Principles

Purcell Effect

Optical-environment control of emission rate, effective quantum efficiency, and lifetime

Changing only the distance from an emissive layer to a metal electrode can change the emission lifetime even when material composition, concentration, and intrinsic quantum yield remain identical. The field reflected back to the emitter changes the electromagnetic states available to it and therefore its total decay rate.

This optical-environment control of spontaneous emission is the Purcell effect. It shares the same layered electromagnetic environment as microcavity interference: the microcavity article treats the spectrum and direction of outcoupled light, while this article treats the emitter decay dynamics.

Optical Environment and Decay Rate

In a homogeneous reference environment, the total decay rate is

\Gamma_0=\Gamma_{\mathrm{em},0}+\Gamma_{\mathrm{nr},0} =\frac{1}{\tau_0}, \qquad q_0=\frac{\Gamma_{\mathrm{em},0}}{\Gamma_0}.

Here, $\Gamma_{\mathrm{em},0}$ is the intrinsic decay rate into electromagnetic channels, $\Gamma_{\mathrm{nr},0}$ is the internal material nonradiative rate, $\Gamma_0$ is the intrinsic total rate, $\tau_0$ is the intrinsic lifetime, and $q_0$ is the intrinsic quantum efficiency.

The layered environment multiplies the electromagnetic decay rate by the Purcell factor $F$ while approximately leaving the material nonradiative rate unchanged:

\Gamma_{\mathrm{em}}=F\Gamma_{\mathrm{em},0}, \qquad \Gamma=F\Gamma_{\mathrm{em},0}+\Gamma_{\mathrm{nr},0}.

The electromagnetic channels here include external outcoupling, substrate, waveguide, absorption, and evanescent coupling. Near a metal, an increased $F$ can predominantly feed absorption or SPPs and does not necessarily produce more far-field photons.

Effective Quantum Efficiency and Lifetime

Eliminating the two intrinsic rate components using $q_0$ gives

\frac{\Gamma}{\Gamma_0} =1-q_0+q_0F \equiv\frac{b}{b_0},

where $b/b_0$ is the decay-rate ratio between the layered and reference environments. The effective lifetime and effective quantum efficiency are

\tau_{\mathrm{eff}} =\frac{\tau_0}{1-q_0+q_0F},

q_{\mathrm{eff}} =\frac{q_0F}{1-q_0+q_0F}.

Here, $\tau_{\mathrm{eff}}$ is the lifetime in the optical environment and $q_{\mathrm{eff}}$ is the fraction entering any electromagnetic channel. All three expressions use the same $F$ , so decay rate, lifetime, and effective quantum efficiency cannot be adjusted independently.

Condition	Lifetime	Effective quantum efficiency	Efficiency interpretation
$F>1$ and $q_0<1$	Shorter	Higher	Check whether the enhancement reaches outcoupling or a loss channel
$F<1$ and $q_0<1$	Longer	Lower	One orientation or loss channel may be suppressed, but total electromagnetic decay is weaker
$q_0=1$	Changes with $F$	Remains 1	Purcell modulation changes lifetime and channel allocation but cannot raise 100% further
Very large $F$ together with large EVA/ABS	Usually much shorter	Can be higher	EQE can still fall because the enhancement mainly feeds metal loss

Maximizing $F$ is therefore not an OLED optical-design objective. A useful design increases the target outcoupling fraction while controlling guided, absorptive, and evanescent loss.

Wavevector Meaning of the Purcell Factor

The Purcell factor is the integral of normalized dissipated power across all in-plane wavevectors:

F(\lambda,z,o)=\int_0^\infty f(u;\lambda,z,o)\,\mathrm du.

Here, $u$ is the in-plane wavevector normalized to the EML wavenumber, $f$ is normalized dissipated power per unit $u$ , $\lambda$ is wavelength, $z$ is dipole position in the EML, and $o$ denotes dipole orientation. The integral contains propagating, guided, and evanescent regions, making $F$ sensitive to wavelength, position, and orientation.

Horizontal and vertical dipoles see different reflected fields and generally have different factors $F_h$ and $F_v$ . Even if the input orientation ratio is isotropic, the environment reweights their emission contributions through $F_h$ and $F_v$ . A strong microcavity can enhance horizontal dipoles and suppress vertical dipoles, pulling the total outcoupling toward the high-LEE horizontal component.

Angular patterns, optical modes, and Purcell factors of different dipole orientations in free space and a strong microcavity — Figure 1 | The same microcavity feeds back differently on horizontal and vertical dipoles. In this example the horizontal dipole has a larger Purcell factor and air-mode contribution, while the vertical dipole mainly enters waveguide and SPP channels.

Broadband-Emitter Average

The Purcell factor varies with wavelength. For an emitter with photon-number weight $\Lambda_N(\lambda)$ , first calculate

\overline F= \frac{\int_{\lambda_1}^{\lambda_2}\Lambda_N(\lambda)F(\lambda)\,\mathrm d\lambda} {\int_{\lambda_1}^{\lambda_2}\Lambda_N(\lambda)\,\mathrm d\lambda},

where $\lambda_1$ and $\lambda_2$ bound the calculated spectrum, $\Lambda_N$ is the photon-number spectral weight, and $\overline F$ is the spectrum-averaged Purcell factor. The overall $b/b_0$ , $q_{\mathrm{eff}}$ , and $\tau_{\mathrm{eff}}$ then follow by substituting $\overline F$ into the rate equations above.

Both $q_{\mathrm{eff}}(F)$ and $\tau(F)$ are nonlinear. Directly averaging wavelength-resolved quantum efficiencies or lifetimes gives a different statistic. When comparing simulation with time-resolved measurements, confirm whether the reported lifetime is derived from the overall rate or is an arithmetic mean of wavelength-resolved lifetimes.

Interpreting the Results

Quantity	Direct meaning	Read together with
$F$	Enhancement or suppression of electromagnetic decay relative to the reference	Dissipated-power spectrum and every Mode fraction
$b/b_0$	Total decay-rate ratio	$q_0$ and $F$
$q_{\mathrm{eff}}$	Fraction of excitons entering any electromagnetic channel	NRA and outcoupling fractions
$\tau_{\mathrm{eff}}$	Lifetime after optical-environment modulation	Intrinsic lifetime and the experimental time-resolved definition
TOC/BOC	Fractions that actually cross an external boundary	Conversion efficiency $C$ is still needed to obtain device EQE

Next Step

Read Emission Structure to turn the EML, emitter, spectrum, and detector quantities from these five principle articles into a runnable model.

Reference

Purcell, E. M. Spontaneous Emission Probabilities at Radio Frequencies. In Confined Electrons and Photons; Springer, 1995; p 839.
Chance, R. R.; Prock, A.; Silbey, R. Molecular Fluorescence and Energy Transfer near Interfaces. Adv. Chem. Phys. 1978, 37, 1–65.
Wasey, J. A. E.; Barnes, W. L. Efficiency of Spontaneous Emission from Planar Microcavities. J. Mod. Opt. 2000, 47, 725–741.
Cho, H.; Chung, J.; Song, J.; et al. Importance of Purcell Factor for Optimizing Structure of Organic Light-Emitting Diodes. Opt. Express 2019, 27, 11057.
Meerheim, R.; Furno, M.; Hofmann, S.; Lüssem, B.; Leo, K. Quantification of Energy Loss Mechanisms in Organic Light-Emitting Diodes. Appl. Phys. Lett. 2010, 97, 275.

Transfer-Matrix Method

From Snell's law and Fresnel boundaries to multilayer matrix solving

Limits of the TMM Model

Failure scenarios for the TMM assumptions and the direction of the resulting error