goal of the lecture - kit · 2 modelling of oleds: motivation • try to understand oled behaviour...

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Goal of the lecture

• Microscopic understanding of OLEDs- Modelling of electrical behaviour of OLEDs- Computer simulations

• Devices: Single carrier (monopolar), OLEDs- Space charge limited current- Injection limited current- Electric field distribution, charge carrier densities- Charge carrier confinement

• Transient behaviour• Outlook: Laser diodes

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Modelling of OLEDs: Motivation

• Try to understand OLED behaviour- Some parameters cannot be measured

• Understand measurments• Extraction of parameters from measurements

- Some parameters cannot be measured directly• Optimisation and design of devices• Prediction of new effects

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Modelling of OLEDs: Principle of operation

• For electrical modelling, we need:- Charge carrier injection- Charge carrier transport- Formation and decay of excitons

Cathode

Organic film(s)

Anode

Air

Substrate

Exciton formation

Spontan. emission

Injection, transport

Ex=0

x=d

x

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• Continuity equations for the particle densities (1D)

• Change of density in a small volume dV due to flux (left picture) or creation/decay of particles (right)

• Drift-diffusion approximation for particle fluxes

Modelling of OLEDs: Basic equations

dV

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Cathode

Organic film(s)

Anode

Air

Substrate

Exciton formation

Spontan. emission


Ex=0

x=d

x

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• Drift-diffusion approximation for particle fluxes- Directed motion in electric field F: Drift (mobility µ)- Brownian motion due to density gradients: Diffusion (Diffusion

coefficient D = µkBT/q)

Charge carrier transport

F

Overall motion

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Charge carrier mobility

• Poole-Frenkel type mobility

- Very often found in organic semiconductors- µ0 and F0 taken from measurements

From I-V-characteristics: Campbell et al., Applied Physics Letters, Vol. 75, p.841,1999

From TOF-measurements: Campbell et al., Applied Physics Letters, Vol. 74, p.2809,1999

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Cathode

Organic film(s)

Anode

Air

Substrate

Exciton formation

Spontan. emission


Ex=0

x

x=d

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Injection

• Injection influences efficiency and turn-on voltage• Influenced by choice of electrode and organic material• Influenced by interface properties (dipoles etc.)• Still not fully understood• Still not fully solved in real devices• Injection gives the boundary conditions for the

continuity equations of the charge carriers- Particle flux at electrodes

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Injection: Fowler-Nordheim tunneling

• Fowler-Nordheim: Field-induced tunneling of charge carriers across a triangular potential barrier

Experimental verification: Plot ln(J/(d/V)2) vs. d/V for single-carrier devices

E

Electrode organic sem.

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Injection: Fowler-Nordheim tunneling

• Campbell et al., Journal of Applied Physics, Vol. 82, p.6362, 1997: Fit of Fowler-Nordheim tunneling to I-V-characteristics– Currents can only be fitted

over one order of magnitude for higher temperatures

– Deduced barrier heights vary with temperature and are completely wrong

⇒Fowler-Nordheim tun-neling does not work

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Injection: Thermionic emission, Schottky effect

• Carriers with enough energy can cross the energy barrier: Thermionic emission

• Energy barrier lowered due to potential of image force: Schottky effect

T

E A*: Richardson constant

Image force potential:

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Injection: Thermionic emission, Schottky effect

• Barrier lowering is of the same order as the barrier itself• Experimental verification: Plot ln(J/T2) vs. V1/2/T• Proportionality factor is

106-1010 times smaller Richardson constant!

⇒Richardson-Schottky does not work

Campbell et al., Journal of Applied Physics, Vol. 86 , p.5004, 1999

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Injection: Carrier backflow

• Experimental verification: Vary the mobility while leaving the barrier the same (Shen et al., Physical Review Letters, Vol.86, p. 3867, 2001)

⇒Thermionic injection with backflow works quite well

T

E

Scott et al. Chem. Phys. Lett. 299, 115–119 (1999)

• Mobility in organic semiconductors rather low:- Injected carriers may flow back to the contact and recombine

with their image charges: Injection current is decreased

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Cathode

Organic film(s)

Anode

Air

Substrate

Exciton formation

Spontan. emission


Ex=0

x=d

x

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Exciton formation

• Excitons formed from electrons and holes: Bimolecular process

• Langevin-Process: Rate limited by diffusion of holes and electrons towards each other

T

S

ExcitonFree carriersOnly one fourth of excitons generated in the light emitting singlet state (S). Rest: Triplets (T), non radiative

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Exciton transport

• Excitons only subject to diffusion (no charge)• Diffusion coefficient from measurements• Complete dissociation at electrodes: nexc = 0

Ele

ctro

de

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Determination of electric field

• Often: Solving Poisson‘s equation- May cause numerical problems

• Instead: Time evolution equation for local electric field• Starting with Maxwell‘s equation and applying the

divergence operator

we see that

is spatially constant (current conservation). It is the total current through the device

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Determination of electric field

• Integration of the equation over the device (in 1D)

leads to an expression for the total current through the device (V: applied voltage):

• If a linear dielectric is assumed, we finally arrive at

for the time derivative of the field

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• Spatial discretization (grid):- Transform spatial derivatives into differences

- A system of ordinary differential equations is obtained• Time discretization

- Transform time derivatives into differences- A system of linear equations is obtained

• Solution of linear equations- Gives the solution (particle densities, electric field)

• Details of numerical method more complicated- Simple schemes (as above) often unstable

Numerical method

xxi-1 xi xi+1

ni-1 ni ni+1

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Current: Space charge and injection limitation

• Simulated I-V-characteristics for a d = 100 nm TPD hole-only device for different injection barriers

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• Ohmic contacts, monopolar device, Poole-Frenkel mobility: Murgatroyd‘s formula (extension of Child‘s law)

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• Particle densities

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Light output

• I-V-characteristics for a d = 100 nm Alq3 OLED (bipolar)• Also transition from space charge (SCLC) to injection

(ILC) limited current

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Light output and efficiency

• L-V-characteristics and power efficiency• Decrease of efficiency with φb due to decreased

quantum efficiency (SCLC-ILC)

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• Low φb: Charge carriers confined by field, ≈100% QE• High φb: Charge carriers may leave device without

having formed an exciton

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• Unequal hole and electron mobility- Exciton formation near electrode- Exciton dissociation and radiation quenching

• Field dependent exction formation rate

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Improvement of light output

• Problem: Ohmic contacts not easy to achieve- Materials often unstable, chemically reactive etc.- Injection limited current

• Solution- Confine carriers without electric field- Blocking layers- Most simple: Bilayer device with one transport layer- More advanced: Multilayer to keep emission away from

electrodes

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Improvement of light output

• Simulation of TPD-Alq3 bilayer OLED• dTPD = dAlq3= 50 nm; U = 10.5 V• Quantum efficency ≈ 95%

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Transient behaviour

• Application of a current pulse, Alq3 OLED, d = 100 nm• Delay of conduction current and light emission• Voltage rises while OLED is not conducting

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Transient behaviour

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Transient behaviour

• Electrons and holes move towards each other from injecting electrodes

• Emission becomes significant when there is enough overlap between electron and hole density

tt t

goal of the lecture - kit · 2 modelling of oleds: motivation • try to understand oled behaviour...

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