Claudia Ambrosch-Draxl Chair of Atomistic Modelling and Design of Materials University of Leoben Theoretical approaches towards the understanding of organic semiconductors: from electronic and optical properties to film growth
Outline Materials Density Functional Theory in a Nutshell Electronic structure and cohesive properties Optical Properties Excitonic effects Cohesive and Surface Energies Importance of van der Waals interactions Interfaces Organic molecules on metal substrates Film Morphology Energy barriers
Materials
Materials Molecular crystals Oligoacenes 2A, 3A, 4A, 5A Oligothiophenes 2T, 4T, 6T b c Oligophenylenes 2P, 3P, 4P, 6P a b
Density Functional Theory
DFT in a Nutshell The Kohn-Sham Equation exact with the effective potential auxiliary only approximation external potential
The Band Structure 6P@Cu(110)(2x1)O G. Koller, S. Berkebile, M. Oehzelt, P. Puschnig, C. Ambrosch-Draxl, F. P. Netzer, and M. G. Ramsey, Science 317, 351 (2007).
The Band Structure DFT versus ARUPS Fourier transform G. Koller, S. Berkebile, M. Oehzelt, P. Puschnig, C. Ambrosch-Draxl, F. P. Netzer, and M. G. Ramsey, Science 317, 351 (2007).
Optical Properties
Optical Absorption Molecular orientation hν 2.0 1.5 polymer film Im(n) 1.0 0.5 substrate P. Puschnig and CAD, Adv. Eng. Mat. 8, 1151 (2006). E. Zojer et al., PRB 61, 16538 (2000). 0.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 E [ev]
Light scattering The random phase approximation independent particle approximation ω c k S E Energy ω v k E F wave vector
Beyond the RPA The Bethe-Salpeter Equation (BSE) Two-particle wavefunction KS states from GS calculation Effective two-particle Schrödinger equation matrix form
1D Polyacetylene E B =0.55 ev 7.8 nm P. Puschnig and C. Ambrosch-Draxl, Phys. Rev. Lett. 89, 056405 (2002). M. Rohlfing and S. G. Louie, Phys. Rev. Lett. 82, 1959 (1999).
3D Polyacetylene E B =0.05 ev 7.8 nm 1.7 nm P. Puschnig and C. Ambrosch-Draxl, Phys. Rev. Lett. 89, 056405 (2002).
The Bethe-Salpeter Equation Beyond the RPA
The BSE: 1D versus 3D Polyacetylene 1D 3D P. Puschnig and C. Ambrosch-Draxl, Phys. Rev. Lett. 89, 056405 (2002).
Anthracene Higher pressure... @smaller band gap @ enhanced screening @ wider extension of e-h wavefunction @ smaller exciton binding energy K. Hummer, P. Puschnig, and CAD, Phys. Rev. Lett. 92, 147402 (2004).
Oligoacenes Larger molecules... @smaller band gap @ enhanced screening @ wider extension of e-h wavefunction @ smaller exciton binding energy K. Hummer and C. Ambrosch-Draxl, Phys. Rev. B 71, 081202(R) (2005).
Energetics
Energetics The cohesive energy vacuum E coh = ( E bulk / n mol E molecule )
Exchange correlation functionals Energetics
Non-local correlations Rydberg et al., Phys. Rev. B 62, 6997 (2000). Dion et al., Phys. Rev. Lett. 92, 246401 (2004). Chakarova-Käck et al., Phys. Rev. Lett. 96, 146107 (2006). Energetics
Cohesive Energies Various oligomers D. Nabok, P. Puschnig, and CAD, Phys. Rev. B 77, 245316 (2008).
Energetics The surface energy vacuum γ = ( E slab E bulk / 2A )
Surface Energies Biphenyl 001 d D. Nabok, P. Puschnig, and Claudia Ambrosch-Draxl, Phys. Rev. B 77, 245316 (2008).
4A (100) 4A (010) 4A (001) 4A (110) Surface Energies γ [mj/m 2 ]
Equilibrium crystal shapes Wulff's construction D. Nabok, P. Puschnig, and CAD, PRB 77, 245316 (2008). Jo et al., anthracene single crystal on graphite (0001), Surf. Sci. 592, 37 (2005). Surface Energies
Organic / Metal Interface
Organic / Metal Interface 1T@Cu(110) P. Sony, P. Puschnig, D. Nabok, and CAD, PRL 99, 176203 (2007).
1T@Cu(110) γ i = γ Cu(110) + γ organic -E ads / A = 1.70 + 0.15-0.30 = 1.55 [J/m 2 ] top view charge density difference, side view Organic / Metal Interface
Energetics Summary γ a << γ i γ s γ a is 10 50 times smaller than metal surface energy γ s Cu D. Nabok et al., PRB 77, 245316 (2008). M. Methfessel et al., PRB 46, 4816 (1992). Δγ = γ a + γ i - γ s = 2γ a E ads /A 0
Film Morphology
2.5nm Experimental observations Sexiphenyl on mica Mound formation on disordered mica. Separation unchanged after nucleation has stopped. Mass transport between mounds must be supressed. Ehrlich-Schwoebel barrier in organic film growth? 6P AFM image
6P on Mica The Ehrlich-Schwoebel Barrier AFM image, film thickness 30nm T. Michely and J. Krug, Springer 2004 ESB = 0.67 ev G. Hlawacek, P. Puschnig, P. Frank, A. Winkler, CAD, and Ch. Teichert, Science 321, 108 (2008).
Computational details Simulation cell of 31 6P molecules (1922 atoms) Huge number of structural degrees of freedom Transition state theory: more than 5000 total energy & force calculations Not feasible by ab-initio approaches within DFT Empirical potentials: 5-10 seconds per configuration local minimum #1 E b = -1.28 ev local minimum #2 E b = -1.80 ev Simulations
Transition State Theory The nudged elastic band method local minimum local minimum saddle point
Assuming a rigid molecule ΔE ESB =0.91eV transition coordinate Transition State Theory
www.borer-cartoon.ch/.../deutscher.gif The Barrier
The Barrier Bend your knees www.borer-cartoon.ch
The step-edge edge barrier 2 3 ΔE ESB =0.61eV 4 1 5 intermolecular interaction bending energy 6 1 2 3 4 5 6 Transition State Theory
6P on Mica Alternative to measure the ESB 2 nd layer nucleation experiment island density ESB = 0.26 ev T. Michely and J. Krug, Islands, Mounds and Atoms, Springer 2004
6P on Mica What is wrong? ESB 0.26 ev 0.67 ev
Level-dependent ESB? 6P on Mica
Dependence on the tilting angle ΔE ESB =0.26eV 3 2 1 intermolecular interaction 4 5 bending energy 6 1 2 3 4 5 6 The Potential Energy Surface
Level-dependent ESB Summary
Summary For organic molecular crystals a variety of case studies has shown that DFT is a precise tool for the energetics if vdw forces are included Exciton binding energies are suppressed by pressure or in long molecules Surface Energies are typically 10-50 times smaller than in metals Interfaces are dominated by van der Waals interaction Film morphologies depend on the complex nature of the molecules
Thanks to Dmitrii Nabok Peter Puschnig Kerstin Hummer Adi Winkler Priya Sony Gregor Hlawacek Christian Teichert Paul Frank Georg Koller Mike Ramsey Steve Berkebile The Team
The END Thank You for Attention!