Charge transport in Disordered Organic Semiconductors Eduard Meijer - PowerPoint PPT Presentation

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

Outline • Introduction: Ordered vs. Disordered semiconductors The field-effect transistor • Parameter Definition: Threshold voltage and Mobility • Modelling the temperature dependence • Temperature dependence of the field-effect mobility • Field dependence of the conductivity • Conclusions

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

Introduction Disordered Semiconductor • Non equivalent sites • Variation in energy levels

Introduction Disordered Semiconductor • Localized states have a Gaussian distribution • Charge carriers hop between localized states DOS DOS E F LUMO E E E F E E F DOS HOMO The 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 , 12964 (1998)

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

Introduction Field-Effect Transistor Poly(2,5-thienylene vinylene) (PTV) S n C 6 H 13 Poly(3-hexyl thiophene) (P3HT) S n Pentacene

Introduction Field-Effect Transistor 10 -3 V ds =-30 V 10 -4 • P-type semiconductors 10 -5 V ds =-2 V 10 -6 • Charge carrier density 10 -7 I ds [A] is varied with applied V g . 10 -8 pentacene 10 -9 • Mobility ~ 10 -3 -10 -1 cm 2 /Vs 10 -10 10 -11 -35 -30 -25 -20 -15 -10 -5 0 5 x10 -5 V g [V] 8 V g =-20 V 6 I ds [A] V g =-15 V 4 2 V g =-10 V 0 -20 -15 -10 -5 0 V ds [V]

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

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

Parameter definition Instead of the threshold voltage for accumulation FETs the flatband voltage is important # 20 10 V g =-10 V V g =-19 V 19 10 Semiconductor x Drain Source Au Au -3 ] SiO 2 18 10 ρ [cm ++ Si n Gate 17 10 16 10 0 2 4 6 8 10 x [nm] Assumption that all induced carriers move with one mobility is still found to be reasonable*: ∂ I ds L µ FE = ∂ V g WC i V ds # Appl. Phys. Lett. 80 , 3838 (2002) *Tanase et al. submitted.

Modelling the temperature dependence We use a hopping model in an exponential density of states* (based on polyled modelling) DOS   E N E   = t g ( E ) exp   E F k T k T   B 0 B 0 *M.C.J.M. Vissenberg and M. Matters, Phys. Rev. B. 57 , 12964 (1998)

Modelling the temperature dependence 4 modelling parameters Width of exponential distribution Flat-band voltage T 0   4     T T T    π    sin 0 ( ) T   0 − 2 1   −       ε σ ε C V V  T  T WV T 2 k T T       = 0 i g FB I d s 0 B 0 s         ( ) ds − ε 3 ε α Lq 2 T T 2 k T 2 B         0 s B 0 s c     Conductivity prefactor Overlap parameter between localized sites

Modelling the temperature dependence PTV S n

Modelling the temperature dependence Pentacene

Modelling the temperature dependence P3HT C 6 H 13 S n

Modelling the temperature dependence T 0 [K] σ 0 [10 6 S/m] α -1 [Å] V FB [V] PTV 382 5.6 1.5 1 Pentacene 385 3.5 3.1 1 P3HT 425 1.6 1.6 2.5 But what do these parameters mean? → Look at the temperature dependence in a different way

Temperature dependence of the field-effect mobility 2 10 µ 0 V g =-25 V 1 10 V g =-20 V 0 10 V g =-15 V -1 10 E a V g =-10 V -2 2 /Vs] 10 V g =-5 V -3 10 µ FE [cm -4 10 -5 T 0 *=E MN /k B 10 -6 10 -7 10 -8 10 0 2 4 6 8 10 12 14 -1 ] 1000/T [K Typically observed: • Thermally activated behaviour • E a depends on the amount of induced charge (V g ) Appl. Phys. Lett. 76 , 3433 (2000)

Temperature dependence of the field-effect mobility Common intersection point at T 0 *:     1 1   µ = µ − − exp E     FE 00 a k T k T *     B B 0 100 ln( µ 0 ) ~ E a → prefactor µ 0 [cm 2 /Vs] 10 Meyer-Neldel Rule * . 1 S n 0.1 k B T 0 *=38 meV for pentacene 0.0 0.1 0.2 0.3 k B T 0 *=42 meV for PTV E a [eV] * W. Meyer and H. Neldel, Z. Tech. Phys. 18 , 588 (1937).

Temperature dependence Discussion No improved linearity for : 1 1 1 − − − T , T , T . 2 3 4 k B T 0 * ~ 40 meV for pentacene, PTV, P3HT C 60 and sexithiophene * . → common origin? What are µ 0 and T 0 * ? ? +

Temperature dependence Discussion Jump rate from site to site j , E j The energy for a hop is supplied by phonons. + i , E i Jump rate:    δ    δ δ G S H       υ = υ − = υ − exp exp exp       0 0 k T k k T       B B B δ = δ − δ with G H T S Entropy change results in Meyer-Neldel rule A. Yelon and B. Movaghar, Phys. Rev. Lett. 65 , 618 (1990). D. Emin Phys. Rev. B 61 , 14543 (2000).

Temperature dependence Discussion ln( µ 0 ) ~ E a → attempt frequency ↑ Single phonon → entropy ↑ Multi phonon Etc. A. Yelon and B. Movaghar, Phys. Rev. Lett. 65 , 618 (1990).

Temperature dependence Discussion + + Single or multi-phonon? E a E a + h ω 0 > E a h ω 0 < E a A. Miller and E. Abrahams, Phys. Rev. 120 , 745 (1960). D. Emin Phys. Rev. Lett. 32 , 303 (1974).

Field dependence of the in-plane conductivity E Au Glass

Field dependence in PTV -7 10 209 K 187 K -8 10 170 K 156 K -9 145 K S 10 135 K n σ [S/cm] 125 K -10 10 115 K -11 10 -12 10 -13 10 0 1 2 3 4 5 6 7 1/2 [(V/ µ m) 1/2 ] E Synth. Metals. 121 , 1351 (2001).

Field dependence in PTV -3 10 -4 10 49MV/m -5 34MV/m 10 25MV/m -6 10 15MV/m -7 10 σ [S/cm] -8 10 -9 10 -10 10 T 0 * -11 10 -12 10 -13 10 0 2 4 6 8 10 -1 ] 1000/T [K     − ∆ 1 1   µ = µ + − exp B F     0 k T k T k T *     B B B 0

Field dependence of the mobility     − ∆ 1 1   µ = µ + − exp B F     0 k T k T k T *     B B B 0 For PTV: T 0 * � 520 K For P3HT: T 0 * � 550 K Related? #     1 1   µ = µ − − exp E ( V )     FE 00 a g k T k T *     B B 0 For PTV: T 0 * � 490 K For P3HT: T 0 * � 510 K # A. Peled, L. Schein, Phys. Scripta 44 , 304 (1991).

Conclusions • Hopping in an exponential DOS gives a reasonable description of the charge transport • Meyer-Neldel rule is related to the Field dependence • T 0 * found in MNR and the field-dependent mobility indicates a multiphonon process (entropy) • Entropy considerations are important to describe the charge transport (polaron)