Device Equilibration
********************

When an OLED circuit is connected, the voltage over the device
gradually increases until steady-state conditions are reached. This
voltage ramp can be included as part of the OLED simulation.


Circuit Closure
===============

We will investigate circuit closure for the phosphorescent OLED
constructed in the exciton tutorial.

Note:

  A pre-made "project file" is available for the circuit closure
  tutorial.

We open the exciton project using **File → Open** in BBinput. This
will allow us to re-use the previously-constructed phosphorescent
stack.

On the *Parameters* page, we will use the *Load preset* button to load
the *Single voltage point* template. On the *Main* settings tab, we
set the operating voltage to 5 V. The *Excitonics* modules should be
enabled in the *Modules* tab.

In the *Termination* tab, we set the *Convergence threshold* to 0.05.
This will automatically terminate the simulation once the system is
within 5% of the steady-state current.

The *Annealing and Equilibration* tab allows configuration of the
voltage ramp. We set the starting voltage to 0 V.

   [image]Voltage ramp configuration in the parameter set

The ramp implementation increments the voltage over a fixed number of
intervals, resulting in a stepped gradient. Here, we set the number of
steps to 10.

The total duration of the voltage ramp is specified in terms of the
number of Monte Carlo steps. We will use the first 2 output intervals.
(These are set at 100,000 steps in the *Output* settings, giving us an
annealing duration of 200,000 steps.)

Separate report and output intervals can be specified during the
voltage ramp, allowing you to use different parameters compared to the
rest of the simulation. In order to obtain output at the end of every
ramp stage, we set both the report and output intervals equal to
1/10th of the ramp duration.

We can use **File → Save** and **File → Run** to start the simulation.

After the simulation has concluded, we can view the output with
BBresults (**SCM → BBresults**). Transient current profiles can be
viewed in the **Sweep → Convergence → Overview** section.

   [image]Change in the transient current while simulating the circuit
   closure

When the voltage ramp is applied, charges are gradually accelerated
towards the center of the emissive layer. This results in a faster
approach towards the steady-state device current compared to a
constant-bias simulation.


Circuit Disconnect
==================

When the OLED circuit is disconnected, the external voltage drops
near-instantly. This behavior can be investigated using the transient
response feature.

During this process, we first want the device to be operating at
steady-state conditions, i.e. having a stable internal field. A pre-
equilibration stage may be specified in the simulation settings to
allow the system to de-correlate from the initial state, approaching
the device equilibrium. Simulation statistics will then only be
generated for the samples obtained after pre-equilibration.

We load the **annealing.bee** project creating in the previous step.
On the *Parameters* page, we will use the *Load preset* button to load
a clean *Single voltage point* template. The starting voltage is kept
at 5 V. Check that the *Excitonics* module has been enabled on the
*Modules* tab.

The pre-equilibration is configured in the *Annealing and
Equilibration* tab. We set a number of equilibration steps equal to 5
times the output interval. As with the voltage ramp, custom report and
output intervals may be specified during the pre-equilibration stage.
As we are interested in the dynamic behavior here, we will use the
regular simulation intervals.

   [image]Pre-equilibration stage in the parameter set

We will move to the *Transient Parameters* tab to configure the
voltage switch. We create a new checkpoint at 10 microseconds, at
which time the voltage will be set to 0 V.

   [image]We use a checkpoint to switch off the voltage from 5 V to 0
   V after 10 microseconds

For this tutorial, we will only simulate a short window immediately
after the device is disconnected. On the *Termination* tab, we set the
*Target simulation time* to 100 microseconds.

We can use **File → Save** and **File → Run** to start the simulation.
Once the simulation has started, we can monitor the output with
BBresults (**SCM → BBresults**).

At the start of the simulation, the device current (**Trajectory →
Convergence → Overview → Trajectory Convergence**) will behave as
usual.

   [image]Change in the transient current during the equilibration
   stage

As the equilibration phase proceeds, the device is gradually filled
with carriers (**Trajectory → Convergence → Overview → Current Density
per Layer**).

   [image]Current densities at the end of the equilibration stage

Once the equilibration phase has ended, the simulation statistics will
reset, such that the measured data will only cover the simulation
window of interest. Meanwhile, the carrier distribution of the device
is retained. The measurements therefore start from a pre-charged
device.

When monitoring the graphs in BBresults, we can see when the reset in
the statistics happens as the post-equilibration data replaces the
figures.

   [image]Change in the transient current post-equilibration. (Samples
   generated during the equilibration phase are now omitted by
   BBresults)

The voltage drop was configured to occur after 10 microseconds. The
offset is measured from the end of the equilibration phase. This is
also why we did not see any changes in the device operation while the
pre-equilibration was ongoing.

Once the circuit has been disconnected, a rapid drop in charge density
is observed. Emission events (**Sweep → Time Progress → Excitonic →
Transient Radiative Exciton Decay Rate**) continue to occur during a
small window of time (around 5 microseconds). The residual charges in
the device recombine near the emitters, causing the depletion of
charges in the device.

   [image]Change in the emission rate post-equilibration

The exciton density (**Sweep → Time Progress → Excitonic → Transient
Triplet Density**) rapidly approaches zero during this time.

   [image]Change in the triplet density post-equilibration

Residual charges (**Sweep → Time Progress → Electronic → Transient
Electron Density** and **Transient Hole Density**) are seen to persist
for a long time afterward, even after emission has stopped. These
carriers are mostly located in the transport layers. With the
electrons and holes located in different parts of the device, they are
incapable of forming new excitons. In the absence of an external
field, the mobility of the carriers is low, and recombination
therefore takes a long time.

   [image]Change in the electron density post-equilibration

For an OLED with a surface area of 2x2 mm^2, a corresponding
capacitance (**Device → Overview → Performance → Capacitance**) is
calculated to be around 200 pF, which is typical for these types of
3-layer devices.

If the device where to be re-connected, the residual charges in the
device would result in a shortened delay for emission to restart.
However, care should be taken as a discharge into the external circuit
can also occur.
