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)

p-electron clound in anthracene Electron density sections through central molecular plane, with each contour line representing an increase of 500 electrons/nm3

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 Externally applied H ~ 1 to 10 kG Energetics of spin states Zero-field splitting EZF ~ 0.1 cm1 ~ 1 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 the electric 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 s Vibration ~ 10-10 – 10-12 s Vertical transition Bathochromic: red-shift Hyposochromic: blue-shift

Effects of domain overlap & corresponding wave amplitudes Mirror image rule

Mirror image rule

Rigorous relatioship between absorption & fluorescence Radiative & non-radiative processes Kasha’s rule

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

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 is a non-radiative transition between two isoenergetic vibrational levels belonging to electronic states of different multiplicities. Delayed fluorescence T1S1 can occur when the energy difference between S1 & T1 is small and when the lifetime of T1 is long enough. Triplet-triplet annihilation In concentrated solutions, a collision between two molecules in 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 transitions Once a molecule is excited and reaches triplet state T1, it can absorb a different wavelength because triplet-triplet transitions 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 transfer RET: resonance energy transfer FRET: fluorescence resonance energy transfer

Energy transfer can result from different interaction mechanisms 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.

CI: Coulombic interaction EE: electron exchange 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.

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

Exciplexes

Lifetimes and quantum yields Excited-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 d-pulse response of the system, decrease according to a single expontial.

Quantum yields

τr = 1/krs 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:

quenching The sum kM of the rate constants for de-excitation processes is equal to the reciprocal excited-state lifetime t0: 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/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 non-fluorescent complex

static Sphere of effective quenching