Dynamics of Electrons at Organic/Dielectric Interfaces

Transcription

1 Dynamics of Electrons at Organic/Dielectric Interfaces S. Fratini 1 (simone.fratini@grenoble.cnrs.fr) G. Rastelli 1,2, S. Ciuchi 2, A. F. Morpurgo 3 1 LEPES, CNRS Grenoble, France 2 INFM-CNR SMC and Dipartimento di Fisica, Universitá di L Aquila, Italy 3 Kavli Institute of Nanoscience, Delft University of Technology, The Netherlands Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 1

2 Outline Organic FETs, influence of gate dielectric Fröhlich polaron formation, activated transport narrow bandwidth polarizability of gate dielectric Comparison Theory/Experiments Perspectives Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 2

3 Single Crystal Organics FETs [Sundar et al. Science 2004] organic, molecular semiconductor polar gate dielectric Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 3

4 Organic Semiconductor (rubrene) VdW bonding, a = 7.2A o low overlap integrals t narrow bands B 0.4 ev (HOMO) [da Silva Filho et al. Adv. Mat. 2005] Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 4

5 Bulk/FET transport mobility is metallic-like, µ(t) T α α large thermal fluctuations t/t 1 at RT [W. Warta et al. PRB 1985] [V. Podzorov et al. PRL 2005] Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 5

6 Dependence on gate dielectric ε o = 1, 3, 4, 9, 25, (AIR, Parylene,Si0 2,Al 2 0 3,Ta ) Air-gate: µ 1/T 3/2 ε o ր: 50cm 2 /V s = 0.1cm 2 /V s ε o ր: metallic-like insulator-like behavior Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 6

7 Microscopic model H = H R e + H R e ph }{{} rubrene +He ph I + HI ph + }{{} Hph G }{{} INTERFACE polar gate 2D holes, tight binding: H R e = t <ij> c i c j Fröhlich interaction at interface [Mori & Ando, PRB 1989] H I e ph = β k,q e qz ( ) c q k+q c k a q + a q transfer integral t 50meV organic/gate dielectric constants ε 0 ε β = (κ + ε 0 )(κ + ε ) interface modes ω s meV distance charges/dielectric z 1 nm Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 7

8 Polaron Formation Self-trapping: the electron (hole) polarizes the gate dielectric, and remains trapped in its own polarization potential = Polaron binding energy, radius E P β d 2 q e 2qz (2π) 2 q = a B z β(ryd) eV R P a a 1 t a B πβ Ryd 0.03 β small polaron Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 8

9 Small polaron transport [Austin & Mott, Adv. Phys 1969; Fratini & Ciuchi PRL 2003] polaron trapped on site, hopping barrier E p t incoherent hopping at RT thermally activated µ = µ 0 e T coherent band-like motion at low temperature, but strong mass renormalization (usually negligible at RT) Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 9

10 Adiabatic hopping (ω s t) Simple model: Two Sites t E t E p integrate out electrons Mω2 sx 2 q effective classical potential 2 X q µ = ( ea 2 ) ωs T e /T activation barrier: = 1 2 E p t ea 2 7cm2 /V s Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 10

11 Comparison with experiments Matthiessen s rule: 1 µ = 1 µ R + 1 µ p fitting parameters,ω s : µ P = ( ea 2 ) ωs T e /T Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 11

12 Results overall agreement: = 1 2 E p t = a B 2z β t ω s bulk z 6.5A o (1 st layer) t t (finite ω s /t, long-range) parylene (weak polarizability) Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 12

13 Improving the microscopic model anti-adiabatic corrections ω s t long-range interactions, beyond two-site model intermediate coupling regime E P t, R P a = AE P t A 1/2, t < t β anisotropic band structure t a > t b spread of wavefunction on z direction Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 13

14 Conclusions the mobility of organic FETs evolves from metallic-like to insulating-like upon increasing the dielectric constant of the gate material the crossover is explained in terms of the formation of small polarons, due to the polarizability of the gate dielectric narrow bands in the organic material transport in organic materials: an open problem Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 14

15 References: - Tunable Frohlich Polarons in Organic Single-Crystal Transistors I. N. Hulea et al, Nature Materials 5, 982 (2006) cond-mat/ Organic transistors: A polarized response V. Coropceanu and J-L Brédas, Nature Materials 5, 929 (2006) - Dynamical Mean-Field Theory of Transport of Small Polarons S. Fratini, S. Ciuchi, PRL 91, (2003) Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 15

16 Small polaron transport [Austin & Mott, Adv. Phys 1969; Fratini & Ciuchi PRL 2003] polaron trapped on site, hopping barrier E p t incoherent hopping at RT thermally activated µ = µ 0 e T ւ µ 0 ω s T adiabatic µ 0 t2 anti-adiabatic Ep T ց fits with anti-adiabatic formula give results that are not internally consistent... truth is in between? (remind ω s t) Dynamics of Electrons at Organic/Dielectric Interfaces, Dec. 12, 2006, ELECMOL p. 16