Advanced Simulation Methods for Charge Transport in OLEDs

Transcription

1 FLUXiM Advanced Simulation Methods for Charge Transport in OLEDs Evelyne Knapp, B. Ruhstaller Overview 1. Introduction 2. Physical Models 3. Numerical Methods 4. Outlook

2 ICP Team Interdisciplinary team of 8 physicists, 4 mathematicians und 3 engineers 1996 Section NMSA Spin-offs: 2002 Foundation CCP Numerical Modeling GmbH, Foundation ICP Fluxim AG,

3 Research Activities The main focus is applied research and development in the following areas: Micro systems, sensors, actors Fuel cells Organic optoelectronic and photovoltaics Simulation software

4 AEVIOM Advanced Experimentally Validated OLED model Philips Research Eindhoven Project Coordinator: Reinder Coehoorn Philips Research Aachen Zürich University of Applied Sciences Fluxim Eindhoven University of Technology Technical University Dresden Sim4Tec University of Groningen University of Cambridge

5 Principle of OLED Operation X Fundamental Processes: 1 Anode 2 Hole transport layer (HTL) h!" 4 3 EML X Electron transport layer (ETL) Cathode 1. Charge Injection 2. Charge Carrier Transport 3. Exciton Formation 4. Radiative Decay 5. Light Extraction Real stack consists of up to 12 layers!

6 Simulation of Organic LEDs LUMO! Cathode! Anode! HOMO! Novel physical models require better numerical methods Transient simulations and IV curves need multiple simulations Efficient simulations are crucial Experimental data from CSEM, simulation by ICP

7 Modeling of charge carrier transport Gummel solver Newton solver Bipolar Injection Organic material properties Disorder (Gaussian DOS) Mobility Generalized Einstein relation Traps (Exponential DOS) Multilayer OLEDs Exciton dynamics Parameter extraction Coupling to optical model Impedance simulations Overview-Task list

8 Organic Materials Gaussian Disorder Energy LUMO HOMO Small molecules and polymer LEDs/solar cells Charge transport by hopping between uncorrelated sites Width of DOS-disorder parameter σ ( mev) DOS DOS(ɛ) = N t 2πσ exp [ ( ) ] 2 ɛ ɛ0 2σ

9 Governing Equations in OLEDs Poisson equation: ɛ ψ = q(n p) Continuity equation: J p + q p t = qr(p, n) Drift-Diffusion: J p = qµ p p ψ qd p p similar for electrons

10 Governing Equations in OLEDs Poisson equation: ɛ ψ = q(n p) Continuity equation: J p + q p t = qr(p, n) Drift-Diffusion: J p = qµ p p ψ qd p p similar for electrons mobility & diffusion coefficient are affected by the Gaussian DOS!

11 Generalized Einstein Relation E p = DOS(E)f(E)dE ordered material DOS E Statistics Einstein relation Boltzmann D µ = kt q DOS(E), f(e)

12 Generalized Einstein Relation E p = DOS(E)f(E)dE DOS ordered material E disordered material Gaussian Statistics Boltzmann Fermi-Dirac Einstein relation D µ = kt q D µ = p q p E F DOS(E), f(e)

13 Generalized Einstein Relation E p = DOS(E)f(E)dE DOS ordered material E disordered material Gaussian Statistics Boltzmann Fermi-Dirac Einstein relation D µ = kt q D µ = p q p E F DOS(E), f(e)

14 Extended Gaussian Disorder Model (EGDM) D p = k BT q µ 0(T, p, F )g 3 (p, T ) µ p (T, p, F )=µ 0 (T )g 1 (p, T )g 2 (F, T ) g 1 (p, T ) g 2 (F, T ) g 3 (p, T ) Nonlinear equations for mobility and diffusion coefficient Mobility depends on temperature, field and density S. L. M. van Mensfoort, R. Coehoorn, Phys. Rev. B 78, (2008)

15 Cathode Effects of EGDM Transport % &'$!( " Anode organic material field [V m^-1] # $!!$!# constant Assumption of ohmic contact: Dirichlet boundary conditions n 1 =0.5N t n 2 =0.5N t 16V relative carrier density!"! &!! &!!& &!!" &!!' &!!# ( )*+,-(&$(. (! "! #! $! %! &!! device [nm]

16 Cathode Effects of EGDM Transport % &'$!( " Anode organic material field [V m^-1] # $!!$!# field dependent Assumption of ohmic contact: Dirichlet boundary conditions n 1 =0.5N t n 2 =0.5N t 16V relative carrier density!"! &!! &!!& &!!" &!!' &!!# )*+,-(&$(. /"(&$(. (! "! #! $! %! &!! device [nm] (

17 Cathode Effects of EGDM Transport % &'$!( " Anode organic material Assumption of ohmic contact: Dirichlet boundary conditions n 1 =0.5N t n 2 =0.5N t 16V relative carrier density field [V m^-1] &!! # $!!$!#!"! &!!& &!!" &!!' &!!# density dependent )*+,-(&$(. /"(&$(. /&(&$. (! "! #! $! %! &!! device [nm] (

18 Cathode Effects of EGDM Transport % &'$!( " Anode organic material field [V m^-1] # $!!$!# EGDM Assumption of ohmic contact: Dirichlet boundary conditions n 1 =0.5N t n 2 =0.5N t 16V relative carrier density!"! &!! &!!& &!!" &!!' &!!# )*+,-(&$(. /"(&$(. /&(&$. 0123(&$(. (! "! #! $! %! &!! device [nm] (

19 EGDM on single layer OLED IV Curve (hole-only device) IV Curve (hole-only device with 1eV built-in potential)!"!" %&'()*+,'-./0'& 1. 2!,& Diffusion effects Field- and density-dependent # 8!" $!" "!"!$!"!!" σ k B T =6 σ k B T =3!"!#!"!!!" "!"! +34/56,'7&8 Effects of different disorder parameters In good agreement with: S. L. M. van Mensfoort, R. Coehoorn, Phys. Rev. B 78, (2008, Fig 9)

20 Recombination Profiles V V normalized recombination rate const!=3!= device [m] x device [m] x 10 7 Bipolar simulation with constant mobility and EGDM for and normalized recombination rate const!=3!=6 ˆσ =3 ˆσ =6 Effects of disorder clearly visible

21 Thermionic Injection metal organic LUMO Φ e Fermi energy workfunction Contact Region

22 Thermionic Injection metal organic LUMO Φ image = e2 1 16πɛɛ 0 x Φ e Fermi energy workfunction Contact Region

23 Thermionic Injection metal organic LUMO Φ image = e2 1 16πɛɛ 0 x Φ e Fermi energy workfunction qex Contact Region

24 Thermionic Injection metal organic LUMO Φ e Φ B Fermi energy workfunction Φ e eex e 2 16πɛɛ 0 x

25 Thermionic Injection metal organic metal organic LUMO e -!! n Fermi Energy/ Workfunction Density at contact depends on position of Gaussian DOS Dependent boundary conditions

26 Effects of Injection Dependence of the current density on the injection barrier at 2V No effect if injection barrier < 0.5 ev Higher currents with image potential Agrees with Monte Carlo results In good agreement with: J.J.M. van der Holst, M.A. Uijttewaal, R. Balasubramanian, R. Coehoorn, P.A. Bobbert, G.A. de Wijs and R.A. de Groot (EUT, PRE), Phys. Rev. B (2009).

27 Trap Effects in OLEDs localized sites with higher electron affinity impurities, chemical defects Model trap distribution: Expontential, Gaussian discrete levels: shallow, deep exponential DOS Gaussian DOS ɛ ψ = q(n p + n total DOS t p t ) DOS J p + q p t = qr(p, n) J p = qµ p p ψ qd p p energy

28 Trap IV Curves!"!" +!'(/ !" & +(),-.*!" "!"!&!"!!"!"!!& simulation analytic experiment!"!%" m=1 m=8.1 m=2!"!#!"!$!"!%!" "!" %!" $ '()'* trap density influences current density Analytical solution for Gaussian DOS: M. M. Mandoc, B. de Boer, G. Paasch, P. W. M. Blom, Phys. Rev. B (2007).

29 Multi-layer Devices Stack of organic material to optimize recombination profiles and light emission

30 Spatial Discretization 1-dimensional finite volume method Domain divided into n grid points Anode Cathode Reformulation of problem F 1 (ψ, p, n) = ɛ ψ q(n p)! =0 F 2 (ψ, p, n) = ( qµ p p ψ qd p p)+q p t + qr! =0 F 3 (ψ, p, n) = ( qµ n n ψ + qd n n) q n t qr! =0 Integration over each box

31 Scharfetter-Gummel Discretization Neglecting recombination and assuming a constant current density through the device Boundary values and Analytic solution Analytic solution serves as Ansatz function Scharfetter-Gummel discretization

32 Spatial Discretization Exponential fitting for drift-diffusion (F2 and F3) Scharfetter-Gummel discretization with generalized Einstein relation and density- and fielddependent mobility System of (3 x n) strongly coupled equations F 1 ( x) F ( x) = F 2 ( x) F 3 ( x) x = ψ 1 : ψ n n 1 : n n p 1 : p n Dirichlet boundary conditions: Values for potential and carriers given at electrodes

33 Variables sets Problem Formulation carrier concentrations (ψ, p, n) quasi-fermi level (ψ, φ p, φ n ) Assumption: Boltzmann statistics ( ) q(φp ψ) p = n int,eff exp kt ( ) q(ψ φn ) n = n int,eff exp kt Slotboom (ψ, Φ p, Φ n ) ( ) qφp Φ p = exp kt ( ) qφn Φ n = exp kt ( ) qψ p = p i Φ p exp kt ( ) qψ n = n i Φ n exp kt

34 Discretized Equations De-coupled solving Gummel algorithm F3 F2 F1 } Coupled solving Newton algorithm Find x* so that F(x*)=0. F(x) = F(x * ) + J(x * )(x " x * ) $ #F 1 (x)! #F (x) ' 1 & #x 1 #x ) & N ) J(x) = & " # " #F N (x)! #F (x) ) & N ) %& #x 1 #x N () Taylor Series Jacobian Matrix * x k +1 = x k " J(x k ) "1 F(x k ) Iteration function F1 F2 F3 }

35 Algorithms Gummel steady-state transient Newton steady-state transient Initial guess no bias applied, Boltzmann approximation Gummel steady-state Damping Newton Damping Homotopy

36 Convergence - Steady State L2-Norm: F = n F k 2 k=1 #!! %&'()*+)',)./00,*01)*23,45 '!! '!!( '!!'! )*23, ,9*1/41!":&; <7=,9,45 >?)@ 1!!"#!"$!"%!"& ' )*+,-* 1 1$!'&*23&43*) #!!" #!!#! #!!#" Gummel Newton #!!$!! " #! #" $! -.)*/.-&'0

37 Convergence - Steady State F = n L2-Norm: F k 2 k=1 #! #! 3*+4'(5'+6' /./00,*01)*23,45 '!! '!!( '!!'! )*23, ,9*1/41!":&; <7=,9,45 >?)@ 1!!"#!"$!"%!"& ' )*+,-* 1 -$!+*(./*0/(',%122. #! " #!! #!!" Gummel Newton Convergence for Gummel and Newton algorithm Fewer iterations needed for Newton algorithm #!!#! /! " #! #" $! %&'()&%*+,

38 Transient Simulations Implicit Euler time step

39 Modeling of charge carrier transport Bipolar Gummel solver Newton solver Injection Organic material properties Disorder (Gaussian DOS) Mobility Generalized Einstein relation Traps (Exponential DOS) Multilayer OLEDs Exciton dynamics Parameter extraction Coupling to optical model Impedance simulations Outlook

40 Exciton Dynamics!!! Poisson Equation Charge Current Charge Continuity!! Exciton Current Exciton Continuity! Light-emission (from dipoles) & Light-incoupling Electro-optical Coupling Terms Opto-electronic Coupling Terms Extended version of the models published by Ruhstaller et al., J. Appl. Phys. 89, 4575, (2001) and Ruhstaller et al., IEEE JSTQE 9, (3) 723, (2003)

41 Outlook Modeling of charge carrier transport (1st generation) Gummel Newton Bipolar (1st generation) Injection (2nd generation) Organic material properties Disorder (2nd generation) Mobility (2n generation) Generalized Einstein relation (2nd generation) Traps (2nd generation) Multilayer OLEDs (1st generation) Exciton dynamics (1st generation) Parameter extraction Optical simulations Impedance simulations

42 Acknowledgement We acknowledge the financial support of RF7 Thanks for your attention!