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 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 Outline Materials Molecular crystals Oligoacenes b 2A, 3A, 4A, 5A c Oligothiophenes 2T, 4T, 6T Oligophenylenes 2P, 3P, 4P, 6P b a Materials Density Functional Theory The Kohn-Sham Equation auxiliary exact with the effective potential only approximation external potential DFT in a Nutshell 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). The Band Structure Optical Properties … Molecular orientation 2.0 hν Im(n) 1.5 1.0 polymer film 0.5 substrate 0.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 E [eV] P. Puschnig and CAD, Adv. Eng. Mat. 8, 1151 (2006). E. Zojer et al., PRB 61, 16538 (2000). Optical Absorption The random phase approximation independent particle approximation ck E S Energy =ω =ω vk EF wave vector Light scattering The Bethe-Salpeter Equation (BSE) Two-particle wavefunction KS states from GS calculation Effective two-particle Schrödinger equation matrix form Beyond the RPA EB=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). 1D Polyacetylene EB=0.05 eV 7.8 nm 1.7 nm P. Puschnig and C. Ambrosch-Draxl, Phys. Rev. Lett. 89, 056405 (2002). 3D Polyacetylene The Bethe-Salpeter Equation Beyond the RPA Polyacetylene 1D 3D P. Puschnig and C. Ambrosch-Draxl, Phys. Rev. Lett. 89, 056405 (2002). The BSE: 1D versus 3D 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). Anthracene 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). Oligoacenes Energetics The cohesive energy vacuum Ecoh = – ( Ebulk / nmol – Emolecule ) Energetics 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 Various oligomers D. Nabok, P. Puschnig, and CAD, Phys. Rev. B 77, 245316 (2008). Cohesive Energies The surface energy vacuum γ = ( Eslab – Ebulk / 2A ) Energetics Biphenyl 001 d D. Nabok, P. Puschnig, and Claudia Ambrosch-Draxl, Phys. Rev. B 77, 245316 (2008). Surface Energies 4A (100) 4A (010) 4A (001) 4A (110) γ [mJ/m2] Surface Energies 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 1T@Cu(110) P. Sony, P. Puschnig, D. Nabok, and CAD, PRL 99, 176203 (2007). Organic / Metal Interface 1T@Cu(110) γi = γCu(110) + γorganic - Eads / A = 1.70 top view + 0.15 - 0.30 = 1.55 [J/m2] charge density difference, side view Organic / Metal Interface Summary γa << γi ≤ γs γa is 10 – 50 times smaller than metal surface energy γs Cu D. Nabok et al., PRB 77, 245316 (2008). M. Methfessel et al., PRB 46, 4816 (1992). Δγ = γa + γi - γs = 2γa – Eads/A ≈ 0 Energetics Film Morphology 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? 2.5nm 6P AFM image Experimental observations 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). 6P on Mica 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 Eb = -1.28 eV local minimum #2 Eb = -1.80 eV Simulations The nudged elastic band method local minimum local minimum saddle point Transition State Theory Assuming a rigid molecule ΔEESB=0.91eV transition coordinate Transition State Theory www.borer-cartoon.ch/.../Deutscher.gif The Barrier … Bend your knees … www.borer-cartoon.ch The Barrier … The step-edge barrier 3 2 ΔEESB=0.61eV 4 5 1 intermolecular interaction bending energy 1 2 3 4 6 5 6 Transition State Theory Alternative to measure the ESB 2nd 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 6P on Mica Level-dependent ESB? 6P on Mica Dependence on the tilting angle ΔEESB=0.26eV 2 1 3 4 5 intermolecular interaction bending energy 1 2 3 4 6 5 6 The Potential Energy Surface Level-dependent ESB 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 Summary Thanks to … Dmitrii Nabok Priya Sony Kerstin Hummer Gregor Hlawacek Adi Winkler Georg Koller Paul Frank Peter Puschnig Christian Teichert Steve Berkebile Mike Ramsey The Team The END … Thank You for Attention!
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