force a coarser mesh which reduces simulation times significantly. Since the in-plane wave vector is conserved, it is not necessary to use a mesh as fine as the one generated automatically by the meshing algorithm. See the Simulation tips (override in Si) page from the CMOS image sensor application for a discussion on this technique.

### Parametrization

In order to optimize the OLED design efficiently, we need to automate the process of altering various components of the OLED model systematically. To do this, we take advantage of the "model" analysis group, which allows us to parametrize all simulation objects. For OLED examples, this includes:

1. Parameters of the OLED structure group.

2. Location the mesh override regions (if necessary).

3. Dipole locations and orientations.

4. Locations of the power transmission box surrounding the dipole (which changes alongside with the dipole locations).

A screenshot of the "model" analysis group

### Sources: simulating incoherent, isotropic emission

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 a ensemble of incoherent, isotropic dipole emitters in a small spatial volume can be calculated by

$$<|\vec{E}|^2> = \dfrac{{|p_0|}^2}{3}[{|E_a|}^2 + {|E_b|}^2 + {|E_c|}^2]$$

where Ea, Eb and Ec are the electromagnetic fields generated by a single dipole along the x, y and z axes (to see the derivation of this formula, please see the Incoherent unpolarized dipole page). Since FDTD is a coherent simulation method, this means that we must run 3 separate simulations of the same dipole oriented along the x/y/z axes and sum up the results incoherently (as shown in FDTD and coherence).

For the OLED examples in this section, we simulate 1 dipole at a time in the emission layer and then use the automated parameter-sweeping tool in FDTD to sweep the various dipole locations and orientations and add the results incoherently.

A screenshot of using the Parameter Sweep to sweep over 3 dipole orientations.

The number of dipole locations required depends on the symmetry of the OLED patterning. Please see each example for a separate discussion.

## Results

### Background on 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 during later discussions of the results that can be obtained from FDTD based OLED simulations.

 $$\gamma _{rad}$$ 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. $$\gamma _{loss}$$ 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. $$\gamma _{em} = \gamma _{rad} + \gamma _{loss}$$ 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. $$\gamma _{nr}$$ 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. $$\gamma _{excitation}$$ 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.

### Extraction efficiency

The light extraction efficiency (LEE) for 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. 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.

$$\begin{array}{c}LEE = \dfrac{\gamma_{rad}}{\gamma_{rad} + \gamma_{loss}} \\ LEE = \dfrac{LEE_{pattern}}{LEE_{no\: pattern}} \end{array}$$

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 files 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.

### Radiative decay rate enhancement

The electromagnetic decay rate of the emitter will be influenced by the surrounding structures (eg. the metal cathode, PC patterning, etc). Calculation of the absolute electromagnetic decay rate is beyond the scope of an FDTD simulation, but it is possible to calculate how the surrounding structure enhance this decay rate. This is possible because the electromagnetic decay rate enhancement is equal to the enhancement of the local density of radiative states in the active layer, which in turn is equal to the power radiated by a dipole source in an FDTD simulation normalized to the power radiated in a homogeneous medium. Fortunately, this last quantity is straightforward to calculate with FDTD. Indeed, this decay rate enhancement is also known as the Purcell factor and is a standard result returned by dipole sources. Therefore, by measuring the power radiated by the sources in a particular OLED design, it is possible to calculate the decay rate enhancement relative to a homogeneous region of the emitting region.

$$\dfrac{\gamma_{em}}{\gamma^0_{em}} = \dfrac{dipolepower}{sourcepower} = Purcell\: factor$$

where gamma_em is the total radiative decay rate with patterning, gamma0_em is the total radiative decay rate without patterning. It then allows us to calculate the decay rate enhancement between those designs. In the following example OLED structures, the patterning has little effect on the total power radiated by the dipole. The patterning primarily improves the extraction efficiency.

Additional resources:

Source - Dipole

dipolepower script function

Greens function and LDOS calculations

### More

With additional knowledge of your emitter, such as the non-radiative decay rate, it is possible to further characterize your OLED device. For example, the Internal Quantum Efficiency (IQE) can be calculated as:

$$IQE = \dfrac{\gamma_{rad}+\gamma_{loss}}{\gamma_{rad}+\gamma_{loss}+\gamma_{nr}}$$

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