Analyzing doping efficiency in doped injection layers

Introduction

Doped injection layers are commonly used to lower injection barriers between electrode and organic materials, and to increase charge carrier mobility in injection layers. In these injection layers, a charge transfer between dopand and host molecule generates electron-hole pairs which may separate, leading to free charge carriers. How many dopands become active and how many free charge carriers are generated is determined by a complex interplay of various properties such as absolute transport energy levels (EA/IP), coulomb binding energies and energy disorder.

In this tutorial, we will analyze doping efficiency in an injection layer of Alpha-NPD doped with F4TCNNQ using LightForge based on ab-initio input from QuantumPatch. In LightForge all molecular sites are neutral to start with, and a charge transfer between a dopand and a neighboring host molecule can occur during the dynamic relaxation of the system. After equilibration, we will analyze the fraction of activated dopands in dependence of the doping concentration and identify the doping concentration where the Fermi-level of the injection layer is aligned to the electrode, i.e. the doping concentration above which injection into the organic film occurs almost without any barrier.

Computing ab-initio input for the LightForge equilibration

Generating atomistic morphologies with Parametrizer, DihedralParametrizer and Deposit

First, we need to generate atomistic morphologies of doped layers. If you are not yet familiar with Parametrizer, DihedralParametrizer and Deposit, please follow this webinar. Keep in mind that you need to run Parametrizer for both the mol2 input of Alpha-NPD and F4TCNNQ, subsequently Dihedralparametrizer on Alpha-NPD and load molecule.pdb and the respective spf files in the Molecules tab in Deposit. In this use-case we used the following settings:

  • Lx=Ly=50, Lz=180
  • PBC enabled, cutoff = 20.0
  • Number of molecules: 2000
  • Initial Temperature: 4000K; Final Temperature: 300K, Sa Acc Temp: 5K
  • Number of Steps: 130000; Number of SA Cycles: 32
  • DihedralMoves: True

In the molecules tab, include host and dopant molecular data at required concentrations. Keep in mind that very low concentrations may lead to bad statistics.

Deposit scales well with the numbers of cores on a single node up to the number of SA Cycles, so we allocated a full node of 32 cores with 64GB memory in the Resources tab of SimStack.

Electronic structure analysis

Remark: Following the instructions below, the coulomb binding energy VC is computed efficiently using an estimator during the Disorder run. For the extended computation of VC via explicit CT states in QP, follow this description

Subsequently, we need to compute the electronic properties of molecules in the thin film required for the KMC simulation in LightForge: Absolute EA and IP levels, site energy offsets from the mean, coulomb binding energy of the activated host-dopant pairs, and electronic couplings.

Therefore, set up the following QP runs using the morphology from Deposit:

  • Absolute transport levels IP and EA: We are currently benchmarking a method to compute IP and EA in a single QP run with improved accuracy. Until this can be included in the next release, please follow the steps below to compute IP and EAin two separate runs.

    • Follow the IP tutorial and save the output as IPAnalysis.zip
    • To compute corrected transport EA, use the single dopant and host molecule from the Parametrizer module and follow the EA tutorial. Save the output as Host/DopantEAAnalysis.zip
  • Disorder including local energy landcape effects. Either follow the instructions in the mobility tutorial with the following additions:

    • For the core engine "TM core" set threads to 8 and increase memory to 8000. This will speed up the VC estimation in case you allocate more than (number of centers for charged run)*4 cores (see below).
    • To compute coulomb binding energy via a cheap, yet quite accurate estimator after the Disorder run, activate the option "Predict coulomb binding energy distribution" in the Postprocessing tab of QuantumPatch. With this mode, a couple of molecules (number given in the field "number of centers for charged run", we recommend 10 or more) are computed in the charged state at the end of the Disorder run. If you know the permittivity of your material, enter the value here, otherwise 3.0 is a good guess.
    • To include local energy landscape effects in the LightForge simulation (i.e. host transport levels shifted when close to dopants), activate the "Predict site energy distribution" in the Postprocessing tab of QuantumPatch. Supply the non-PBC "structure.cml" from Deposit and uncheck z-Rotation. Set periodic copies to generate samples of appropriate size. Note that this step defines the sample size in LightForge. For deposited samples with a width of 8nm (Lx=Ly=40), extension by 3,2,2 samples is sufficient. Transport will occur along the x-direction. An example of this type of analysis is presented in the band bending use case. Rename the output from Analysis.zip to DisorderAnalysis_VCest.zip
  • Electronic couplings: Follow this tutorial with the following adaption: Set "Inner Part Method" to "nuber of molecules", set to 150. If your guest concentration is very low (2% or below), a higher number of molecules in the core shell may be required to compute couplings for guest-guest pairs. Also note that for pairs where charge transfer is possible, electronic couplings may not converge with standard settings. Please define a second core engine "TM core" with def2-SVP and b3-lyp, but set scf convergence to superextreme. Use this engine as fallback for the core engine. Save the Analysis.zip file as JsAnalysis.zip

  • Lambda: For the time being, we set the reorganization energy manually to 0.2eV.

Equilibrating doped injection layers in LightForge

We are in the progress of setting up a detailed tutorial in LightForge. With the input above, follow this temporary tutorial. If you computed coulomb binding energies explicitly via CT states in QP, follow this temporary tutorial instead.

Analysis

lightforge calculations create a folder /results that contains a variety of outputs and raw data. In the following we will focus on the most relevant results for this particular use case. For a generic description of lightforge outputs, please refer to the according section in the lightforge documentation

Band diagram and coulomb binding energy

The subfolder /results/material/energy_levels contains plots of energetics of the system.

  • The band diagram of the host dopant system is visualized in the file energy_crosssection3_0.035_x.png. This file is created once for each applied field_strengh (0.035 V/nm here) and once for each temperature and simulation. These energy levels of the band diagrams are based on the QuantumPatch input.
  • Coulomb binding energy for host dopant pairs with different distances, VC, is visualized in V_coul_exp_dopant_host.png.
  • The file V_coul_fit_inverse.png displays VC over the inverste distance and the permittivity of the host dopant system derived by fitting classical coulomb interaction to the microscopic data from QuantumPatch.

These results can be used as a first "sanity check" of the calculation, e.g. if energy levels are set as expected, or if VC and fitted permittivity are in a reasonable order of magnitude.

band diagram coulomb binding energy VC permittivity fit

Analysus of current characteristics and DOS

The subfolder /results/experiments/current_characteristics contains analysis of current calculations with respect to the applied temperatures. The values are listed in the current_density_Temperature.dat and also displayed in the figure current_density_Temperature.png. The label of this figure displayes the transport activation energy obtained from the slope of the fit of current density to the inverse temperature. In this case, we obtain a transport activation energy of 150meV and a current desity of 1.024e+03 A/m2 at 300K.

The density of states (DOS) and analysis of doping activation can be found in the directory /results/experiments/particle_densities. Here, the file dos_average.png depics of IP and EA*, and the legend contains the following quantities:

  • the number of dopants (n_dop: 100) and activated dopants (n_ion_p_dop: 99.81), resulting in a fraction of activated dopants of 99.81%.
  • the number of free charge carrier is 9.70 (n_free_p). This value can be normalized to the system size (e.g. 1 Mio molecules) to compare between different materials or different doping concentrations. The system size can be extracted e.g. from the COM_ext.yml file in the QP_output_0/Analysis/files_for_kmc folder (The first part ('COM' until 'Dimensions') of this file lists the xyz-coordinates of each molecule and its type, 0 or 1, host or dopant).
  • Fermi level derived by the intersection of DOS of IP and EA+
  • Transport energy: Holes above this energy contribute to charge transport, whereas holes below this energy are trapped.
current temperature dependency density of states analysis

The results of the search are