OFET Simulation
***************

Organic field-effect transistors (OFET) utilize organic electronics as
charge transport materials in molecular transistors.

OFET modeling in Bumblebee is performed by adding a source-drain field
perpendicular to the primary gate electrodes. This allows the cross-
current behavior to be modeled.

   [image]Default probe-field OFET device geometry used by Bumblebee

The OFET device uses an organic conductor to channel carriers between
the transistor source and drain. Dielectric layers are used to shield
the gates.

Bumblebee uses 2 gate electrodes by default. In order to model single-
gate OFETs, an insulator can be used to cut off access to one of the
gates.

   [image]Single-gate OFET device configuration


Create Materials
================

In this tutorial, we will discuss the modeling of an OFET memory
device, using a charge trapping layer for polaron confinement.

   [image]OFET memory device configuration (MOFET)

We will not focus on the role of excitons in this tutorial. For this
reason, the OFET components will be treated as transport layers. (If
desired, excitonic processes can be added to the OFET simulation to
account for internal loss mechanisms.)


Conductive Layer
----------------

Pentacene is used in the conductive channel. To create a new material,
go to the *Materials* page and use the [image: AddButton][image]
button. Click on the *Transport Material* template.

Add the name *Pentacene* and in the *Electronic* tab, set a HOMO level
of -6.1 eV and a LUMO level of -3.9 eV. Change the electron mobility
prefactor to 0.5 to study the effect of a slower diffusion rate of the
electron species compared to the holes. Under *Excitonic*, we use a
singlet binding energy of 1.2 eV and a triplet binding energy of 1.4
eV. Default Gaussian broadening is used for both polaron and exciton
energy levels. Click on *Save new material*.


Dielectric Layer
----------------

SiO2 is used as a dielectric. For this, go to the *Materials* page and
use the [image: AddButton][image] button to create a new material.
Click on the *Transport Material* template.

Add the name *SiO2*. Under *Electronic* we set a HOMO level of -9 eV
and a LUMO level of -1 eV. For *Excitonic*, we use a singlet binding
energy of 2 eV and a triplet binding energy of 2.1 eV. Default
Gaussian broadening is used for both polaron and exciton energy
levels.

Both electron and hole mobility prefactors are set to 0.1 under
*Electronic* to account for polaron blocking behavior of the
dielectric.

In the *Advanced* tab, we can specify a source-drain injection
prefactor. For the dielectric, this value is kept at 0 to block off
the transistor contacts, which are meant to connect only to the
conductive layer. Save this material by clicking on *Save new
material*.

   [image]Source-drain injection prefactor setting in the Advanced
   material configuration


Memory Layer
------------

PVN is used as the charge storing material in the memory layer. We
again use the *Transport material* template to create this material.

We set a HOMO level of -6.2 eV and a LUMO level of -1.2 eV. For the
excitons, we use a singlet binding energy of 1.1 eV and a triplet
binding energy of 1.5 eV. Default Gaussian broadening is used for both
polaron and exciton energy levels.

The source-drain injection prefactor for the memory layer is set to 0,
as only the conductive layer interacts with the transistor contacts.


Create a Stack
==============

Under the *Stack* page, click on the [image: AddButton][image] button
under *Layers* to create a new layer. We will use the anode as the
active gate. Therefore, we start by placing a 15 nm SiO2 layer. This
is followed by a 10 nm PVN layer and a 35 nm Pentacene layer. The
*Name*, *Composition* and *Thickness(nm)* can be changed by double-
clicking on it. On the top right of the image, change the option to
*Full layer thickness*. The input should be the same as shown in the
figure below. Click on *Save stack* to save the input.

   [image]PVN-MOFET stack setup in BBinput


Create a Parameter Set
======================

Navigate to the *Parameters* page in BBinput. Select *Load preset* and
choose the *OFET* template. This will automatically enable the
*Transistor* module in the parameter set, which adds the source-drain
contacts to the device. Polaron injection at the gates is also
disabled. This prevents polaron hopping into the vacuum.

Note:

  If you want to model the OFET in a cross-current setup, with active
  gates, electrode injection can be re-enabled by adjusting the
  injection and collection prefactors in the *Advanced* tab.

Note:

  The exciton module is not enabled by default in the *OFET* template.
  If you want to model excitonic processes inside the OFET, remember
  to manually enable this module.

Note that the source-drain contacts are not shown in the (one-
dimensional) energy level diagram. The location of the source-drain
channel is instead controlled by the source-drain contacts set in the
material parameters.

We now proceed to configure the gate contacts. On the *Main* tab, the
device voltage is set to 10 V. The anode contact is taken as the
transistor gate. We assume a Au contact and set the Fermi level to
-5.1 eV. The cathode will represent the interface with the air. We set
the Fermi level to 0 eV to avoid interactions with the device.

The *OFET* tab allows configuration of the transistor voltage. The
drain-source field is initially set to 3 V. Technical parameters are
provided for controlling the gate field.

   [image]Transistor configuration in the parameter set

The single-gate transistor has zero electric field at the vacuum
interface. This condition is maintained as charge carriers populate
the device, resulting in a change in the electric field inside the
stack.

An update is performed at a given field check interval to correct the
gate field for the changing polaron distribution. By default, this is
implemented as an external field correction. The field is adjusted
incrementally using the field control step size. Alternatively,
polaron exchange with the gate can be enabled to adjust the carrier
distribution.

To avoid oscillations in the electric field, a field control margin is
defined. Field updates are only performed when the gate field error
exceeds this value.

The adjustment to the gate field is performed to maintain the vacuum
level. The position of the vacuum is located at the cathode by
default.

Save the parameters.


Starting the Simulation
=======================

Sweeps of the gate voltage can be used to obtain OFET transfer curves.
For this tutorial, we perform a voltage sweep from -10 to 10 V using
11 steps. Due to the limited disorder in our MOFET materials, we will
only set a single trajectory. Use **File → Save** and **File → Run**
to start the simulation.

   [image]Gate-voltage sweep configuration in the simulation settings

Tip:

  Parameter sweeps can also be performed for the drain-source field
  strength to investigate the effect of cross-field interactions on
  the device current.

See also:

  To simulate memory programming/erasure cycles, transient switches
  can be used to adjust the device polarity during the simulation.
  Consult the transient response tutorial for more details.


Simulation Output
=================

To check the results of the simulation, open **BBresults** by going to
**SCM → BBresults** and load the *.bee* file.

Polaron mobility, channel conductivity and transfer curves are
available in the **Device → OFET** section of BBresults. The output is
split into 2 tabs: **Simulated** and **Interpolated**. The
**Simulated** tab contains the simulation output of the voltage sweep.
The **Interpolated** tab post-processes the results to construct more
detailed transfer curves. This typically produces more accurate
voltage-dependencies (particularly near 0.0 V). We will therefore
focus on the **Interpolated** output here.

The **Drain-source polaron mobility curves** report the effective
channel conductivity and effective mobility of the carriers inside the
MOFET. The values that we see here are typical for organic electronic
materials.

The conductivity of electrons is approximately twice as high as for
the holes. This is also reflected in the measured currents, which can
be attributed primarily to a lower saturation density for the
electrons. In turn, similar values are obtained for the effective
mobilities as these are mostly determined by the transport through the
pentacene layer.

   [image]Mobility and conductivity measurements for the PVN-MOFET

We can visualize the accumulation of charges from the **Device →
Profiles → Electron Density per Voltage** and **Hole Density per
Voltage** tabs. At positive voltages, electrons are injected into the
device. Hole injection occurs at negative voltages. Our source-drain
contacts are connected to the pentacene layer. Injected electrons do
not go into the PVN memory layer due to the high energy barrier
between LUMO states. This confines the electrons to the channel,
resulting in a shorter effective path length and a higher effective
mobility.

   [image]Voltage-dependent electron density in the PVN-MOFET

   [image]Voltage-dependent hole density in the PVN-MOFET

We can view the electrostatic potential inside the OFET stack (**Sweep
→ Overview → Profiles → Potential**). The gate field inside the
semiconducting channel has been screened. Polarization is therefore
confined to the dielectric layer.

   [image]Electrostatic potential profile at forward gate bias

The transfer curves of the OFET are available in the **Device → OFET →
Transfer Curve** section. These curves show the saturation of the
drain-source current in relation to the applied gate voltage. The
drain-source current is proportional to the effective conductivity
within the simulated regime. This indicates a limited co-axial
transport through the PVN memory layer. Charging of the memory
therefore occurs primarily through exchange with the conductive
transistor channel.

   [image]Transfer curves for the PVN-MOFET

The output curves of the OFET are available in the **Device → OFET →
Output Curve** section. These curves provide the JV characteristics of
the drain-source channel at various gate voltages. An increased gate
voltage enhances the polarization of the dielectric, creating the
*field effect* that enhances the transistor conductivity. We can see
that the PVN-MOFET is operating in the linear regime, with sub-
saturated currents.

   [image]Output curves for the PVN-MOFET

At higher drain-source voltages, higher charge densities in the device
may cause the output curves to level off as the conductive channel is
filled. Excitonic events may also introduce additional loss processes
at higher carrier concentrations, resulting in non-ideal efficiencies.
