This example is intended to give an illustrative introduction to the results returned by the stack dipole sources with the stack GUI.
Download and open the associated oled_simulation.fsp, and inspect the stack GUI object. Below is a basic schematic of a typical OLED device.
This device is designed to emit out the top through the semi-transparent ITO/Al anode, and a glass encapsulation is included. In the stack dipole tab a dipole source is placed in the middle of the emission layer, here this is layer 4. If we click run, the results will be returned in a few seconds and can be visualized as a function of the emission angle theta.
STACKDIPOLE
The results returned by stack dipole are
- radiance \( \frac{W}{\text{steradian }m^2 }\)
- luminance \( \text{candela } m^2 \)
- X, Y, and Z tristimulus values
Radience and luminance are measures of the extraction efficiency. Radiance is a photometric quantity while luminance, is a measure of apparent brightness to the human eye. Given that luminance is a related to how intense light appears to the human eye, if we had a device that was emitting in the infrared it’s luminance would be zero; however, the radiance will be finite no matter the frequency range. To see how the layer dimensions effect these values we reduce the thickness of the top Al layer to 10nm. We can see that the amplitude of the radiance increases due to less loss in the system.
X, Y, and Z tristimulus values are basis vectors of the CIE 1931 color space, describing the perceived color quantitatively. These values are related to the luminance; for more information on color spaces see the chromaticity section of OLED Methodology. Minimizing the angular dependence of the color shift can be an important design specification see Planar OLED Microcavities - Color Shift and Extraction Efficiency
A key input for the color is the emission spectrum of the dipole, as the perceived color is very sensitive to both the intrinsic spectra of the emitting material and any microcavity effects due to the surrounding layers. When modelling realistic devices, accurate spectra should be used. In this example we have a spectral function of the form.
spectrum = width^2/( (lambda-lambda_peak)^2 + width^2);
The first part of this example uses a Green OLED spectrum where width, and lambda_peak are 20nm and 520nm. Changing the peak wavelength in the spectrum script to 620nm would correspond to shifting the devices emission spectrum to red.
If we do this and plot the color coordinates of these two emissions spectra, we see that the overlap with the different bases has changed. For example, Z is a essentially a blue basis spectrum, and we can see that it has very little contribution to the color output of the red emitting device at all angles, as we would expect.
You will notice that all the results are integrated over the bandwidth and so do not depend on wavelength. One thing to note is that the results returned by stackdipole have SI units for radiance/luminance. Since the source spectrum is normalized to a photon probability, converting to dimensional quantities requires a few inputs: current density j, exciton fraction ef, singlet triplet ratio st. For more info on how stackdipole is calculated see FDTD vs stackdipole - halfspace emission in a multilayer stack
STACKPURCELL
The results returned by stack Purcell are
- power [normalized]
- power_density [normalized\steradian]
In power we have the purcell factor F vs wavelength which is the enhancement of spontaneous emission of a dipole in a microcavity. It is proportional to the strength of the microcavity resonance Q, and inversely proportional volume of the microcavity mode. Equivalently, it is the ratio of the total power emitted by the dipole in the microcavity to the power emitted by the same dipole in a homogeneous medium.
You can copy the dipole placement from the stackdipole tab for convenience. Run the solver and visualize the results. We can see that the cavity enhancement is peaked in the Green region, but there is significant enhancement across the bandwidth.
Next is the angular and wavelength dependent power density of radiated emission Frad. To achieve an optimal device one must strike a balance between enhancing emission F, and increasing extraction efficiency \( \eta \) which may come at some cost to F.
$$ \text{Purcell factor} = F(\lambda) = \frac{P_{rad} + P_{non rad}}{P_0} $$
$$ \text{Power density} = F_{rad} (\theta, \lambda) = \frac{P_{rad}}{P_0} $$
$$ \text{Extraction efficiency} = \eta = \frac{F_{rad} (\theta, \lambda) }{F (\lambda)} = \frac{ P_{rad} }{P_{rad} + P_{nonrad} } $$
For more information see FDTD vs stackdipole - halfspace emission in a multilayer stack