The quality factor of microcavity organic lasers, designed for operation under electric pumping, has been numerically investigated. The microcavity structure consists of an organic light emitting diode set in between multilayer dielectric mirrors centered for an emission at 620 nm. In order to optimize the quality factor, different parameters have been studied: the impact of high and low index materials used for the multilayer mirrors, the role of a spacer inserted in between the mirrors to obtain an extended cavity, and the effect of an absorbing electrode made of metallic or transparent conductive oxide layer. The results of our different optimizations have shown a quality factor (Q) as high as 15 000.
© 2011 OSA
Since the discovery of conductive properties of doped polyacetylene in 1977 crowned in 2000 by the Nobel Prize in Chemistry won by Heeger, the field of organic optoelectronics has become a major research area. Remarkably, Organic Light Emitting Diodes (OLEDs) have already reached the industrial mass-production level with lifetime over thousands of hours, and colors spanning the entire visible spectrum. Other devices such as photodetectors, photovoltaic cells, and field-effect transistors have been developed and pushed towards commercialization. However, although the first optically-pumped organic solid-state semiconductor laser has been demonstrated in 1996 , the electrically pumped organic laser diode has never been demonstrated to the best of our knowledge. Indeed, in 2000, Schön et al  have won an unfortunate fame by claiming the “first organic injection laser”, until it was revealed later that the results had been falsified.
An abundant literature has been published during the past decade aiming to point out the real bottlenecks for electrically-driven laser operation [3, 4]. In order to achieve net gain (gain > losses) under reasonable current density (far below current-induced destruction of the device <<1kA/cm2), one has to face important limiting losses. Among them are losses occurring in the metal electrodes [5, 6], thermal effects and a series of non radiative losses, i.e. exciton-exciton annihilation (EE-A) and polaronic absorption. Polarons have wide absorption bands that overlap the emission spectrum, resulting in a strong reabsorption and carrier-exciton quenching. Moreover, the low carrier mobility of organic films, makes high current densities (typically >1A/cm2)  difficult to achieve under constant current, though higher pump current density are available under pulsed excitation [8, 9].
Because of all these reasons, we believe that scientific strategies favoring lasing effect at low current density should be considered to overcome the challenge of the organic laser diode.
Several types of optically pumping microcavity structures [10–16] with organic gain medium have been demonstrated with laser threshold levels as low as 200 W/cm2 . A lower limit of the current density is required to reach the threshold, which can be estimated by using the threshold for optical pumping. In a carrier-balanced diode structure, where most of the electron and hole recombinations occur, the current density needed to achieve the same excitation which is required for lasing in the photopumped structures, is approximately :19].
Therefore, to develop an effective electrically pumped organic laser, one part of the strategy consists in lowering the optical losses by optimizing laser structures [20, 21]. Hence, more effort must be dedicated to the optical aspects.
In this paper, we focus on the optical laser cavity aspects. More specifically, we will identify the requirements on the laser cavity performance in order to achieve lasing with the state of the art conventional OLED organic material as a medium gain.
In this context we first concentrate on the identification of the quality factor needed to achieve the threshold reduction down to the level of the state of the art OLED current density. After that, we will focus on the optimal design of laser cavity that exhibits a quality factor as high as the latter one.
By analyzing several results already published by many authors and dealing with organic laser under optical pumping, we provide an empirical approach that leads to an estimation of the quality factor needed to realize an electrically pumping organic laser at a current density comparable to that supported by OLEDs.
The main optically pumped organic laser results reported in the literature are plotted in Fig. 1 with log-log scales. For each of these experiments, the quality factor is plotted on the X axis, while the Y axis represents the laser threshold. Although all these experiments were done under optical pumping, the laser threshold is expressed in terms of the equivalent current density. This corresponds to the current density necessary to achieve the same photon density (see Eq. (1). The actual threshold would be much higher because of losses associated with contacts and charge carriers absorption.
Keeping in mind that a log-log scale should be carefully considered, the extrapolation of the presented data leads to a rough estimation of the quality factor needed to realize an electrically pumping laser at a current density comparable to that supported by OLEDs.
For the case of a pump current compatible with the DC mode operation of an OLED (typically in the range 10-1000 mA/cm2), a quality factor higher than 40000 is required. In the pulsed operation regime, an OLED can stand a current density up to 1 KA/cm2 which could be considered if Q > 10000.
Therefore, we will focus our investigation on the optimal design of a microcavity compatible with the electrical pumping with a quality factor as high as the one mentioned above.
In this particular context, the purpose of this work is to design an electrically pumped organic semiconductor laser based on a top emitting OLED inserted in a high quality factor planar microcavity similar to vertical cavity surface emitting lasers inorganic counterparts  (inorganic VCSELs).
Numerical simulations based on the matrix transfer method  have been used to calculate and optimize the microcavity optical properties (reflectance, absorptance and transmittance) in such a way to obtain high quality factor. The key parameters are: the material complex refractive indices, the nature of used materials, the number of mirror stacked layers and the thicknesses of mirrors and OLED layers. The microcavities are considered as passive systems which receive light from an external broad-band spectrum source and filtering it. The transmittance exhibits a transmission peak, i.e. the so called resonance, located within a stop-band i.e. the bandwidth of the cavity mirrors. The quality factor is deduced from the resonance wavelength λ and from its linewidth δλ.
It is worth noting that the calculated quality factor of the passive filtering system does not take into account the non-linear process that leads to the competition of the laser modes. In other terms, this method might underestimate the quality factor calculated. However, the obtained value should be considered as a necessary condition to have the lasing effect (a starting point).
This paper is organized as follow:
- - In section II, the investigated microcavity is described and the structure parameters are identified. Then, the different elements of the microcavity are analyzed numerically as a function of the structure parameters to optimize the quality factor;
- - In section III, extended microcavities that could induce a substantial increase of the quality factor are investigated;
- - In section IV and V, we present our discussion and conclusion of the study.
2. Half wavelength multilayer microcavity
The electrically pumped organic microcavity considered in this work is shown in Fig. 2 . It consists of a bottom dielectric multilayer mirror, a top emitting OLED and a top dielectric multilayer mirror.
The mirrors are made of two alternate low and high refractive index dielectric materials deposited into 2N + 1 layers with a quarter wavelength optical thickness for each layer. The bottom mirror is different from the top one since the top layer is made of a transparent and conductive oxide (TCO) material. The OLED heterostructure consists of a transparent and conductive anode, a 4,4′,4″-tris-(3-methylphenylphenylamino) triphenylamine (m-MTDATA) as hole injection layer (HIL), N,N'-diphenyl-N,N'-bis(1-naphthyl)-1,1'-biphenyl-4,4-diami (NPD) as a hole transport layer, 4-(dicyanomethylene)-2-methyl-6-(p-dimethylaminostyryl)-4H-pyran (DCM) with an emission peak at 620 nm doped into the Tris(8-hydroxyquinolinato) aluminum (Alq3) host material is used as the emissive layer (EL), Bathocupuroine (BCP) as a hole injection layer, Alq3 as an electron transport layer and finally the aluminum cathode.
To avoid the organic layers deterioration due to the top mirror deposition, the latter should be fabricated separately before OLED realization (the active medium). Once the deposition of the OLED onto the bottom mirror is performed, the top mirror is placed closer to the rest of the device using a micro-positioning to control its position and therefore the cavity length.
2.1. The construction parameters of the mirrors
The construction parameters are imposed to the fact that each layer of the microcavity structure has to fulfill both the OLED and the laser requirements, in the point of view of the electrical and optical requirements. More specifically, and regarding the optical requirements, the construction parameters include the choice of the couple of high and low refractive index materials, whose index contrast impacts the wavelength range of the mirror.
The reflectance of two types of mirrors presenting the same number of layers but made from two different well known couple of materials (respectively TiO2/SiO2 and Ta2O5/SiO2 [31–33]), are firstly compared. Figures 3 and 4 show the reflectance and the absorption for M1 (TiO2,/SiO2), M2 (Ta2O5/SiO2) based mirrors made of 21 layers (S21 HL10 H2), respectively. They were designed and optimized to have a maximum reflectivity at the central emission wavelength of the targeted OLED structure, i.e. an emission at λ0 = 620 nm which is the peak emission of the Alq3:DCM guest-host system .
Note that we performed several simulations based on data obtained from different references. However, in order to take into account experimental issues, we have used refractive indices that we measured by ellipsometry. Our samples were prepared by IBAD (Ion Beam Assisted Deposition) method using an e-beam and ion-beam sources.
Considering the mirror alone, the couple TiO2/SiO2 exhibits the largest stop-band as indicated on Fig. 3 (160 nm for TiO2/SiO2 and 130 nm for Ta2O5/SiO2) due to the high ration of nH and nL. Both stop-band bandwidths are broader than the emission spectrum of the active organic material, which is favourable to lower threshold value.
According to the inset of Fig. 3, one can notice that the TaO5/SiO2 couple presents a higher reflectance in the vicinity of the DCM/Alq3 emission peak. Moreover, compared to the TiO2/SiO2 (Fig. 4), the Ta2O5/SiO2 presents the lowest absorptance over the whole visible spectrum. The latter results strongly suggest that higher quality factors could be obtained using TaO5/SiO2 rather than TiO2/SiO2.
The overlap between the electro-luminescence spectrum of the DCM and the reflectance of the mirror is an important parameter for the laser threshold reduction. In order to optimize the mirror reflectance spectra, we varied the central wavelength λ0 by adjusting the optical thicknesses of the dielectric layers in order to maximize the convolution product of the reflectance spectrum and the DCM electroluminescence spectrum. The convolution products exhibit a maximum at λ0 = 605 nm, and λ0 = 625 for mirror M1 and M2 respectively.
In order to investigate the impact of the number N of bilayers of the mirrors, we now consider complete microcavities made of Ta2O5/SiO2. Hence, rather than reflectance and transmittance spectrum, the quality factor calculated from the FWHM of the resonant peak, is then considered. Figure 5 displays the transmittance spectrum of different microcavities made with different number N of stacked layers. Inset shows the quality factor and the FWHM of the transmittance as a function of the number of bilayers. The quality factor saturates at 1600 when N exceeds a value of Ns = 9. This indicates that the increase of reflectivity with higher N is compensated by a higher absorption.
2.2. The electrodes optimization
The microcavity optimization also involves the optimization of the electrodes used in OLEDs to ensure a good charge injection and a low absorption. As shown in Fig. 2, the TCO layer is used as a high refractive index material for the bottom mirror as well as the anode of the OLED. Therefore, it is expected to exhibit a high work function, which is compatible with the HOMO (Highest Occupied Molecular Orbital) level of the hole injection layer (HIL), a good conductivity and a low absorption. ITO exhibit a low resistivity, a high transmission in the visible range (~98%) and a high work function (4.6 eV) . However, an ITO coating layer thicker than 120 nm is necessary to provide an adequate conductivity . Such a thickness is larger than the 77 nm required for a quarter wavelength optically thick layer. In order to bypass this issue, to achieve a low resistivity and a low absorption, we replaced the ITO layer by an ITO/Ag/ITO tri-layer anode. This material yielded the desired electrical properties without a significant effect on its optical properties . The thickness of each ITO layer can be as low as 30 nm, and that of the silver (Ag) must be lower than 14 nm to avoid a significant decrease in transmission.
Multilayers mirrors ended with ITO(12nm)/Ag(6nm)/ITO(12nm) transparent and conductive anode offer interesting optical and electrical properties as shown in Fig. 6 . Indeed, such multilayers mirrors exhibit a reflectance up to 99.96% and an absorptance as low as 0.03% at the desired resonance wavelength (620 nm).
Regarding to the metallic cathode layer, two problems arise from the use of this layer in the microcavity: an increase of the absorptance which leads a double reflection occurring from both the metallic layer and the top dielectric mirror. Therefore the top-emitting OLED and the laser requirements emphasize the use of an ultra thin layer performing both the low absorptance and the semi transparent properties.
In order to limit the absorption at the metal cathode, we suggest the utilization of the same approach applied to the anode. The cathode aluminum layer is replaced by a multilayer of Al (3 nm) / Ag (5 nm) followed by a Ta2O5 layer. The aluminum layer used to ensure a low work function compatible with the LUMO level (Lowest Unoccupied Molecular Ortbital) of the underlying organic layer, and thus a better electron injection. The silver layer is necessary to offer a better conductivity and finally the Ta2O5 layer, with higher refractive index, used to increase the transparency of the cathode. This tri-layer structure has been used recently to make transparent organic solar cells .
2.3. Organic layers thicknesses
Organic layer thicknesses are adjusted in order to provide a balance between the electron and the hole transport, such that a total OLED optical thickness of a half wavelength with a standing waves anti-anode located at the EL is obtained (Fig. 7 ). The resulting optimized OLED heterostructure is structured as follow: glass/bottom mirror (ITO/Ag/ITO included)/ m-MTDATA (48 nm)/NPD (40 nm)/Alq3:DCM (40 nm)/BCP (25 nm)/Alq3 (25 nm)/Al(3 nm)/Ag(5 nm)/Top mirror
Although the micro-cavity has been designed to have an emission at 620 nm, it can be noticed from Fig. 5, that the emission peak is slightly shifted toward low frequencies. This discrepancy is due to the optical field penetration in the dielectric mirrors that generates a phase shift proportional to the penetration depth. Thus, the effective length is given by :
Therefore the microcavity length is equal to the thickness of organic layers increased by the optical penetration term:
Consequently, to overcome the effect of phase shift we varied the total optical thickness of the OLED by a fraction of λ around a multiple of λ/2. For a thickness of 297 nm the emission is centered at 620 nm. Moreover, this adjustment leads to a quality factor enhancement up to 3000 (FWHM = 0.3 nm) due to the fact that the dielectric mirrors have been designed to have a broad stop band centred at 620 nm.
Considering all the above mentioned optimizations, the quality factor hardly exceeds 3000. Therefore, the optimized microcavity does not match yet the optical requirements identified in Fig. 1.
3. Extended cavity
To further improve the quality factor, one approach consists of using an extended microcavity by incorporating a spacer with a thickness of a multiple of λ/2. As can be seen from the Eq. (4)  (which relates the Q factor of the cavity to the mode linewidth Δλ, where the cavity optical length is L and the reflectivities of dielectric mirrors are Rtop and Rbot), the quality factor is proportional to the microcavity length. Therefore, we add a matching layer (or spacer) between the cathode of the OLED and the top mirror (Fig. 8 ); this layer can be a dielectric layer or more simply air or nitrogen if the top mirror is mounted on micromanipulators. The thickness of the space must be an odd multiple of λ/2 to avoid any shift in the wavelength resonance of the system.
As shown by the transmittance spectra in Fig. 9 the linewidth is reduced significantly when the cavity is extended as a consequence of the Fabry-Perot effect.
For spacing values up to 5λ/2 (Fig. 9(b)), the transmittance exhibits only one transmission peak within the spectral range of the mirrors, whereas for 11λ/2 (Fig. 9(c)) and higher spacing values the reduction of the microcavity free spectral range leads to the existence of several transmission peaks within the spectral range of the mirror stop-band. The first case is more favourable to single mode emission; however a less restricting design rule has been applied. Indeed, up to 19λ/2 (Fig. 9(d)) the satellite transmission peaks are located outside of the electroluminescence spectrum of Alq3:DCM, or a ratio of at least 100 (20 dB) is supported between the amplitude of the central peak at 620 nm and those of side peak transmission at 605 nm and 633 nm. In this configuration with extended cavity up to 19λ/2, the quality factor Q reaches ~1.5 x 104 (Fig. 9(a) inset).
The transfer-matrix-based simulations demonstrate that an OLED based on the Alq3:DCM2 guest-host system embedded in a microcavity extended to 19λ/2 with optimized the Ta2O5/SiO2 multilayer mirrors and an ITO(12 nm)/Ag(6 nm)/ITO(12 nm) transparent and conductive anode is able to exhibits narrow linewidth (0.05 nm FWHM) transmission peaks and a quality factor up to Q = 1.5x104.
This structure match the optical requirements for pulsed electrical excitation of organic laser as provided from Fig. 1 (Q>10 000).
In this work we have used the approach based on the matrix transfer method that only takes into account the filtering properties of the microcavities. The simulations were performed with an incidence angle normal to the microcavity and external light source. Nevertheless, the organic emitting dipoles are located inside the cavity and they potentially emit light in any direction. Therefore, the current work neglects the leaky modes and the guided modes. For half wavelength microcavity and its multiples, the cavity length is still short and this assumption remains valid because only few direction of emission is allowed . A trade-off on the length of the microcavity will give both a large value of the quality factors and a small mode volume which limits leaky and guided modes. Further developments will need to take into account the modification of the spontaneous emission provided by the small mode volume. Indeed, the modification of the spontaneous emission plays a complementary role in the current strategy by reducing the laser threshold. More specifically, in thin microcavities, the coupling of spontaneous emission into the lasing mode significantly increases the quality factor. Such microcavities can substantially modify the spatial distribution of spontaneous emission of the material placed within the cavity. In the photon mode picture, this can be considered as a reduction of the total number of allowed modes for spontaneous emission. If the number of photon modes is reduced, then more of the spontaneous emission is channeled into the lasing mode which effectively increases the emission cross section and ultimately reduces the pumping rate required to achieve the lasing threshold.
In this work, we report the investigation of the optimal design of a high quality optical cavity toward the development of an organic laser diode.
As a first approach, the current density limit required to reach threshold is estimated by analyzing the already published results on optically pumped organic laser.
Our results emphasizes that for a pump current compatible with the DC mode operation of an OLED (typically the range of 10-1000 mA/cm2), a quality factor higher than 40000 is required. In the pulsed operation regime, an OLED can stand a current density up to 1 KA/cm2 which could be considered if Q > 10000.
Optimization of various parameters in dielectric mirrors, microcavity length, and extended microcavity demonstrated that it would be possible to obtain a quality factor as high as 1.5x104. According to that, a considerable reduction of the laser threshold is expected, to reach a threshold level compatible with OLED operation.
Experimental Works are under progress to demonstrate the feasibility of such a device.
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