From Order to Disorder

Transcription

1 ORGANIC ELECTRONICS Principles, devices and applications Charge Transport D. Natali Milano, Novembre 011 From Order to Disorder From delocalized to localized states 1

2 The Two-Site approximation a,v a b,v b E 1 E Splitting& delocalization E V a,v b E 1 Mott Electronic processes in non-crystalline materials, Clarendon Press 1979 The Two-Site approximation a,v a b,v b a,v a a,v b DV E E 1 E E 1 E Splitting& delocalization V a,v b E Localization V a V b E 1 Mott Electronic processes in non-crystalline materials, Clarendon Press 1979

3 Density of States Due to energetic diosrder DOS is gaussian (or an onential tail), having s of about mev. Bassler, Phys. Stat. Sol. B 175(1993) 15 Density of States Due to energetic diosrder DOS is gaussian (or an onential tail), having s of about mev. Bassler, Phys. Stat. Sol. B 175(1993) 15 3

4 Elelctron Energy Hopping Charge carriers are localized Transport occurs by hopping between localized states HoP! Hopping thermally activated tunnelling L L 4

5 Elelctron Energy Hopping thermally activated tunnelling L L Hopping: effect of temperature (1) L r 5

6 Hopping: effect of temperature () L High T: p [ HOP] r 1 L Nearest neighbor fixed range hopping Hopping: effect of temperature (3) L intermediate T: p [ HOP] r L Variable range hopping: an optimum hopping distance Madelung, Introduction to Solid State Theory, Springer Verlag

7 E E X Axis Title X Axis Title Hopping & Gaussian DOS: transport B energy(1) L E TR A level of most probable excitation EXISTS And does not depend upon the site starting energy (for tail states ) Y Axis Title Schmechel, PHYS.REV. B 66, 3506 ~00 Hopping & Gaussian DOS: effect of low density B L s E TR 9 s E Excitation from Y Axis Title E ETR E s to E TR 3 7

8 E X Axis Title L Hopping & Gaussian DOS: effect of low density B s E TR 9 s E Excitation from Y Axis Title E ETR E s to E TR 3 Hopping & Gaussian DOS: effect of high density B L E TR E F 0 E ETR EF Excitation Y Axis from Title E F to E TR Coehoorn et al., PHYS. REV. B 7,

9 Coehoorn Phys rev B L Hopping & Gaussian DOS: effect of high density B E TR E F ETR EF 5 s E F Excitation Y Axis Title from E to E TR F 9 Coehoorn et al., PHYS. REV. B 7, Mobility ression μ(t, n, F) = μ 0 αa 0.4σ g 1 (F, T) g (F, T) Density enhancement At higher density, the E F to E TR distance diminishes 9

10 Coehoorn Phys rev B Coehoorn Phys rev B Mobility ression μ(t, n, F) = μ 0 αa 0.4σ g 1 (F, T) g (F, T) Density enhancement E-field enhancement The applied field modifies energetic barriers Mobility ression μ(t, n, F) = μ 0 αa 0.4σ g 1 (F, T) g (F, T) Density enhancement E-field enhancement 10

11 energy Coehoorn Phys rev B Mobility ression μ(t, n, F) = μ 0 αa 0.4σ g 1 (F, T) g (F, T) Density enhancement Higher at larger disorder E-field enhancement Higher at larger disorder Einstein relation D g3( T, n) e = DOS center =6 Chemical potential Density of Occupied States A disordered s.c. is practically always degenerate! Tessler Appl. Phys. Lett., Vol. 80, No. 11, 18 March 00 11

12 Einstein relation D g3( T, n) e Diffusion enhancement g3( T, n) Diffusion vs. Mobility enhancement relation Diffusion enhancement g3( T, n) D g3( T, n) e Density enhancement 1

13 Hopping and spatial current distribution s=75mev s=150mev Bobbert PHYSICAL REVIEW B 79, Correlated Gaussian Disorder Model(1) The energetic disorder is spatially correlated The deepest valley are the widest ones 13

14 Correlated Gaussian Disorder Model() The electric field lowers the escape barriers The deepest (and widest) valleys are more affected Correlated Gaussian Disorder Model(3) Intermediate limiting traps Few deep traps Many shallow traps 14

15 Correlated Gaussian Disorder Model(4) Traps width W is electric field dependent: for energy autocorrelation in the form Barrier lowering and hence is Intermediate limiting traps W 1 1 p 1 p r, eew W E E p p 1 p=1, dipolar disorder PooleFrenkel behavior Parris, Phys. Stat. Sol. (b) 18, 47 (000) Correlated vs Uncorrelated μ(t, n, F) μ 0 αa 0.9σ μ(t, n, F) μ 0 αa 0.4σ Bobbert Organic Electronics 10 (009)

16 in addition: Coulombic interactions Zhou PHYSICAL REVIEW B 75, Bobbert et al PHYSICAL REVIEW B 83, (011) Polarons(1) Relaxation of excess slow carriers 16

17 Polarons() Relaxation of excess slow carriers Large polaron: Increased effective mass Small polaron: self-localized in a potential well Sources: intramolecular vibrations Intermolecular vibrations Electronic polarization Distortion energy Electronic energy Polarons(3) Role of the number of p carbon atoms Burdett, Chemical Bonding in Solids, Oxford University press

18 Polaron Hopping 1 Thermal fluctuations create Coincidence Event Holstein, Ann.Phys , 35 Disorder and polarons Parris Phys.Rev.Lett. 87, 001, Polaronic effect + Energetic Disorder Charge density dependence almost supressed in the polaron model Fischuk PHYSICAL REVIEW B 76,

19 Elelctron Energy Polaronic effect + Energetic Disorder The transport energy lies higher in the polaron model -> The relative change due tue Fermi level lifting is smaller Fischuk PHYSICAL REVIEW B 76, Back to Hopping Rate E un processo di tunnelling termicamente attivato L L 19

20 Xtal structure and transfer integral: two etylene molecules L Mixed bonding/antibonding interaction Full (anti)bonding interaction HOMO splitting larger than LUMO splitting Bredas, Chem. Rev. 004, 104, ; 007, 107, 96 p 6T dimer: intermolecular distance effect [HOP] L 0

21 6T dimer: translation effect L H HOMO oscillations larger than LUMO ones L Electron transfer rates: electronic coupling and reorganization energy Hutchison, J. AM. CHEM. SOC. 005, 17,

22 Single Crystal: bandlike transport? Large e-coupling fluctuations -> dynamic disorder ->charge localizaton but, band like transport, T -n Troisi, J. Phys. Chem. A 006, 110, , Adv. Mater. 007, 19, Doping Interstitial: the problem of stability for small dopants (eg metals: Li +, K +, I 3-..) Molecular doping is better The effect of the dielectric constant (binding energy/dopant density) Gregg, Chemistry of Materials, 16, 004, p

23 Molecular Doping(1) n-type doping Leo et al. Chem. Rev. 007, 107, Molecular Doping(): CN substitution result target The supposed dopant acts as a trap!!! Vaid, Chem.Mater 003, 15, 49 3

24 Molecular Doping() Leo et al. Chem. Rev. 007, 107, N-type doping 4

25 The End 5