Computing charge carrier mobility

The aim of this application is the prediction of the charge carrier mobility for Alq3 and BCP, which is comparable with a TOF “measurement”. A combination of all relevant tasks is listed below:

  • Synthesis of the molecule (Parametrizer, DihedralParametrizer)
  • Morphology generation (Deposit)
  • Spectroscopic measurements (QuantumPatch, lightforge)

The corresponding virtual experiments are presented in Figure 1, which present the corresponding icons of our software tools, ordered in our workflow scheme SimStack, downloadable here. All the details of the settings of the individual calculations are predefined in the downloaded files. For further details of the calculation a more complex study of the mobility of a-NPD is also presented at our documentation page. The starting point is the chemical structure of BCP and Alq3, visualized in Figure 2. Each calculation is performed individually, but in the same fashion, except the part of the DihedralParametrizer, which can be skipped for Alq3 based on its rigidness. First of all, the  molecular structure needs to be studied in detail. Therefore, the Parametrizer tool is used to calculate the chemical properties, such as the partial charges of the atoms, different bond lengths. Different levels of quantum chemical calculations can be selected.

  •  As input for the Parametrizer you can use a pre-optimized 3D structure either generated with our “synthesis” equivalent tool in the mol2 format, or use the input provided in the trial version. The Parametrizer generates two relevant files: molecule.pdb and molecule.spf

Afterwards, the DihedralParametrizer takes care of the dihedral angles, which is important for the correct deposition of the molecules in the next step.

  • Load molecule.pdb and molecule.spf in the DihedralParametrizer module to generate customized energy profiles for rotation of flexible side groups of your molecule. The relevant output of the DihedralParametrizer module is a file named dihedral_forcefield.spf, which can be seen as an improved version of the molecule.spf of the Parametrizer output.

The next step is the formation of the morphology, enabled by the Deposition tool. Here, the size of the final layer needs to be defined and shall contain at least 10 nm. 

  • Therefore, we select in the Deposit tool to insert 1200 molecules one by one into an initially empty box, which has defined dimensions of Lx=40, Ly=40, Lz=120 (in Angstrom). Thus, the resulting box ranges from -40 A to +40 A in x and y-direction. As input for Deposit (Molecules tab), use molecule.pdb from the Parametrizer module and the dihedral_forcefield.spf from the DihedralParametrizer module or molecule.spf of Parametrizer.

The results of these parts deliver the samples for the spectroscopic-type calculations, performed with QuantumPatch (QP) and lightforge (lf). The QP icon is presented twice in the workflow scheme,  which makes the handling easier and more intuitive. 

  • In the first QP calculation the intermolecular couplings between 80 molecules in the center of the morphology are predicted. The calculation is performed using DFT with a BP86 functional and a def2-svp basis set, using the embedded Turbomole software. Surrounding molecules can be treated with different levels of theory. Molecules, which are in a sphere of 15 A around the 80 molecules in the core can be also treated with the same level of theory or cheaper methods such as DFTB+ or XTB. All molecules in a range of 25 A are calculated using DFTB+ for CBP or XTB for Alq3, and all other molecules, which are more than 25 A away and in a shell of 60 A can be included as static point charges. Further details of the QP calculations are explained here
  • In the second QP task, the disorder of the orbital energies of 150 molecules are predicted. Therefore, DFT with B3LYP and a def2-svp basis set is used, using also Turbomole software. The surrounding molecules are treated as in the first QP run. As input for both QP runs just the structurePBC.cml of the deposit run, and nothing else, is required.

The last step in this experiment is a calculation, using the lf package, which finally presents the mobilities of the materials.

  • This simulation requires to include the individual files of the QP runs. Furthermore, many settings are possible in a lf simulation, however, all relevant settings, to generate a hole mobility for the Alq3 or BCP morphology are defined in the downloaded examples. Further explanations of the software tool are presented here. The last essential input for this calculation is a molecule.pdb of the corresponding morphology, resulting from the Parametrizer run. Finally, the lf run creates a folder results, in which you can find the the subfolders experiments, current_characteristics and there finally a mobility.png and mobilities_all_fiels.dat, presenting the final results of this study. 

The results for the CBP hole mobility match the experimental measurements of Ref. 1 really well, as displayed in the following figure. The employed level of theory, using just XTB for all molecules expect the core ones, does deliver good results. Therefore, simulations with also more molecules in DFT calculations can improve the match between the calculation and the experiment further.

In the following the results of the electron mobility of Alq3 is explained and visualized in a figure, the mobility was calculated using the introduced workflow and furthermore extensions of the Workflow with different levels of theory in the QP calculations: we use a QP setup in which just DFT calculations are used (full DFT, green squares) to calculate the requested inputs for LF. Another QP setup, in which just the core molecules are calculated with DFT and all others are calculated with XTB (full XTB, cyan diamonds) and a mixed QP setup, in which the core molecules and all surrounding molecules in a 10 A shell are calculated with DFT, while the other molecules are calculated with XTB (hybrid XTB, blue triangles).

Finally, we used the QP outputs for the LF calculation and then we compare the calculated electron mobility with two experimentally measured electron mobilities of Alq3 (TOF and SCLC measurement of Ref. 2, 3). The comparison shows that the simulation slightly overestimates the measured mobility. Additionally, it introduces a dependency between the accuracy and the employed level of theory. Thus, the full DFT run shows the best predicted values and the cheaper calculations overestimate the mobility more.

1. A. Hoping Appl. Phys. Lett. 92, 213306 (2008)

2. P. Friederich, Adv. Mater. 2017, 29, 1703505

3. H. H. Fong and S. K. So, J. Appl. Phys. 100