Chapter 3. Light emitting diod

Electron configuration

Covalent bond

Organic semiconductors: extensively conjugated molecular systems such as fully conjugated polymers or cata-condensed polyacenes (PAH, e.g., anthracene)

Electron density sections through central molecular plane, with each contour line representing an increase of 500 electrons/nm3

-electron clound in anthracene

Molecular orbitals

types of electronic transitions in polyatomic molecules

The total spin quantum number S = Σ si

The multiplicities M = 2S + 1

Spin of electrons

Statistical states

Ms:Magnetic quantum number

Energetics of spin states

Zero-field splitting EZF ~ 0.1 cm1 ~ 1 kG

Externally applied H ~ 1 to 10 kG

Spin interaction

Coulomb repulsion

Electronic excitation and de-excitation in organic molecules

Jabloński Diagram

probability of transition. The Beer-Lambert Law. Oscillator strength

The molecules whose absorption transition moments are parallel to theelectric vector of a linearly polarized incident light are preferentially excited.

The probability of excitation is proportional to the square of the scalar product of the transition moment and the electric vector. This probability is thus maximum when the two vectors are parallel and zero when they are perpendicular.

Frank-Condon principle

Electronic transition ~ 10-15 sVibration ~ 10-10 – 10-12 s

Vertical transition

Bathochromic: red-shiftHyposochromic: blue-shift

Effects of domain overlap & corresponding wave amplitudes

Mirror image rule

Mirror image rule

Rigorous relatioship between absorption & fluorescence

Kasha’s rule

Radiative & non-radiative processes

Internal conversionInternal conversion is a non-radiative transition between two electronic states of the same spin multiplicity.

FluorescenceEmission of photons accompanying the S1 S0 relaxation is called fluorescence.

In most cases, the absorption spectrum partly overlaps the fluorescence spectrum. At r. t., a small fraction of molecules is in a vibrational level higher than 0 in the ground state as well as in the excited state. At low temp, this departure from the Stokes Law should disappear.

It should be noted that emission of a photon is as fast as absorption of a photon (~1015 s). However, excited molecules stay in the S1 state for a certain time (a few tens of picoseconds to a few hundreds of nanoseconds, depending on the type of molecule and the medium) before emitting a photon or undergoing other de-excitation processes (internal conversion, intersystem crossing).

From S1, internal conversion to S0 is possible but is less efficient than conversion from S2 to S1, because of the much larger energy gap between S1 and S0.

Experimental schematic for detection of the Stokes’ shift

The energy of the emission is typically less than that of absorption. Hence, fluorescence typically occurs at lower energies or longer wavelengths.

After the 1850s, Stokes became involved in administrative matters, and his scientific productivity decreased.

Some things never change.

Stokes shift

Intersystem crossing and subsequent processes

Intersystem crossingis a non-radiative transition between two isoenergetic vibrational levels belonging to electronic states of different multiplicities.

Delayed fluorescenceT1S1 can occur when the energy difference between S1 & T1 is small and when the lifetime of T1 is long enough.

Triplet-triplet annihilationIn concentrated solutions, a collision between two moleculesin the T1 state can provide enough energy to allow one of them to return to the S1 state leads to a delayed fluorescence emission.

Triplet-triplet transitionsOnce a molecule is excited and reaches triplet state T1, it can absorb a different wavelength because triplet-triplettransitions are spin allowed.

Energy transfer

Distinction between radiative and non-radiative transfer

hopping

Excitation energy transfer

heterotransfer

homotransfer

Radiative energy transfer

(rate constant)

(lifetime of excited state)

Non-radiative energy transfer

EET: excitation energy transfer or electronic energy transferRET: resonance energy transfer

FRET: fluorescence resonance energy transfer

Energy transfer can result from different interaction mechanisms. The interactions may be Coulombic and/or due to intermolecular orbital overlap.

* * The Coulombic interactions consist of long-range dipole-dipole interactions (Forster’s mechanism) and short-range multi-polar interactions.

* * The interactions due to intermolecular orbital overlap, which include electron exchange (Dexter’s mechanism) and charge resonance interactions, are of course only short range.

It should be noted that for singlet-singlet energy transfer, all types of interactions are involved, whereas triplet-triplet energy transfer is due only to orbital overlap.

The total interaction energy can be expressed as a sum of two terms: a Columbic term Uc and an exchange term Uex. The Coulombic term corresponds to the energy transfer process in which the initially excited electron on the donor D returns to the ground state orbital on D, while simultaneously an electron on the acceptor A is promoted to the excited state. The exchange term corresponds to an energy transfer process associated with an exchange of two electrons between D and A.

CI: Coulombic interaction

EE: electron exchange

Formation of excimers and exciplexes

Excimers

An excimer is located at wavelengths higher than that of the monomer and does not show vibronic bands.

P3HT PL heating-1

500 550 600 650 700 750 800 8500

50

100

150

200

250Heating-1 30 oC

70 oC

110 oC

150 oC

190 oC

210 oC

220 oC

230 oC

240 oC

250 oC

260 oC

exc

= 470 nm

HT-PL of PT-6 (fresh toluene solution cast), exc

= 550 nm (95/03/27)

Em

issio

n in

tens

ity (a

. u.)

Wavelength (nm)

S

C6H13

[ ]n

Exciplexes

Lifetimes and quantum yields

Lifetimes and quantum yieldsExcited-state lifetimes

The rate constants for the various processes will be denoted as follows:

A very short pulse of light at time 0 brings a certain number of molecules A to the S1 excited state by absorption of photons. These excited molecules then return to So.The rate of disappearance of excited molecules is expressed by the following differential equation:

iF(t), the -pulse response of the system, decrease according to a single expontial.

Quantum yields

When the fluorescence quantum yield and the excited-state lifetime of a fluorophore are measured under the same conditions, the non-radiative and radivative rate can be easily calculated by means of the following relations:

τr = 1/krs

quenching

The sum kM of the rate constants for de-excitation processes is equal to the reciprocal excited-state lifetime :

Kq : the observed rate constant for the bimolecular process

The fluorescence characteristics (decay time and/or fluorescence quantum yield) of M* are affected by the presence of Q as a result of competition between the intrinsic de-excitation and these intermolecular processes.

Overview of the intermolecular de-excitation of excited molecules leading to fluorescence quenching

4.2.1 Phenomenological approach

(static quenching)

Dynamic quenching

Stern-Volmer kinetics (ignore the transient effects)

i(t) = i(0) exp (-t/)

KSV : Stern-Volmer constant

I0/I vs. [Q] Stern-Volmer plot

Static quenching

The term static quenching implies either the existence of a sphere of effective quenching or the formation of a ground-state non-fluorescent complex (Figure 4.1)

Sphere of effective quenching

Formation of a ground-state non-fluorescent complex

I ～ [M]

Simultaneous dynamic and static quenching

dynamic

static non-fluorescent complex

static

Sphere of effective quenching