Theoretical approaches towards the understanding of organic semiconductors:

Transcription

1 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

2 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

3 Materials

4 Materials Molecular crystals Oligoacenes 2A, 3A, 4A, 5A Oligothiophenes 2T, 4T, 6T b c Oligophenylenes 2P, 3P, 4P, 6P a b

5 Density Functional Theory

6 DFT in a Nutshell The Kohn-Sham Equation exact with the effective potential auxiliary only approximation external potential

7 The Band Structure G. Koller, S. Berkebile, M. Oehzelt, P. Puschnig, C. Ambrosch-Draxl, F. P. Netzer, and M. G. Ramsey, Science 317, 351 (2007).

8 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).

9 Optical Properties

10 Optical Absorption Molecular orientation hν polymer film Im(n) substrate P. Puschnig and CAD, Adv. Eng. Mat. 8, 1151 (2006). E. Zojer et al., PRB 61, (2000) E [ev]

11 Light scattering The random phase approximation independent particle approximation ω c k S E Energy ω v k E F wave vector

12 Beyond the RPA The Bethe-Salpeter Equation (BSE) Two-particle wavefunction KS states from GS calculation Effective two-particle Schrödinger equation matrix form

13 1D Polyacetylene E B =0.55 ev 7.8 nm P. Puschnig and C. Ambrosch-Draxl, Phys. Rev. Lett. 89, (2002). M. Rohlfing and S. G. Louie, Phys. Rev. Lett. 82, 1959 (1999).

14 3D Polyacetylene E B =0.05 ev 7.8 nm 1.7 nm P. Puschnig and C. Ambrosch-Draxl, Phys. Rev. Lett. 89, (2002).

15 The Bethe-Salpeter Equation Beyond the RPA

16 The BSE: 1D versus 3D Polyacetylene 1D 3D P. Puschnig and C. Ambrosch-Draxl, Phys. Rev. Lett. 89, (2002).

17 Anthracene Higher band enhanced wider extension of e-h smaller exciton binding energy K. Hummer, P. Puschnig, and CAD, Phys. Rev. Lett. 92, (2004).

18 Oligoacenes Larger band enhanced wider extension of e-h smaller exciton binding energy K. Hummer and C. Ambrosch-Draxl, Phys. Rev. B 71, (R) (2005).

19 Energetics

20 Energetics The cohesive energy vacuum E coh = ( E bulk / n mol E molecule )

21 Exchange correlation functionals Energetics

22 Non-local correlations Rydberg et al., Phys. Rev. B 62, 6997 (2000). Dion et al., Phys. Rev. Lett. 92, (2004). Chakarova-Käck et al., Phys. Rev. Lett. 96, (2006). Energetics

23 Cohesive Energies Various oligomers D. Nabok, P. Puschnig, and CAD, Phys. Rev. B 77, (2008).

24 Energetics The surface energy vacuum γ = ( E slab E bulk / 2A )

25 Surface Energies Biphenyl 001 d D. Nabok, P. Puschnig, and Claudia Ambrosch-Draxl, Phys. Rev. B 77, (2008).

26 4A (100) 4A (010) 4A (001) 4A (110) Surface Energies γ [mj/m 2 ]

27 Equilibrium crystal shapes Wulff's construction D. Nabok, P. Puschnig, and CAD, PRB 77, (2008). Jo et al., anthracene single crystal on graphite (0001), Surf. Sci. 592, 37 (2005). Surface Energies

28 Organic / Metal Interface

29 Organic / Metal Interface 1T@Cu(110) P. Sony, P. Puschnig, D. Nabok, and CAD, PRL 99, (2007).

30 γ i = γ Cu(110) + γ organic -E ads / A = = 1.55 [J/m 2 ] top view charge density difference, side view Organic / Metal Interface

31 Energetics Summary γ a << γ i γ s γ a is times smaller than metal surface energy γ s Cu D. Nabok et al., PRB 77, (2008). M. Methfessel et al., PRB 46, 4816 (1992). Δγ = γ a + γ i - γ s = 2γ a E ads /A 0

32 Film Morphology

33 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

34 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).

35 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 = ev local minimum #2 E b = ev Simulations

36 Transition State Theory The nudged elastic band method local minimum local minimum saddle point

37 Assuming a rigid molecule ΔE ESB =0.91eV transition coordinate Transition State Theory

38 The Barrier

39 The Barrier Bend your knees

40 The step-edge edge barrier 2 3 ΔE ESB =0.61eV intermolecular interaction bending energy Transition State Theory

41 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

42 6P on Mica What is wrong? ESB 0.26 ev 0.67 ev

43 Level-dependent ESB? 6P on Mica

44 Dependence on the tilting angle ΔE ESB =0.26eV intermolecular interaction 4 5 bending energy The Potential Energy Surface

45 Level-dependent ESB Summary

46 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 times smaller than in metals Interfaces are dominated by van der Waals interaction Film morphologies depend on the complex nature of the molecules

47 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

48 The END Thank You for Attention!