Amorphous Disorder
******************

The disordered nature of typical OLED materials gives rise to a
diversity in molecular environments. This diversity is accounted for
by including e.g. energy level broadening and is an important feature
in describing charge transport inside the device.

The description of the molecular disorder can have a strong impact on
the simulated performance. Various settings are provided to customize
the disorder character. Distribution functions for the polaron/exciton
energies have been discussed in the basic tutorials. This tutorial
will cover methods for introducing spatial correlation between
molecular energy levels.


Correlations between Molecular Energy Levels
============================================

Energy level distributions are typically specified for HOMO, LUMO,
singlet and triplet energy levels in order to model the variations in
energy levels due to amorphous disorder in the molecular environment.
By default, the distributions of the HOMO and LUMO energies are
treated as being uncorrelated. The HOMO shift and the LUMO shift are
then computed independently from one another. This behavior is
exhibited by the majority of OLED materials.

Some materials can exhibit a correlated HOMO-LUMO shift, resulting in
small-bandwidth emission. This is typically observed when the HOMO or
LUMO wavefunction is shielded on the center of the molecule, resulting
in limited interaction with the polarized environment. Anti-correlated
HOMO-LUMO shifts, meanwhile, are typically observed for molecules with
torsional disorder.

The HOMO-LUMO correlation can be set in the **Parameters → Volume →
Energy Landscape → HOMO and LUMO Correlation** field.

* **Correlated** will link the shifts in the HOMO and LUMO levels.

* **Anticorrelated** will make the shift in the HOMO level opposite to
  the shift in the LUMO level.

   [image]Configuration of energy level shifts in the parameter set

Note:

  The magnitude of the energy level shifts may still differ between
  HOMO and LUMO, according to the distributions that have been
  specified in the *Materials* page.

Exciton energies can be correlated to the HOMO-LUMO shifts. The change
in exciton binding energy is then scaled to be proportional to the
change in band gap. Select the **Correlate polaron and exciton
levels** option to enable this behavior.

Exciton energies can be correlated to the HOMO-LUMO shifts. This
behavior occurs when the singlet/triplet wavefunctions resemble the
LUMO, which can typically be characterized by a small binding energy.
Correlation between the polaron and exciton energy can be enabled
through the **Correlate polaron and exciton levels** option. The
change in exciton binding energy is then scaled to be proportional to
the change in the band gap.

Note:

  Be default, the exciton energy levels and the exciton binding
  energies are linked together in order to maintain thermodynamic
  consistency. The exciton energy levels and the exciton binding
  energies can also be decoupled (**Parameters → Advanced → Propagate
  exciton shifts to binding energy**). The shifts in the exciton
  energy levels are then instead applied to the exciton binding
  energies, which may be relevant for specific analyses of
  experimental probing methods.


Dipole Orientation
==================

The polaron and exciton energy level broadening can be modified by
specifying a dipole field. Dipolar interactions between molecules can
stabilize electronic states, such that the stable states in the energy
level distribution will be located at the crests of the dipole field.
This results in a degree of spatial ordering compared to a uniformly
distributed system.

A disordered arrangement of dipoles can be generated by selecting the
**Correlated HOMO and LUMO energies with dipole field** option in the
*Energy Landscape* settings in the parameter set. The dipolar coupling
at each gridpoint will then be evaluated to determine the spatial
energy level distribution.

Dipole strengths are provided for each material to allow scaling of
the interactions based on the composition morphology. An isotropic
dipole distribution is used by default. Alternatively, biased dipole
fields can be specified as part of the dipole settings of the
materials.

A spontaneous orientation factor (SOP) can be specified on the
*Materials* page (**Advanced → Dipoles**). The SOP quantifies a net
alignment of the dipoles with the layer film.

   [image]Material dipole parameters

Because dipolar interactions fall off naturally at the layer
interfaces, the inclusion of a spatial energy correlation to the
dipole field allows modeling of giant surface potential (GSP) effects
on device operation. This effect is further augmented by intrinsic SOP
of the materials.

Note:

  Variations in the *transition* dipole moment affect intermolecular
  exciton transfer processes, and can be specified by including the
  transition dipole moment distribution in the *Materials* page. This
  process is analogous to the above description of the *molecular*
  dipole distribution.To include orientational variance in the
  transition dipole moment during excitonic simulations, the
  **Parameters → Advanced → Include Orientational Disorder** option
  can be enabled.
