Luminescence from oriented emitting dipoles in a birefringent medium

Chang-Ki Moon; Sei-Yong Kim; Jeong-Hwan Lee; Jang-Joo Kim

doi:10.1364/OE.23.00A279

1. Introduction

Light emission from organic materials has been an important research topic during the last few decades because of its scientific and technological importance, particularly due to the success of organic light emitting diodes (OLEDs). The classical dipole model has been used to understand emission characteristics from thin films and devices [1–7], such as emission patterns [4,7–11], power dissipation modes including the outcoupling efficiency from thin films and devices [7,9,10,12–22], position of recombination zones in electroluminescent (EL) devices [12], and the orientation of emitting dipoles in thin films [18,23–28]. Until recently, the emitting dipoles were commonly assumed to be randomly oriented in an isotropic medium for small molecule based organic EL devices because there are no apparent driving forces that would yield a preferred dipole orientation for the emitters. Recently, however, a large number of organic thin films have been reported to possess a preferred orientation, leading to optical birefringence [29–32]. Furthermore, some emitters doped in organic semiconducting layers showed preferentially oriented transition dipole moment along the horizontal direction (parallel to the substrate) [18,23–28]. For these systems, the assumption of a random orientation of the dipoles in an isotropic medium no longer applies and thus leads to inaccurate predictions for the emission patterns (intensity and spectrum) and power dissipation modes in thin films and related devices. Wasey et al. [5] attempted to analyze emission in a polymer layer while accounting for birefringence. They proved that emitting dipoles are aligned horizontally in a spin coated thin polymer film by the analysis of far-field radiation from the film. Further research analyzed dipole radiation in the anisotropic medium with an arbitrary optical axis [33]. However, unfortunately, they did not perform the quantitative analysis of the dipole orientation in a birefringent medium and did not correlate the dipole orientation and the optical birefringence with the outcoupling efficiency of OLEDs.

In this paper, we present an optical model originally developed by Chance el al [1]. to describe the luminescence from emitting dipoles in a birefringent medium and validate the theoretical model through its applications to a dye doped organic thin film and OLEDs to describe the far-field radiation, outcoupling efficiency, and orientation of emitting dipoles.

2. Theoretical background

2.1. Luminescence from an oriented emitting dipole embedded in a birefringent medium

Consider a dipole embedded in an infinite anisotropic medium whose optical axis is parallel to the z-axis with the refractive index tensor represented by

\tilde{\tilde{n}} = (\begin{matrix} n_{x} & 0 & 0 \\ 0 & n_{x} & 0 \\ 0 & 0 & n_{z} \end{matrix}) .

When the dipole is embedded in this anisotropic medium, the radiated power from the dipole in the absence of an interface is given by [1]

P_{0}^{⊥} = C o n s t \cdot n_{z},

P_{0}^{∥} = C o n s t \cdot n_{x} \frac{3 n_{x}^{2} + n_{z}^{2}}{4 n_{x}^{2}},

where

C o n s t = μ_{0}^{2} ω^{4} / 12 π ε_{0} c^{3},

μ_{0}

is the dipole moment, ω is the oscillation frequency, c is the speed of light, and ⊥ and ∥ represent a vertical and horizontal orientation of the dipole, respectively. If the ordinary refractive index is larger than the extraordinary refractive index (negative birefringence), the radiated power from the horizontal dipole is larger than that of the vertical dipole in the birefringent emitting layer, and vice versa. The net radiated power from the dipole in the absence of an interface is described by taking the dipole distribution as

P_{0} = (1 - α) \cdot P_{0}^{⊥} + α \cdot P_{0}^{∥},

where α is the ratio of the horizontal dipole (2/3 for an isotropic orientation).

If the emitting layer is sandwiched by two layers, as shown in Fig. 1, the spontaneous decay rate of the dipole and the radiation power are modified according to the Purcell effect [34] as follows,

F = \frac{b_{r}}{b_{r,0}} = \frac{P}{P_{0}},

In the above expression, F is the Purcell factor, while

b_{r}

(

b_{r,0}

) and P (

P_{0}

) are the radiative decay rate and the radiated power from the dipole in the structure (in free space), respectively. In the same manner, the Purcell factor for the outcoupled power,

F_{out},

can be defined as the ratio of the outcoupled power,

P_{out},

to the radiated power in free space,

P_{0},

as

F_{out} = \frac{P_{out}}{P_{0}} .

Modification of the radiated power from the dipole in the structure can be described by the integration of the power dissipation function p(u) [1]:

\frac{P^{⊥, ∥}}{P_{0}} = 1 + \frac{2 n^{2}}{2 μ_{0} k^{3}} Im (E_{R}^{⊥, ∥}) = \int_{0}^{\infty} p^{⊥, ∥} (u) d u,

where k is the wavenumber, u is the normalized in-plane wave vector, and

E_{R}

denotes the reflected electric field at the position of the dipole. The net radiated power emitted by the dipole in the structure is described by the power dissipation function for each dipole orientation and electric field polarization as

\begin{matrix} P = (1 - α) \cdot P^{⊥} + α \cdot P^{∥} \\ = (1 - α) \cdot P_{0}^{⊥} \int_{0}^{\infty} p^{⊥, TM} (u) d u + α \cdot P_{0}^{∥} \cdot (\int_{0}^{\infty} p^{∥, TM} (u) d u + \int_{0}^{\infty} p^{∥, TE} (u) d u) . \end{matrix}

If the dipole is located at distances d and s from the interfaces between layer 1 and 2, and layer 2 and 3, respectively, the power dissipation functions for the dipole in the anisotropic medium are obtained by calculating the radiated electric field from the dipole using the appropriate boundary conditions as

p^{⊥, TM} = \frac{3}{2} (\frac{n_{z}}{n_{x}}) Re {\frac{[1 - R (d, r_{12}^{TM})] \cdot [1 - R (s, r_{13}^{TM})]}{1 - R (d + s, r_{12}^{TM} r_{13}^{TM})} \cdot \frac{u^{3}}{l_{1}}},

p^{∥, TM} = (\frac{3 n_{x}^{2}}{3 n_{x}^{2} + n_{z}^{2}}) Re {(\frac{n_{z}^{2}}{n_{x}^{2}}) \cdot \frac{[1 + R (d, r_{12}^{TM})] \cdot [1 + R (s, r_{13}^{TM})]}{1 - R (d + s, r_{12}^{TM} r_{13}^{TM})} \cdot (1 - u^{2}) \cdot \frac{u}{l_{1}}},

p^{∥, TE} = (\frac{3 n_{x}^{2}}{3 n_{x}^{2} + n_{z}^{2}}) Re {\frac{[1 + R (d, r_{12}^{TE})] \cdot [1 + R (s, r_{13}^{TE})]}{1 - R (d + s, r_{12}^{TE} r_{13}^{TE})} \cdot \frac{u}{l_{1}}},

where

l_{j} = {(n_{j}^{2} / n_{1}^{2} - u^{2})}^{1 / 2},

r^{TM,TE}

are the Fresnel’s reflection coefficients of the TM and TE waves at the interfaces as described in Appendix, and R denotes a reflection coefficient that includes a phase shift in the anisotropic medium containing the dipole described by

R (x, y) = y \cdot \exp (2 i k_{0} l_{1} n_{x} x) .

Wave propagation in the anisotropic medium is affected by the refractive index of the medium parallel to the direction of electric field polarization. The relation between the wave vector components and the propagation angle is illustrated in Fig. 1. If the out-of-plane wave vector

l_{1}

is real, the wave vector components of a TE wave obey the relations

\sin θ_{1} = u,

\cos θ_{1} = l_{1},

while the relations for a TM wave are

\sin θ_{1} = \frac{n_{z}}{n_{1}} u,

\cos θ_{1} = \frac{n_{x}}{n_{1}} l_{1} .

Here,

n_{1}

is the effective refractive index of layer 1 calculated using the refractive index ellipsoid when the power propagation angle measured from the substrate is

θ_{1} .

Fig. 1 Dipole embedded in an anisotropic medium sandwiched by two layers. The y-axis is perpendicular to the x-z plane. Arrows represent the relation between wave vector components for different electric field polarizations.

Download Full Size | PDF

To calculate the outcoupled power, $p_{out},$ we decompose the power dissipation function into contributions from the positive and negative z-directions for a real out-of-plane wave vector $l_{1}$ as follows [3]:

\begin{matrix} Re (\frac{{1 \pm R (d, r_{12})} \cdot {1 \pm R (s, r_{13})}}{1 - R (d + s, r_{12} r_{13})}) = \frac{1}{2} {| \frac{1 \pm R (d, r_{12})}{1 - R (d + s, r_{12} r_{13})} |}^{2} \cdot (1 - {| R (s, r_{13}) |}^{2}) \\ + \frac{1}{2} {| \frac{1 \pm R (d, r_{13})}{1 - R (d + s, r_{12} r_{13})} |}^{2} \cdot (1 - {| R (s, r_{12}) |}^{2}) . \end{matrix}

The first and the second terms on the right-hand side of the above expression represent the power propagating in the positive and negative z-directions, respectively. Using the relation between reflectance, transmittance, and absorption,

1 - {| R |}^{2} = T + A,

we divide the outcoupled power of the dipole to layer 3 using Eq. (8)-(10) as

p_{out}^{⊥, TM} = \frac{3}{4} (\frac{n_{z}}{n_{x}}) {| \frac{1 - R (d, r_{12}^{TM})}{1 - R (d + s, r_{12}^{TM} r_{13}^{TM})} |}^{2} \cdot T_{13}^{TM} \cdot Re (\frac{u^{3}}{l_{1}}),

p_{out}^{∥, TM} = \frac{1}{2} (\frac{3 n_{x}^{2}}{3 n_{x}^{2} + n_{z}^{2}}) (\frac{n_{z}^{2}}{n_{x}^{2}}) {| \frac{1 + R (d, r_{12}^{TM})}{1 - R (d + s, r_{12}^{TM} r_{13}^{TM})} |}^{2} \cdot T_{13}^{TM} \cdot Re [(1 - u^{2}) \cdot \frac{u}{l_{1}}],

p_{out}^{∥, TE} = \frac{1}{2} (\frac{3 n_{x}^{2}}{3 n_{x}^{2} + n_{z}^{2}}) {| \frac{1 + R (d, r_{12}^{TE})}{1 - R (d + s, r_{12}^{TE} r_{13}^{TE})} |}^{2} \cdot T_{13}^{TE} \cdot Re (\frac{u}{l_{1}}),

where the transmittance of the TM and TE waves (

T_{13}^{TM,TE}

) in this case are described in Appendix. The outcoupled power is calculated by integrating Eq. (16)-(18) up to the critical angles. Since the critical angles for an external medium consisting of air are

u_{air}^{TM} = 1 / n_{z}

and

u_{air}^{TE} = 1 / n_{x}

for the birefringent medium,

P_{out}

is described by

\begin{matrix} P_{out} = (1 - α) \cdot P_{out}^{⊥} + α \cdot P_{out}^{∥} \\ = (1 - α) \cdot P_{0}^{⊥} \int_{0}^{u_{air}^{TM}} p_{out}^{⊥, TM} (u) d u + α \cdot P_{0}^{∥} \cdot [\int_{0}^{u_{air}^{TM}} p_{out}^{∥, TM} (u) d u + \int_{0}^{u_{air}^{TE}} p_{out}^{∥, TE} (u) d u] . \end{matrix}

2.2. Efficiency of an organic EL device with a birefringent emitting layer

The external quantum efficiency (EQE) of an organic EL device is defined as the quantum ratio of the number of the photons emitted from the structure to air to the number of injected charge carriers. The emission process in the device can be divided into 4 steps and the EQE can be described as an integration of those elements [7]:

η_{EQE} = γ \cdot χ \cdot \int_{λ} s (λ) \cdot q_{eff} (λ) \cdot η_{out} (λ) d λ .

Here γ is the electrical balance factor (# of generated excitons / # of injected charge carriers), χ is the ratio of radiative excitons with spin statics (# of radiative excitons / # of generated excitons), s(λ) is the normalized photon spectrum of the emitter (# of radiative excitons with λ / # of radiative excitons) satisfying

\int_{λ} s (λ) d λ = 1,

q_{eff} (λ)

is the effective radiative quantum efficiency (# of emitted photons with λ / # of radiative excitons with

E_{λ}

), and

η_{out} (λ)

is the outcoupling efficiency (# of emitted photons to air / # of emitted photons with wavelength λ).

Because of the modification of the radiative decay rate in the structure, the effective radiative quantum efficiency and the outcoupling efficiency of an organic EL device are described in terms of the Purcell factors as:

q_{eff} (λ) = \frac{b_{r} (λ)}{b_{nr} + b_{r} (λ)} = \frac{q \cdot F (λ)}{1 - q + q \cdot F (λ)},

η_{out} (λ) = \frac{P_{out} (λ)}{P (λ)} = \frac{F_{out} (λ)}{F (λ)} .

The EQE is then obtained using

η_{EQE} = γ \cdot χ \cdot \int_{λ} s (λ) \cdot \frac{q \cdot F_{out} (λ)}{1 - q + q \cdot F (λ)} d λ .

The Purcell factors can be obtained by calculating the radiated power emitted by the dipole in the absence of an interface

P_{0}

, in the structure P, and the outcoupled power

P_{out}

as given by Eq. (3), (7), and (19), respectively.

2.3. Far-field radiation

In the expression for the outcoupled power, the in-plane wave vector u can be converted to a solid angle. Then, Eq. (19) becomes a function of the solid angle in layer 3 ( $θ_{3}$ ) as

P_{out} = \int_{0}^{π / 2} [(1 - α) \cdot P_{0}^{⊥} \cdot {p^{'}}_{out}^{⊥,TM} (θ_{3}) + α \cdot P_{0}^{∥} \cdot {{p^{'}}_{out}^{∥,TM} (θ_{3}) + {p^{'}}_{out}^{∥,TE} (θ_{3})}] \sin θ_{3} d θ_{3},

and the outcoupled powers as a function of

θ_{3}

are given by

{p^{'}}_{out}^{TM} (θ_{3}) = p_{out}^{TM} (u) \cdot \frac{n_{3} l_{3}^{TM}}{n_{z} u},

{p^{'}}_{out}^{TE} (θ_{3}) = p_{out}^{TE} (u) \cdot \frac{n_{3} l_{3}^{TE}}{n_{x} u},

where

l_{3}^{TM} = {(n_{3}^{2} / n_{z}^{2} - u^{2})}^{1 / 2}

and

l_{3}^{TE} = {(n_{3}^{2} / n_{x}^{2} - u^{2})}^{1 / 2}

. The far-field radiation power spectrum per unit area from the dipole with respect to viewing angle

θ_{3}

is described according to the photon spectrum

s (λ)

as

I (θ_{3}, λ) = [(1 - α) \cdot P_{0}^{⊥} \cdot {p^{'}}_{out}^{⊥,TM} (θ_{3}, λ) + α \cdot P_{0}^{∥} \cdot {{p^{'}}_{out}^{∥,TM} (θ_{3}, λ) + {p^{'}}_{out}^{∥,TE} (θ_{3}, λ)}] \cdot s (λ) .

3. Experimental

A mixed layer of 4,4’,4”-tris(carbazol-9-yl)-triphenylamine [TCTA] and bis-4,6-(3,5-di-3-pyridylphenyl)-2-methylpyrimidine [B3PYMPM] was used as a dielectric birefringent medium and a phosphorescent dye of bis(2-phenylpyridine)iridium(III)(2,2,6,6-tetramethylheptane-3,5-diketonate) [Ir(ppy)₂tmd] [20,35] doped in the mixed layer was used as an emitter. The mixed layer of TCTA and B3PYMPM was reported as an exciplex-forming host in OLEDs [11,18,20,36–38] that enables effective energy transfer to the Ir(ppy)₂tmd. Figure 2 shows the structure of the OLEDs with thick TCTA:B3PYMPM layers. The structure of the OLEDs consists of glass substrate / ITO (70 nm) / MoO₃ (1 nm) / TCTA (10 nm) / TCTA:B3PYMPM:Ir(ppy)₂tmd (45.8:45.8:8.4 mole %, 125 nm) / B3PMYPM (10 nm) / LiF (1 nm) / Al (100 nm). The doping region of Ir(ppy)₂tmd was varied for different emission zones in the same device structure. Four kinds of OLEDs were fabricated, having 20-nm-thick EMLs located 40 nm, 55 nm, 70 nm, and 110 nm from the Al cathode and are referred to device 1, 2, 3, and 4, respectively. Thin MoO₃ and LiF layers were used for efficient hole and electron injection, respectively. The films and OLEDs were fabricated using thermal evaporation in vacuum.

Fig. 2 Structure of OLEDs with a mixed host of TCTA:B3PYMPM with different doping regions.

Download Full Size | PDF

Variable angle spectroscopic ellipsometry (VASE, J. A. Woolam M-2000 spectroscopic ellipsometer) was used to analyze the molecular orientation and optical constants (refractive index n and extinction coefficient k) of the TCTA:B3PYMPM film deposited on the pre-cleaned silicon substrate. Optical constants were analyzed using J. A. Woolam Complete EASE software. Analysis of the optical constants was initiated using the Cauchy model at the transparent region, expanded to the whole region by the B-spline model satisfying the Kramers-Krönig consistency, and completed by inserting Gaussian oscillators into the result of the B-spline model. The uniaxial model was applied using separate analyses for the ordinary and the extraordinary axes. An angle-dependent photoluminescence (PL) analysis [23] was applied to determine the orientation of the transition dipole moment of Ir(ppy)₂tmd in the TCTA:B3PYMPM host. We analyzed the dipole orientation with a 30 nm thick film of the Ir(ppy)₂tmd-doped TCTA:B3PYMPM layer deposited onto a fused silica substrate. The substrate was attached to a half-cylinder lens made of fused silica and fixed on a programmedrotation stage. The molecules in the film were excited by a He-Cd laser (325 nm, CW) and angle-dependent intensity profiles of the PL escaping through the lens were measured using a fiber spectrometer (Maya2000, OceanOptics Inc.). For the analysis, TM-polarized light was selected using a linear polarizer. The experimental set-up and details are described in [18] and [23].

The current-voltage-luminescence characteristics of the OLEDs were analyzed using the Keithley 2400 and the SpectraScan PR 650 (Photo Research). The angle-dependent emission spectra of the devices were measured using an Ocean Optics S2000 fiber optic spectrometer with constant current for angles ranging from 0° to 85°. Measurements were performed automatically using the programmed rotation stage. The EQEs of the OLEDs were obtained by calculating the ratio between the numbers of emitted photons and injected electrons and calibrated by considering the angle-dependent emission distribution of the OLEDs.

4. Results and discussion

4.1. Optical birefringence and the dipole orientation

The optical constants of the TCTA:B3PYMPM layer displayed negative birefringence (n_o > n_e) as shown by Fig. 3(a), indicating the horizontal orientation of the molecules in the mixedlayer. The difference between the ordinary and extraordinary refractive index n is ~0.2 in the visible region. Planar-shaped B3PYMPM molecules with hydrogen bonds result in a horizontal molecular orientation even in the vacuum-deposited organic film [31,39]. Although they were mixed with the TCTA molecules, the horizontally preferred molecular orientation was observed in the mixed film.

Fig. 3 (a) Optical constants of TCTA:B3PYMPM layer. (b) Angle-dependent PL intensity profile of the Ir(ppy)₂tmd in the TCTA:B3PYMPM film at λ = 520 nm (circle) is compared with the theoretical values for an isotropic dipole orientation (red solid line) and for the emission dipoles with α = 0.74 (black solid line) when considering a birefringent medium, and for α = 0.71 (blue dashed line) and α = 0.75 (green dotted line) without accounting for the birefringence of the emitting layer. Theoretical profiles calculated under the assumption of an isotropic medium fit only part of the experimentally obtained intensity profile.

Download Full Size | PDF

Figure 3(b) shows the angular emission intensity profile of the TM wave from the film at the wavelength λ = 520 nm corresponding to the PL maximum. Optical simulations for the far-field emission of the TM wave from the film to the semi-infinite fused silica substrate was performed using Eq. (27) to determine the dipole orientation of the emitter, under an assumption that the molecules in the thin layer are excited uniformly throughout the layer. The horizontal dipole ratio (α) was taken as a fitting parameter for the experimental data. The experimental data are in good agreement with the theoretical prediction using α = 0.74 across the entire emission angle when the birefringence of the emitting layer was considered. In contrast, the theoretical fittings under the assumption of an isotropic medium with an ordinary refractive index fit only part of the experimental data, i.e., over 40°. In other words, the accuracy of the predicted emission dipole orientation is significantly improved by accounting for the birefringence of the emission layer. The unexpected peak at around 40° in the measurement comes from reflection of the encapsulation glass at the opposite side of the substrate.

4.2. Emission spectra of OLEDs

The emission spectra of the four different OLEDs along the normal direction with respect to the substrate are shown in Fig. 4. The emission spectra exhibit more pronounced longer-wavelength vibronic peaks as the distance between the doping region and the cathode increases. Emission spectra of the OLEDs were used to predict the location of the emission zone in the devices by fitting the far field radiation with the location of the emission zone as a parameter, where the emission zone geometry is assumed to be that of a sheet. The mean emission zones of the four devices were determined to be located at 50 nm (device 1), 60 nm (device 2), 75 nm (device 3), and 120 nm (device 4) from the cathode, all of which are located in the doped regions of the devices. Note that the optical birefringence is not effective in this calculation because only the ordinary refractive index of the medium affects light propagating in the direction normal to the substrate. However, consideration of the birefringence is important in determining the far-field radiation at other angles.

Fig. 4 Emission spectra of OLEDs with different locations in the emission layer at a normal direction with respect to the substrate. Mean emission zones were determined via optical simulation based on the emission spectra.

Download Full Size | PDF

The measured angle-dependent EL spectra of devices 1, 2, 3, and 4 between 0° and 80° are depicted in Fig. 5. As the emission zone was far apart from the cathode, the angular emission spectra were broadened and the intensities at high angles were increased. The calculated far-field radiant spectra with the consideration of the effects of birefringence (solid lines) agreed with the experimental results in intensity, resonance wavelength, spectral width, and angular dependency of the radiation. Calculated angular radiant spectra using the ordinary index without the consideration of the birefringence (isotropic model) are shown in Fig. 5 as the broken lines. The differences between the calculated and the experimental results are not significant in the case of device 1, 2, and 3, but are significant in the device 4, which has a significant difference between the resonance wavelength of the micro cavity and the PL maximum of the Ir(ppy)₂tmd. The birefringent model yielded larger radiant intensities than the isotropic model and better explains the far-field emission characteristics of the device.

Fig. 5 Angle-dependent EL spectra of devices 1, 2, 3, and 4 (points) compared to the calculated far-field radiation spectra when considering the birefringence (solid lines) and for an ordinary index of refraction (broken lines).

Download Full Size | PDF

4.3. Efficiency of OLEDs

Current density-voltage-luminance (J-V-L) characteristics of the four different OLEDs are depicted in Fig. 6(a). They show general diode characteristics with the same turn-on voltage of 2.7 V and low leakage current. EQEs of the OLEDs versus current density are shown in Fig. 6(b). The maximum EQEs were 28.0%, 28.8%, 27.9%, and 11.6% for device 1, 2, 3, and 4, respectively. Their maximum EQEs were obtained at the low current density, indicating that there are electrical losses at high current densities in the devices. Calculated maximum EQEs of OLEDs using Eq. (23) as a function of the distance from the cathode to the emission zone are displayed in Fig. 6(c). We chose the electrical balance factor γ = 1 (no electrical loss), the spin statistics factor χ = 1 due to the phosphorescent emitter, the radiative quantum efficiency q = 0.96 [20], and the ratio of the horizontal dipole α = 0.74 in the calculation. The lines in Fig. 6(c) show the theoretically predicted maximum EQEs using the birefringent model (solid line), the isotropic model using the ordinary refractive index (dashed line), and the isotropic model using the effective refractive index of $n_{i s o} = \sqrt{(2 n_{o}^{2} + n_{e}^{2}) / 3}$ (dotted line). The experimentally obtained EQEs from the OLEDs matched very well with the theoreticalprediction when the birefringence in the emitting layer was considered. However, isotropic model using the effective refractive index or the ordinary refractive index resulted in significant deviation from the experimentally obtained EQEs. Use of the ordinary index in the isotropic model predicted lower EQEs than the experimental ones because the low extraordinary refractive index of the medium reduces the losses from waveguided light and surface plasmon polaritons. In addition, the radiation from the horizontal dipole is enhanced in the negative birefringent medium because the intrinsic radiation power of the horizontal dipole in Eq. (2) is larger than that of the vertical dipole in Eq. (1).

Fig. 6 (a) Current density-voltage-luminance curves of devices 1, 2, 3, and 4. (b) EQE-current density characteristics of devices 1, 2, 3, and 4. (c) The experimentally obtained maximum EQEs (filled circles) of the OLEDs are compared with theoretical calculations performed with a consideration of the birefringence (solid lines), only ordinary refractive index (dashed lines), and effective refractive index (dotted lines) of the emitting layer, under the assumption of no electrical loss in the device. The experimental results are in excellent agreement with the theoretical predictions for emission dipoles in the birefringent medium, and are higher than the values predicted for an isotropic medium neglecting extraordinary index.

Download Full Size | PDF

5. Conclusion

We have presented an optical model for emission in a birefringent medium and have validated the theoretical model by applying it to a thin film and OLEDs. We have demonstrated that optical birefringence affects not only far-field radiation characteristics such as emission spectra from thin films and OLEDs, but also the efficiency of OLEDs. The emitting dipole orientation in a birefringent medium has been successfully analyzed from the far-field radiation pattern of a thin film. In addition, the birefringent model has provided a precise analysis of angle-dependent EL spectra and EQEs of OLEDs with the determined emitting dipole orientation.

Appendix

The Fresnel’s reflection and transmission coefficients for TM and TE polarized light traveling from layer a to b are expressed in terms of the wave vector components and the refractive index of layers a and b. If the layer a has an anisotropic refractive index tensor $\tilde{\tilde{n}}$

\tilde{\tilde{n}} = (\begin{matrix} n_{x} & 0 & 0 \\ 0 & n_{x} & 0 \\ 0 & 0 & n_{z} \end{matrix}),

the Fresnel’s reflection and transmission coefficients for TM and TE polarized light are given by

r_{a b}^{TM} = \frac{n_{x} n_{z} l_{b}^{TM} - n_{b}^{2} l_{a}}{n_{x} n_{z} l_{b}^{TM} + n_{b}^{2} l_{a}},

r_{a b}^{TE} = \frac{l_{a} - l_{b}^{TE}}{l_{a} + l_{b}^{TE}},

t_{a b}^{TM} = \frac{2 n_{x} n_{b} l_{a}}{n_{x} n_{b} l_{b}^{TM} + n_{b}^{2} l_{a}},

t_{a b}^{TE} = \frac{2 l_{a}}{l_{a} + l_{b}^{TE}},

where

l_{a} = {(1 - u^{2})}^{1 / 2},

l_{b}^{T M} = {(n_{b}^{2} / n_{z}^{2} - u^{2})}^{1 / 2},

and

l_{b}^{T E} = {(n_{b}^{2} / n_{x}^{2} - u^{2})}^{1 / 2} .

The reflectance and transmittance of the light traveling from layer a to b are given by

R_{a b} = {| r_{a b} |}^{2},

T_{a b}^{TM} = {| t_{a b}^{TM} |}^{2} \frac{n_{z} l_{b}^{TM}}{n_{x} l_{a}},

T_{a b}^{TE} = {| t_{a b}^{TE} |}^{2} \frac{l_{b}^{TE}}{l_{a}} .

Acknowledgments

This work was supported by the Mid-career Researcher Program through an NRF (National Research Foundation) grant funded by the MSIP (Ministry of Science, ICT and Future Planning) (2014R1A2A1A01002030).

References and links

1. R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978). [CrossRef]

2. W. L. Barnes, “Fluorescence near interfaces: The role of photonic mode density,” J. Mod. Opt. 45(4), 661–699 (1998). [CrossRef]

3. K. A. Neyts, “Simulation of light emission from thin-film microcavities,” J. Opt. Soc. Am. A 15(4), 962–971 (1998). [CrossRef]

4. J. A. E. Wasey and W. L. Barnes, “Efficiency of spontaneous emission from planar microcavities,” J. Mod. Opt. 47(4), 725–741 (2000). [CrossRef]

5. J. A. E. Wasey, A. Safnov, I. D. W. Samuel, and W. L. Barnes, “Effects of dipole orientation and birefringence on the optical emission from thin films,” Opt. Commun. 183(2), 109–121 (2000). [CrossRef]

6. J. A. E. Wasey, A. Safnov, I. D. W. Samuel, and W. L. Barnes, “Efficiency of radiative emission from thin films of a light-emitting conjugated polymer,” Phys. Rev. B 64(20), 205201 (2001). [CrossRef]

7. M. Furno, R. Meerheim, S. Hofmann, B. Lüssem, and K. Leo, “Efficiency and rate of spontaneous emission in organic electroluminescent devices,” Phys. Rev. B 85(11), 115205 (2012). [CrossRef]

8. W. Bulovic, V. B. Khalfin, G. Gu, P. E. Burrows, D. Garbuzov, and S. Forrest, “Weak microcavity effects in organic light-emitting devices,” Phys. Rev. B 58(7), 3730–3740 (1998). [CrossRef]

9. C.-L. Lin, T.-Y. Cho, C.-H. Chang, and C.-C. Wu, “Enhancing light outcoupling of organic light-emitting devices by locating emitters around the second antinode of the reflective metal electrode,” Appl. Phys. Lett. 88(8), 081114 (2006). [CrossRef]

10. C.-L. Lin, H.-C. Chang, K.-C. Tien, and C.-C. Wu, “Influences of resonant wavelengths on performances of microcavity organic light emitting devices,” Appl. Phys. Lett. 90(7), 071111 (2007). [CrossRef]

11. J.-B. Kim, J.-H. Lee, C.-K. Moon, and J.-J. Kim, “Highly efficient inverted top emitting organic light emitting diodes using a transparent top electrode with color stability on viewing angle,” Appl. Phys. Lett. 104(7), 073301 (2014). [CrossRef]

12. M.-H. Lu and J. C. Sturm, “Optimization of external coupling and light emission in organic light-emitting devices: modeling and experiment,” J. Appl. Phys. 91(2), 595 (2002). [CrossRef]

13. L. H. Smith, J. A. E. Wasey, I. D. W. Samuel, and W. L. Barnes, “Light out-coupling efficiencies of organic light-emitting diode structures and the effect of photoluminescence quantum yield,” Adv. Funct. Mater. 15(11), 1839–1844 (2005). [CrossRef]

14. S. Nowy, B. C. Krummacher, J. Frischeisen, N. A. Reinke, and W. Brütting, “Light extraction and optical loss mechanisms in organic light-emitting diodes: Influence of the emitter quantum efficiency,” J. Appl. Phys. 104(12), 123109 (2008). [CrossRef]

15. R. Meerheim, M. Furno, S. Hofmann, B. Lüssem, and K. Leo, “Quantification of energy loss mechanisms in organic light-emitting diodes,” Appl. Phys. Lett. 97(25), 253305 (2010). [CrossRef]

16. S.-Y. Kim and J.-J. Kim, “Outcoupling efficiency of organic light emitting diodes and the effect of ITO thickness,” Org. Electron. 11(6), 1010–1015 (2010). [CrossRef]

17. J.-H. Lee, S. Lee, J.-B. Kim, J. Jang, and J.-J. Kim, “A high performance transparent inverted organic light emitting diode with 1,4,5,8,9,11-hexaazatriphenylenehexacarbonitrile as an organic buffer layer,” J. Mater. Chem. 22(30), 15262–15266 (2012). [CrossRef]

18. S.-Y. Kim, W.-I. Jeong, C. Mayr, Y.-S. Park, K.-H. Kim, J.-H. Lee, C.-K. Moon, W. Brütting, and J.-J. Kim, “Organic light-emitting diodes with 30% external quantum efficiency based on a horizontally oriented emitter,” Adv. Funct. Mater. 23(31), 3896–3900 (2013). [CrossRef]

19. J.-B. Kim, J.-H. Lee, C.-K. Moon, S.-Y. Kim, and J.-J. Kim, “Highly enhanced light extraction from surface plasmonic loss minimized organic light-emitting diodes,” Adv. Mater. 25(26), 3571–3577 (2013). [CrossRef] [PubMed]

20. K.-H. Kim, C.-K. Moon, J.-H. Lee, S.-Y. Kim, and J.-J. Kim, “Highly efficient organic light-emitting diodes with phosphorescent emitters having high quantum yield and horizontal orientation of transition dipole moments,” Adv. Mater. 26(23), 3844–3847 (2014). [CrossRef] [PubMed]

21. H. Shin, S. Lee, K.-H. Kim, C.-K. Moon, S.-J. Yoo, J.-H. Lee, and J.-J. Kim, “Blue phosphorescent organic light-emitting diodes using an exciplex forming co-host with the external quantum efficiency of theoretical limit,” Adv. Mater. 26(27), 4730–4734 (2014). [CrossRef] [PubMed]

22. J. W. Sun, J.-H. Lee, C.-K. Moon, K.-H. Kim, H. Shin, and J.-J. Kim, “A fluorescent organic light-emitting diode with 30% external quantum efficiency,” Adv. Mater. 26(32), 5684–5688 (2014). [CrossRef] [PubMed]

23. J. Frischeisen, D. Yokoyama, C. Adachi, and W. Brütting, “Determination of molecular dipole orientation in doped fluorescent organic thin films by photoluminescence measurements,” Appl. Phys. Lett. 96(7), 073302 (2010). [CrossRef]

24. M. Flämmich, M. C. Gather, N. Danz, D. Michaelis, A. H. Bräuer, K. Meerholz, and A. Tünnermann, “Orientation of emissive dipoles in OLEDs: Quantitative in situ analysis,” Org. Electron. 11(6), 1039–1046 (2010). [CrossRef]

25. T. D. Schmidt, D. S. Setz, M. Flämmich, J. Frischeisen, D. Michaelis, B. C. Krummacher, N. Danz, and W. Brütting, “Evidence for non-isotropic emitter orientation in a red phosphorescent organic light emitting diode and its implications for determining the emitter’s radiative quantum efficiency,” Appl. Phys. Lett. 99(16), 163302 (2011). [CrossRef]

26. M. Flämmich, J. Frischeisen, D. S. Setz, D. Michaelis, B. C. Krummacher, T. D. Schmidt, W. Brütting, and N. Danz, “Oriented phosphorescent emitters boost OLED efficiency,” Org. Electron. 12(10), 1663–1668 (2011). [CrossRef]

27. P. Liehm, C. Murawski, M. Furno, B. Lüssem, K. Leo, and M. C. Gather, “Comparing the emissive dipole orientation of two similar phosphorescent green emitter molecules in highly efficient organic light-emitting diodes,” Appl. Phys. Lett. 101(25), 253304 (2012). [CrossRef]

28. L. Penninck, F. Steinbacher, R. Krause, and K. Neyts, “Determining emissive dipole orientation in organic light emitting devices by decay time measurement,” Org. Electron. 13(12), 3079–3084 (2012). [CrossRef]

29. H.-W. Lin, C.-L. Lin, H.-H. Chang, Y.-T. Lin, C.-C. Wu, Y.-M. Chen, R.-T. Chen, Y.-Y. Chien, and K.-T. Wong, “Anisotropic optical properties and molecular orientation in vacuum-deposited ter(9,9-diarylfluorene)s thin films using spectroscopic ellipsometry,” J. Appl. Phys. 95(3), 881 (2004). [CrossRef]

30. D. Yokoyama, A. Sakaguchi, M. Suzuki, and C. Adachi, “Horizontal molecular orientation in vacuum-deposited organic amorphous films of hole and electron transport materials,” Appl. Phys. Lett. 93(17), 173302 (2008). [CrossRef]

31. D. Yokoyama, “Molecular orientation in small-molecule organic light-emitting diodes,” J. Mater. Chem. 21(48), 19187 (2011). [CrossRef]

32. D. Yokoyama, K. Nakayama, T. Otani, and J. Kido, “Wide-range refractive index control of organic semiconductor films toward advanced optical design of organic optoelectronic devices,” Adv. Mater. 24(47), 6368–6373 (2012). [CrossRef] [PubMed]

33. L. Penninck, P. De Visschere, J. Beeckman, and K. Neyts, “Dipole radiation within one-dimensional anisotropic microcavities: a simulation method,” Opt. Express 19(19), 18558–18576 (2011). [CrossRef] [PubMed]

34. E. M. Purcell, “Spontaneous emission probabilities at radio frequency,” Phys. Rev. 69, 681 (1946).

35. S. Lamansky, P. Djurovich, D. Murphy, F. Abdel-Razzaq, H.-E. Lee, C. Adachi, P. E. Burrows, S. R. Forrest, and M. E. Thompson, “Highly phosphorescent bis-cyclometalated iridium complexes: synthesis, photophysical characterization, and use in organic light emitting diodes,” J. Am. Chem. Soc. 123(18), 4304–4312 (2001). [CrossRef] [PubMed]

36. Y.-S. Park, S. Lee, K.-H. Kim, S.-Y. Kim, J.-H. Lee, and J.-J. Kim, “Exciplex-forming co-host for organic light-emitting diodes with ultimate efficiency,” Adv. Funct. Mater. 23(39), 4914–4920 (2013). [CrossRef]

37. J.-H. Lee, S. Lee, S.-J. Yoo, K.-H. Kim, and J.-J. Kim, “Langevin and trap-assisted recombination in phosphorescent organic light emitting diodes,” Adv. Funct. Mater. 24(29), 4681–4688 (2014). [CrossRef]

38. S. Lee, K.-H. Kim, D. Limbach, Y.-S. Park, and J.-J. Kim, “Low roll-off and high efficiency orange organic light emitting diodes with controlled co-doping of green and red phosphorescent dopants in an exciplex forming co-host,” Adv. Funct. Mater. 23(33), 4105–4110 (2013). [CrossRef]

39. H. Sasabe, D. Tanaka, D. Yokoyama, T. Chiba, Y.-J. Pu, K. Nakayama, M. Yokoyama, and J. Kido, “Influence of substituted pyridine rings on physical properties and electron mobilities of 2-methylpyrimidine skeleton-based electron gransporters,” Adv. Funct. Mater. 21(2), 336–342 (2011). [CrossRef]

Luminescence from oriented emitting dipoles in a birefringent medium

Abstract

1. Introduction

2. Theoretical background

2.1. Luminescence from an oriented emitting dipole embedded in a birefringent medium

2.2. Efficiency of an organic EL device with a birefringent emitting layer

2.3. Far-field radiation

3. Experimental

4. Results and discussion

4.1. Optical birefringence and the dipole orientation

4.2. Emission spectra of OLEDs

4.3. Efficiency of OLEDs

5. Conclusion

Appendix

Acknowledgments

References and links

Cited By

Figures (6)

Equations (36)

Optics Express