Tim Clark: Approaching reality - simulating electronic devices

Tim ClarkTim Clark, of the University of Erlangen-Nürnberg, was the first speaker. The impact of modern hardware and software on simulations has not been an issue of doing things faster and faster, but rather one of doing calculations that we could not do before. Ab initio calculations can now be done on compounds with several hundred atoms, density functional theory calculations on a few thousand atoms, and semiempirical molecular orbital (MO) calculations on 100,000 atoms. Simulations of several microseconds are now standard.

Semiempirical (neglect of diatomic differential overlap, NDDO) molecular orbital (MO) calculations without local approximations are now possible for 100,000 atoms or more with the massively parallel semiEMPIRical molEcular-Orbital Program (EMPIRE) program,1-3 which is freely available to academic groups. Calculation scales with approximately N2.5. We are no longer limited to small or homogeneous, perfect systems, but can now include defects, dopants, impurities or domain boundaries in the calculations, or even calculate amorphous systems.

The results of such calculations can be used to simulate charge-transport through disordered monolayers. Clark’s team has studied self-assembled monolayer field-effect transistors (SAMFETs) handling conformational freedom using classical atomistic molecular-dynamics (MD) simulations, electronic properties using very large scale semiempirical MO theory, and conductance by propagating single electrons or using diffusion quantum Monte-Carlo (DQMC) charge-transport simulations.4-9

The molecules that comprise the SAM contain insulating and semiconducting moieties, so that they serve as both gate dielectric and the active transistor channel in a device:

Transistor

Tim’s team has used simulations to describe and optimize complex systems of self-assembled monolayers on surfaces, not only to explain their morphology, but also to predict molecular compositions and arrangements favorable for improved charge transport.7 In more recent work,10 they have constructed transistors based on SAMs of two molecules that consist of the organic p-type semiconductor benzothieno[3,2-b][1]benzothiophene (BTBT), linked to a C11 or C12 alkylphosphonic acid. Both molecules form ordered SAMs, but the experiments show that the size of the crystalline domains and the charge-transport properties vary considerably in the two systems. Because of the angle of the head groups one can form crystalline domains and the other cannot. This can be reproduced with simple force field calculations.

Sams

The procedure for charge transfer simulations is as follows:

  • Calculate the neutral system and use local properties as external potentials:
    1. Local electron affinity11,12 for electrons, local ionization energy13 for holes
    2. Cluster model or periodic-boundary conditions
  • Monte-Carlo search for conductance paths
  • DQMC simulations14 for many electrons
  • Propagate single charge carriers on these potentials to determine time scales.

Tim showed an MD simulation of the charge transport paths. For the transport calculations, the team employed a fully quantum mechanical description, namely Landauer transport theory.9 In accord with experiment, they found an improved charge transport across BTBT-C11-PA SAMs compared to BTBT-C12-PA SAMs.

DQMC reproduces voltage/current curves (assuming that the number of Monte Carlo steps correlates with time) and reproduces experimentally observed hysteresis. It also revealed dimeric fullerene electron traps.15 Density functional theory calculations indicate that van der Waals fullerene oligomers can form interstitial electron traps in which the electrons are even more strongly bound than in isolated fullerene radical anions. Spectroelectrochemical measurements on a bis-fullerene-substituted peptide provide experimental support. The proposed deep electron traps are relevant for all organic electronics applications in which non-covalently linked fullerenes in van der Waals contact with one another serve as n-type semiconductors.

Finally Tim showed the results of simulations of hole-transport through a self-assembled monolayer substituted with a p-type organic semiconductor and with crystalline domains (see the work above on BTBT linked to a C11 or C12 alkylphosphonic acid). He illustrated hole transport through the monolayers. Hysteresis is not observed in this case. Tim also illustrated well-defined paths through the crystalline domains of the O2(OH)P(CH2)11-BTBT material. The researchers have shown that structural order is particularly important for the electronic properties of semiconducting self-assembled monolayers, and they predict that semiconducting SAMs with a higher degree of crystallinity and larger crystalline regions will exhibit superior performance.

  1. Hennemann, M.; Clark, T. EMPIRE: a highly parallel semiempirical molecular orbital program: 1: self-consistent field calculations. J. Mol. Model. 2014, 20 (7), 2331.
  2. Margraf, J. T.; Hennemann, M.; Meyer, B.; Clark, T. EMPIRE: a highly parallel semiempirical molecular orbital program: 2: periodic boundary conditions. J. Mol. Model. 2015, 21 (6), 144.
  3. Wick, C. R.; Hennemann, M.; Stewart, J. J. P.; Clark, T. Self-consistent field convergence for proteins: a comparison of full and localized-molecular-orbital schemes. J. Mol. Model. 2014, 20 (3), 2159.
  4. Novak, M.; Jaeger, C. M.; Rumpel, A.; Kropp, H.; Peukert, W.; Clark, T.; Halik, M. The morphology of integrated self-assembled monolayers and their impact on devices - A computational and experimental approach. Org. Electron. 2010, 11 (8), 1476-1482.
  5. Jedaa, A.; Salinas, M.; Jaeger, C. M.; Clark, T.; Ebel, A.; Hirsch, A.; Halik, M. Mixed self-assembled monolayer of molecules with dipolar and acceptor character. Influence on hysteresis and threshold voltage in organic thin-film transistors. Appl. Phys. Lett. 2012, 100 (6), 063302/1-063302/4.
  6. Salinas, M.; Jaeger, C. M.; Amin, A. Y.; Dral, P. O.; Meyer-Friedrichsen, T.; Hirsch, A.; Clark, T.; Halik, M. The Relationship between Threshold Voltage and Dipolar Character of Self-Assembled Monolayers in Organic Thin-Film Transistors. J. Am. Chem. Soc. 2012, 134 (30), 12648-12652.
  7. Jaeger, C. M.; Schmaltz, T.; Novak, M.; Khassanov, A.; Vorobiev, A.; Hennemann, M.; Krause, A.; Dietrich, H.; Zahn, D.; Hirsch, A.; Halik, M.; Clark, T. Improving the Charge Transport in Self-Assembled Monolayer Field-Effect Transistors: From Theory to Devices. J. Am. Chem. Soc. 2013, 135 (12), 4893-4900.
  8. Bauer, T.; Schmaltz, T.; Lenz, T.; Halik, M.; Meyer, B.; Clark, T. Phosphonate- and Carboxylate-Based Self-Assembled Monolayers for Organic Devices: A Theoretical Study of Surface Binding on Aluminum Oxide with Experimental Support. ACS Appl. Mater. Interfaces 2013, 5 (13), 6073-6080.
  9. Leitherer, S.; Jaeger, C. M.; Halik, M.; Clark, T.; Thoss, M. Modeling charge transport in C60-based self-assembled monolayers for applications in field-effect transistors. J. Chem. Phys. 2014, 140 (20), 204702/1-204702/10.
  10. Schmaltz, T.; Gothe, B.; Krause, A.; Leitherer, S.; Steinrueck, H.-G.; Thoss, M.; Clark, T.; Halik, M. Effect of Structure and Disorder on the Charge Transport in Defined Self-Assembled Monolayers of Organic Semiconductors. ACS Nano 2017, Ahead of Print.
  11. Ehresmann, B.; Martin, B.; Horn, A. H. C.; Clark, T. Local molecular properties and their use in predicting reactivity. J. Mol. Model. 2003, 9 (5), 342-347.
  12. Clark, T. The local electron affinity for non-minimal basis sets. J. Mol. Model. 2010, 16 (7), 1231-1238.
  13. Sjoberg, P.; Murray, J. S.; Brinck, T.; Politzer, P. Average local ionization energies on the molecular surfaces of aromatic systems as guides to chemical reactivity. Can. J. Chem. 1990, 68 (8), 1440-1443.
  14. Bauer, T.; Jaeger, C. M.; Jordan, M. J. T.; Clark, T. A multi-agent quantum Monte Carlo model for charge transport: Application to organic field-effect transistors. J. Chem. Phys. 2015, 143 (4), 044114/1-044114/9.
  15. Shubina, T. E.; Sharapa, D. I.; Schubert, C.; Zahn, D.; Halik, M.; Keller, P. A.; Pyne, S. G.; Jennepalli, S.; Guldi, D. M.; Clark, T. Fullerene Van der Waals Oligomers as Electron Traps. J. Am. Chem. Soc. 2014, 136 (31), 10890-10893.