Charge transport in Disordered Organic Semiconductors. Eduard Meijer Dago de Leeuw Erik van Veenendaal Teun Klapwijk

Transcription

1 Charge transport in Disordered Organic Semiconductors Eduard Meijer Dago de Leeuw Erik van Veenendaal eun Klapwijk

2 Outline Introduction: Ordered vs. Disordered semiconductors he field-effect transistor Parameter Definition: hreshold voltage and Mobility Modelling the temperature dependence emperature dependence of the field-effect mobility Field dependence of the conductivity Conclusions

3 Introduction Ordered Semiconductor Electron energy Conduction band E g Valence band Simplified band diagram of a semiconductor Hole energy Ordered system: conduction takes place in the extended states (CB&VB)

4 Non equivalent sites Variation in energy levels Introduction Disordered Semiconductor

5 Introduction Disordered Semiconductor Localized states have a Gaussian distribution Charge carriers hop between localized states DOS DOS E LUMO EF E E E F E F HOMO DOS he tail of the Gaussian is approximated by an Exponential H. Bässler, Phys. Stat. Sol. B, 175, 15 (1993). M.C.J.M. Vissenberg and M. Matters, Phys. Rev. B. 57, (1998)

6 Introduction Field-Effect ransistor V ds S D organic semiconductor V g Basic questions: What moves? How (fast) does it move?

7 Introduction Field-Effect ransistor Poly(2,5-thienylene vinylene) (PV) S n C 6 H 13 Poly(3-hexyl thiophene) (P3H) S n Pentacene

8 P-type semiconductors Charge carrier density is varied with applied V g. Mobility ~ cm 2 /Vs x1-5 8 V g =-2 V Introduction Field-Effect ransistor I ds [A] V ds =-3 V V ds =-2 V pentacene V g [V] 5 I ds [A] V g =-15 V V g =-1 V V ds [V]

9 Introduction Field-Effect ransistor 2 important characterization parameters: Charge carrier mobility (steepness of the I ds -V g -curve) hreshold voltage (position of the curve) Standard MOSFE modeling is often used for the parameter extraction: linear: I d, lin W = µ L FE V d C i ( V V ) g th saturation: I = µ C ( V V ) 2 d, sat W 2L FE i g th

10 Parameter definition But standard MOSFE analysis is not allowed, since: hese are accumulation devices (no inversion observed) No extended state transport Non-constant density of states { hreshold voltage can not be defined Mobility depends on the charge density

11 Parameter definition Instead of the threshold voltage for accumulation FEs the flatband voltage is important # Semiconductor Source Au x Au V g =-1 V V g =-19 V Drain ρ [cm -3 ] 1 18 SiO 2 n ++ Si Gate x [nm] Assumption that all induced carriers move with one mobility is still found to be reasonable*: L I ds µ FE = WC i V ds V g # Appl. Phys. Lett. 8, 3838 (22) *anase et al. submitted.

12 Modelling the temperature dependence We use a hopping model in an exponential density of states* (based on polyled modelling) DOS E E F g( E) = Nt k B exp E k B *M.C.J.M. Vissenberg and M. Matters, Phys. Rev. B. 57, (1998)

13 ( ) ( ) sin 2 2 = s FB g i B s c s B s d ds V V C k B k Lq WV I ε ε α π ε σ ε Conductivity prefactor Overlap parameter between localized sites Width of exponential distribution Flat-band voltage Modelling the temperature dependence 4 modelling parameters

14 Modelling the temperature dependence PV S n

15 Modelling the temperature dependence Pentacene

16 Modelling the temperature dependence P3H C 6 H 13 S n

17 Modelling the temperature dependence [K] σ [1 6 S/m] α -1 [Å] V FB [V] PV Pentacene P3H But what do these parameters mean? Look at the temperature dependence in a different way

18 emperature dependence of the field-effect mobility µ µ FE [cm 2 /Vs] *=E MN /k B E a V g =-25 V V g =-2 V V g =-15 V V g =-1 V V g =-5 V / [K -1 ] ypically observed: hermally activated behaviour E a depends on the amount of induced charge (V g ) Appl. Phys. Lett. 76, 3433 (2)

19 emperature dependence of the field-effect mobility Common intersection point at *: µ FE = µ exp E a 1 kb k B 1 * prefactor µ [cm 2 /Vs] S n E a [ev] ln(µ ) ~ E a Meyer-Neldel Rule *. k B *=38 mev for pentacene k B *=42 mev for PV * W. Meyer and H. Neldel, Z. ech. Phys. 18, 588 (1937).

20 emperature dependence Discussion No improved linearity for ,,. k B * ~ 4 mev for pentacene, PV, P3H C 6 and sexithiophene *. common origin? : What are µ and *?? +

21 emperature dependence Discussion Jump rate from site to site + i, E i j, E j he energy for a hop is supplied by phonons. Jump rate: υ = υ exp δg k B = υ δs exp exp kb δh k B with δg = δh δs Entropy change results in Meyer-Neldel rule A. Yelon and B. Movaghar, Phys. Rev. Lett. 65, 618 (199). D. Emin Phys. Rev. B 61, (2).

22 emperature dependence Discussion ln(µ ) ~ E a Single phonon attempt frequency Multi phonon entropy Etc. A. Yelon and B. Movaghar, Phys. Rev. Lett. 65, 618 (199).

23 emperature dependence Discussion + Single or multi-phonon? + E a + E a hω > E a hω <E a A. Miller and E. Abrahams, Phys. Rev. 12, 745 (196). D. Emin Phys. Rev. Lett. 32, 33 (1974).

24 Field dependence of the in-plane conductivity E Au Glass

25 Field dependence in PV σ [S/cm] K K 17 K 156 K 1-9 S 145 K n 135 K K 115 K E 1/2 [(V/µm) 1/2 ] Synth. Metals. 121, 1351 (21).

26 Field dependence in PV σ [S/cm] MV/m 34MV/m 25MV/m 15MV/m * / [K -1 ] µ = µ exp + B F kb kb kb *

27 Field dependence of the mobility + = F k k B k B B B * 1 1 exp µ µ For PV: * 52 K For P3H: * 55 K = * 1 1 ) ( exp k k V E B B g a µ FE µ For PV: * 49 K For P3H: * 51 K Related? # # A. Peled, L. Schein, Phys. Scripta 44, 34 (1991).

28 Conclusions Hopping in an exponential DOS gives a reasonable description of the charge transport Meyer-Neldel rule is related to the Field dependence * found in MNR and the field-dependent mobility indicates a multiphonon process (entropy) Entropy considerations are important to describe the charge transport (polaron)