Mechanism Study and the Role of Coupled Surface Plasmon Polaritons in Optical Out-Coupling Enhanced Top-Emitting OLEDs with a Dielectric Capped Ag Cathode

Classical optical transfer matrix method and micro-cavity theory is applied to compute optical out-coupling of Top-Emitting OLEDs (TEOLEDs). Optical paths of various functional organic films and electrode structures are included in the calculations. Fluorescent Alq 3 green TEOLEDs were fabricated and tested based on theoretical calculations. For TEOLEDs with Ag cathodes plus NPB coatings, we experimentally observed significant enhancements in optical out-couplings compared to that of with bare Ag cathode. We also found that thin-film optics theory is insufficient to explain the observed enhancement. To explain the experimental results, we incorporated near-field radiation of electric dipole and its interactions with Ag cathode film, i.e. , surface plasmon polaritons (SPPs) theory, coupled SPPs in a dielectric/metal/dielectric (D/M/D) structure. Therefore, we demonstrate that optical out-coupling enhancement has three contributing factors in a TEOLED: an increased transmittance of cathode Ag, a varied internal micro-cavity gain, and the dominant improved SPP coupling on both sides of the Ag film cathode.


Introduction
In the field of OLED display application, most manufacturing companies have made a transition to TEOLED technology, due to the nearly 100% aperture rate of TFT (Thin Film Transistor) driven AMOLED (Active Matrix OLED). TEOLEDs [1][2][3][4][5][6] can be fabricated on any solid substrates like silicon wafers or glasses. A TEOLED is constructed using a semi-transparent top cathode such as ITO or Ag thin film and a reflective bottom metal anode.
ITO is a very good transparent anode material. It may be used as cathode. ITO's work function, however, is fairly high which does not suit electron injection, decreasing the performance of the device. Other problematic issues in using ITO include indium, which is a very scarce and expensive element, the use of sputtering that damages the organic functional layer, and brittleness which cannot be used in flexible devices [7,8]. Hence, it is important to explore alternative cathode. Ag is often used as a replacement of ITO for its relatively high optical transparency and good ductility.
In general, a dielectric with high refractive index is deposited on the surface of the metal cathode to promote the out-coupling efficiency. It has been reported that the light extracting efficiency will be increased if an Ag cathode is coated by index matching materials such as inorganic ZnSe, ZnS, MgF2, SiO2, ITO, ZnO, TiO2, organic Alq3, NPB, BCP and so on [9][10][11][12][13][14][15][16]. The degree of enhancement varies widely with different types of material and thicknesses.
Some researchers did the transmittance measurement for cathode with different thicknesses of a capping layer, and found that, despite the transmittance through the cathode being at the maximum value, the total device light extracting efficiency is far from the optimal value and sometimes just the opposite [12]. Leo, et al showed that this efficiency enhancement was mainly due to low absorption and high reflection, which leaded to a high extraction because of the micro-cavity effect [13]. Another paper argued that the enhancement of the efficiency is closely related to suppression of surface plasmon polaritons (SPPs), but these authors did not elaborate on the working physics [14]. It is therefore very important to identify various contributing factors in optical out-coupling.
In this paper, using a combination of classic optics and SPP theory, we study the various possible contributing factors on enhancing optical out-coupling efficiency in a TEOLED.

Metal induced transmission (MIT)
The metal film is usually used as the transparent cathode in TEOLED and its transparency is the core discussed issue. Many works had been done about the metal cathode's fabrication and properties discussion via experimental measurement. A prominent work is to deposit an inorganic or organic dielectric capping layer on the outgoing surface of the metal cathode and the transmittance was proved to be enhanced efficiently [17,18]. The capping layer is sometimes called as refractive index matching layer and the structure is called as the DMD (dielectric/metal/dielectric) structure. But the deep mechanism which often puzzles the researchers is scarcely done, it is often determined with empirical experimental parameters for the metal selection, transparency mechanism and thickness selection without theoretical calculation in many previous literatures [12,14].
In fact, in the thin film optics and optical system research, the metal film is widely used in the design of optical filter. This is just about the issue of metal induced transmission filter (MITF) [19]. From the key knowledge of this point, that is, the absorption and transmittance of a metal film is not only decided by the metal's refractive index n, extinction coefficient k and thickness d, but also decided by the optical impendence of the adjoining dielectric. As far as the design method of MITF, there is a mature method in thin film optics such as the pattern like this, | /4 films | metal film | /4 films | Here, /4 films refers to anti-reflection films. In this paper, we would not apply this method due to the different case of TEOLED and MITF. The above /4 anti-reflection films in MITF are hardly to realize in TEOLED fabrication, which is corresponding to the electron injection and transmission layer of cathode. On one hand, the refractive index of organic electronic materials are relative fixed and not easy to regulate to meet the optical path demand; on the other hand, complex films fabrication will add the difficulties and cost to the OLED. Relative speaking, the design of capping layer on the outgoing surface of a metal cathode is pretty easy and meaningful, which is only involved in dielectric selection and thickness optimization.
We explain the enhanced transmission principle via optical transfer matrix method in thin film optics theory and verify it through real TEOLD fabrication. This calculation method is related to metal's dielectric function, complex refractive index, transmittance, reflectance, and so on, and will be briefly discussed as follows.
The energy reflectance R, transmittance T, absorption A and reflecting phase shift φ of equivalent interface can be expressed as 10 Where Y=C/B, B, C can be obtained by optical transfer matrix calculations as follows: , ηj, ηk+1 are the optical admittance of incidence dielectric, the j layer and emergence dielectric, respectively. For convenience, we only discuss the normal incidence and emergence because the optical admittance is reduced to the union form of refractive index for the s and p polarization wave. δj=2πNjdj/λ, the effective phase thickness of the j layer of dielectric, and Njdj, the optical thickness.
The refractive index of the metal is obtained by fitting the experimental data from the handbook of solid optical constant of Edward D. Palik's. 15 The relative dielectric function of metal can be described as 16 where, ωp the bulk plasma frequency of a sort of metal, γ0 the damping coefficient of free electrons, f0 the ratio of free electrons in an atom, ωj the intrinsic frequency of bound electrons, γj the damping coefficient, fj the ratio of bound electrons, K the total kinds number of bound electrons. The refractive index is the square root of dielectric constant and it is also a complex number for metals.
We use the MATLAB language software to do the simulations and provide the theoretical basis for the metal type and thickness selection [20,21]. The result is, as a transparent or semi-transparent electrode, Ag thin film is better than Al film.

Micro-cavity effect
The difference between a TEOLED and a normal bottom-emitting OLED is its Fabry-Pérot optical resonator micro-cavity effect arising from the high reflectance of the two metal electrodes. The optical resonator can change the light field distribution inside the device, a photon's life time and an emitter's luminescence efficiency [2]. The cavity diagram is provided in Fig. 1, where T2 is the transmittance of top electrode, A2 the absorbance of cathode, R1 and R2 the reflectance of the two electrodes, I0 and E0 the luminescence intensity and electric field of the dipole radiation, I2 and E2 the emergent light, L1 the optical In equation (1), the numerator represents the wide-angle interference, and the denominator represents the multi-beam interference. Where, G(λ) is called as the gain factor, F(λ) micro-cavity factor, ni/di the refractive index and thickness of the i layer of organic material in the micro-cavity, nj/dj those close to the bottom anode, λ wavelength of the emergent light, φ1(λ)/φ2(λ) inside reflecting phase shift of the two electrodes. From equation (1), when constructive interference occurs, the emergent light reaches to the maximum. It should meet the corresponding conditions: m, m'=0, ±1, ±2…, Here λ is the resonant wavelength. Equation (2) represents a constructive multi-beam interference of the total cavity, which determines the thickness of the micro-cavity.
Equation (3) indicates the wide-angle constructive interference of the radiation dipole in the cavity, which is determined by the position of the dipole from the two electrodes. We use φ1, φ2 to replace the value of equation (2,3) and take m=0 to decide the cavity length parameters of a TEOLED. The change of dielectric thickness of the cavity is selective for the wavelength of the emergent light.
The parameters of light path can be computed via optical film transfer matrix method [22][23][24]. We perform simulations through the use of MATLAB [25]. The simulated anode structure is glass/Al(100nm)/organic, and the dielectric constant of the organic layer is 1.7. The optical reflectance R is 87% at λ=528nm (the peak wavelength of bottom emitting green OLED of Alq3).

Experimental
Based on simulations using equations (2) and (3)  We used 100 nm Al as the reflecting anode to fabricate test OLEDs for its excellent smooth film formation properties on glass, which will not induce short circuit. Due to its good conductivity, hole transportation layer NPB thickness was varied to meet the resonance condition (2) and (3) at various phase shift of cathode Ag thickness. Also, we applied NPB as the capping layer material, for it has relative stable property and easy to evaporation.
We fabricated three sets of devices with Ag cathodes of different thickness (20/40/60 nm). The NPB capping layer thickness varied from 0 to 150 nm with interval of 15 nm.
Electroluminescence measurement includes the luminance, I-V curves, current efficiency, luminous power efficiency, and spectra.

Results
In Fig. 3(a) (c), we can see the Full Width at Half Maximum (FWHM) has a maximum value at capping layer thickness 45 nm.
The peak wavelengths do not vary too much at small thicknesses but blue shift occurs when it exceeds 45 nm, see Fig. 3(b). In 3.01 times. The ratio takes on an increasing tendency although the current efficiency decreases.
In Fig. 5, the measured EQE increases with changing the capping layer thickness and reaches a maximum at 45nm.

Discussion
Next, we discuss the mechanism of enhancing the efficiency with a capping layer. Based on classic cavity theory as given by equation (1), the luminous intensity distribution of the emergent light is decided by two factors. One is the transmittance of the transparent electrode T2, and the other is the micro-cavity factor F(λ). These two factors are contradictory to the emergent light.
Because, based on the basic physics, increased T2 will lead to the decreased R2 of the Ag cathode, decreased R2 will lead to a decreased F(λ), then the total gain factor G(λ) can't be certain to increasing or decreasing. The high-impact factor plays a decisive role.
From the real experiments results, we can see, the current efficiencies, EQEs, FWHMs increase with increasing the capping layer thickness before 45nm, i.e., the G(λ) increases. As we know, the FWHM is an indicator of the strength of micro-cavity effect [2], the greater FWHM, the weaker F(λ), the smaller R2 and the greater T2. Can we determine that T2 is the decisive factor? No.
It is necessary to calculate it more accurately.

Transmittance of Ag film Cathode with a Capping Layer
We first simulate the transmittance of Ag cathode with different NPB capping layer thicknesses as shown in Fig. 6(a). In fact, our measured result is that current efficiency and quantum efficiency all increased compared with bare Ag cathode film, as shown in table 1 and Fig. (4) (5). Especially, the 60 nm silver cathode with 45 nm NPB capping layer nearly triples the current efficiency. There must be other factors to induce this result.
In the above discussed film optical simulations, we only consider the optical interference effect in normal direction. In the situations of large angle incidence, the dipole radiation interacting with metal electrodes will produce the SPPs [33] which greatly impact the EQE of the OLED due to the exciton's near-field radiation characteristics.

SPP (Surface Plasmon Polaritons)
According to classic optical theory, when the incident angle is greater than the critical angle of total reflection, an evanescent wave will appear. When the evanescent wave interacts with the thin metal film surface and match the wave-vector or momentum condition, surface plasmon loss will occur. SPPs are a trapped electromagnetic surface mode at the interface between a metal and a dielectric [34]. They are a combined collective oscillation of electromagnetic field and the surface charges of the metal, which can be activated by transverse magnetic (TM) wave. The electromagnetic field of SPPs at dielectric-metal interface can be obtained from the solution of Maxwell's equations in each medium and the associated boundary conditions, and the dispersion relation is illustrated in Fig. 7 [33]. Where, εm is the dielectric function of the metal, εd that of the adjacent dielectric.
Researchers have demonstrated that, due to the loss property of metals, the amplitude of SPPs decays exponentially with increasing distance into each medium from the interface. They can only propagate along the direction of the interface, so it is a kind of guided wave mode, causing non-radiative loss. In Fig. 7, kSpp>k0, commonly, due to the mismatch of the wave-vector, the far-field light cannot activate the SPPs directly, but we still can add wave-vector Δk to activate it by some special means such as Kretschmann method, Otto method, etc [34], which is based on photon tunneling effect. The periodic structure and roughness on metal surface can excite SPPs directly because of the diffraction effect, and vice versa SPPs can be recovered to light through all these methods by reduced wave-vector -Δk [34].
Another means to activate SPP is the near-field method. The near-field excited SPPs widely exist in the OLEDs, an essential factor which leads to the low quantum efficiency of OLEDs.

Role of SPPs in OLED
In OLEDs, since the near-field radiation field can be expressed as a sum of plane waves and each plane wave has its in-plane wave-vector component kx, it can be coupled into SPPs on a near metal surface directly when the momentum condition is matched.
Power lost to SPPs can account for up to 40% of the total power [35] and it is essential to explore whether some of the power lost to SPP modes can be recovered, thereby improving device efficiency.
A classical model [36][37][38][39], the power dissipated of a dipole is also a function of kx, is called the power dissipation spectrum of wavelength (PDS). From it, we can gain insight into the nature of the modes that are present and the strength of power coupled to them. The out-coupling efficiency is obtained by integrating the power of a certain range compared to the total integrated power.
PDS aims at a specific wavelength and power dissipation map (PDM) focuses on all wavelengths. We use color depth to represent the degree of the energy loss. In fact, the profile of PDM just comprises the dispersion relation with more information.
In Fig. 8(a), we provide a PDS of a BEOLED via numerical  In-plane wave-vector k x /2π (um -1 ) Normalized angular frequency ω/2πc(um -1 ) (b) More in-depth research reveals that, strictly, it is incorrect to refer to the SPP modes as coupling one to another respectively; rather they are in an integration of coupled SPPs on both sides.

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Conflict of Interest
The authors declare no competing interests.