Open Access
Add to BibSonomyAbstract
Thin microporous films were formed by dropcasting a toluene solution containing various ratios of polystyrene:polyethylene glycol blends on a glass substrate, with OLEDs on the ITO that coated the opposite side of that substrate. We demonstrate for the first time that such easily-fabricated films with surface and bulk micropores in the index-matching polystyrene can serve as random microlens-like arrays to improve forward OLED light extraction by up to ~60%. A theoretical interpretation of the angular emission profile of the device, considering the geometrical change at the substrate/air interface and the scattering by the pores within the films, was established in excellent agreement with the experiments. The use of such blended thin films provides an economical method, independent of the OLED fabrication technique, for improving the outcoupling efficiency.
©2011 Optical Society of America
1. Introduction
Extensive research has been conducted on OLEDs for their potential applications in flat panel displays, solid-state lighting and integrated (bio)chemical sensing [1–4]. Although efficient and long-lived OLEDs have been realized via utilizing advanced materials and device architectures, a significant limiting issue is their relatively low forward outcoupling efficiency (ηout) [5–19]. Earlier studies have shown that ηout of conventional OLEDs is limited to ~20% due to waveguiding within the organic layers/ITO and the glass substrates, which is caused by total internal reflection at the ITO/glass and glass/air interfaces, respectively [5]. To achieve better light extraction, various methods have been utilized, which can be classified into three major categories: (i) Modification of the emitting species, e.g., increasing the population of horizontally oriented emitting dipoles [6]; (ii) Modification of the ITO/substrate structure or interface, by e.g., utilizing low index grids [5,7], corrugated or nanoporous anode structures [8–10], and high index substrates [11]; (iii) Modification of the substrate/air interface, by e.g., using truncated luminaires [12], ZnS nanocolumns [13], macrolenses [14], and microlenses (μLs) [15–21].
The modification of the substrate/air interface has drawn great interest due to the variety of methods and the fact that it does not interfere with device fabrication. In particular, various methods have been established to construct μLs using, for instance, imprint lithography via-different routes [15–19,22,23] and self-assembled materials [20,21]. However, multi-step substrate transfer and lithography and curing processes in the above-mentioned methods remain a challenge for mass production on large areas. Thus, an economical method with complete independence from the OLED fabrication method is highly desirable.
It should be noted that not only convex-shaped μLs [15–19], but also concave-shaped ones [22,23] can lead to better light extraction as long as they reduce the total internal reflection at the glass/air interface. To our knowledge, this paper demonstrates for the first time index-matching films with micropores, formed by polymer phase separation in blended layers during the drying process, which can be used as “random microlens arrays (μLAs)” to enhance ηout.
Due to intrinsic differences in miscibility of many macromolecular constituents of blends, polymer solutes will typically separate during the drying process of films fabricated by solvent-casting [24]. This de-mixing process of a multicomponent blend often results in a phase separated morphology that may be beneficial for many applications. For example, microporous structures derived from this method have been widely adopted for photonic crystals [25], membrane filters [26], and drug delivery [27]. Earlier research has demonstrated such structures using materials with a refractive index n similar to glass, such as polystyrene (PS) (n~1.55-1.59) [28–30]. In this paper, we show that the micro-porosity formed in films prepared from blends of PS and polyethylene glycol (PEG) can enhance ηout by up to ~60%. Such a simple technique is very promising as it is economical and the fabrication of the film is an independent process, i.e., it can be done before or following device fabrication and encapsulation. Moreover, by controlling the total concentration of the solution, the dropcast volume, and the ratio of the mixed polymers one can easily control the thickness, size and filling factor of the film [28–30]. This advantage will enable future systematic and detailed investigation of the effect of the geometrical properties of the “random μLAs” on extracting light.
2. Experimental procedure
For OLED fabrication, the ITO was patterned and etched to form anode stripes. It was then thoroughly cleaned with surfactant, acetone and isopropanol and treated in a UV/ozone oven. The OLED was fabricated by thermal evaporation of the organic layers, LiF, and Al in a vacuum chamber (background pressure ~10−6 Torr) located in an Ar-filled glovebox. The rate of the organic layers’ evaporation was ~1Å/s. The pixel size was 3×3 mm2.
The PS (molecular weight Mw ~280,000) and PEG (Mws ~200, ~400, ~1,000, and ~8,000) were purchased from Sigma-Aldrich. The microporous films were formed by dropcasting 50-200 μL of toluene solution containing PS:PEG mixtures with different weight ratios (the total concentrations were 60 or 90 mg/mL) on the backside of the OLED ITO/glass substrate. The films were dried under ambient conditions in a fume hood following the dropcasting. Experiments with films washed with methanol, which results in removal of surface PEG, were also conducted, however, this approach did not present an advantage and the enhancement was generally lower than with un-washed films. The best results, presented here, were obtained by using PEG of Mw ~1000 and 200 μL of 60 mg/mL solution to form the film. The SEM images of the films’ surface morphology and side view were taken with a JEOL model 5910v microscope. In order to prevent charging, a 15 nm Ag layer was deposited on top of the films.
To determine n of the PS:PEG film we measured the optical transmission of a film prepared by spin-coating a toluene solution containing 54:6 mg/mL PS:PEG at 3000 rpm on a 200 μm thick sapphire substrate (n ~1.77@ ~500 nm). This procedure was used due to the rough surfaces of the dropcast films and their n value that is very close to that of the glass. The interference fringes yielded n~1.58-1.61 in the range 1.4-2.3 μm.
For measurement of the overall emission spectra, the OLEDs were placed at the window of an integrating sphere with all sides, except for the front emitting surface, covered with black tape. The electroluminescence (EL) spectra were then recorded by an Ocean Optics Chem 2000 spectrometer. For the angular emission profile measurements, the pixels were placed in the center of a goniometer, sufficiently far (~64 cm) from the detector, so that the emitting area could be approximated as a point source. The light intensity was detected through a long dark pipe by a Hamamatsu R6060-02 photomultiplier. The photocurrent was monitored by a Keithley 2400 source-meter.
3. Results and discussion
Mixtures of PS:PEG in toluene with different weight ratios ranging from 1:0 to 1:1 were dropcast onto the backside of the OLED ITO/glass substrate. Figure 1(a) shows schematically the process of micropore formation on the surface and in the bulk of the film, which is similar to earlier descripttions [28,29]. Note that the schematic does not show the non-uniformity in the pore density. The high molecular-weight PS with matching n ~1.55-1.59 has a lower solubility in toluene than the low molecular weight PEG (n ~1.46). Hence, during the drying process of the solution, PS first precipitates while small PEG-rich droplets are formed on the surface and in the bulk. During the evaporation of the solvent, the PEG droplets shrink, leaving behind surface and bulk PEG-coated PS micropores, as shown in Fig. 1(a). The resulting films with ≥ 50% high-Mw PS are mechanically stable due to the entanglement of the long polymer chains. The PEG at the surface can be washed away by polar solvents without dissolution of the PS. However, because of the smaller n of PEG in comparison to PS, the PEG coating of the micropores do not negatively affect the outcoupling function of the film.
Fig. 1 (a) Schematic demonstration of the microporous structure formation of the PS:PEG mixed film during the drying process following dropcasting; note that the actual pore density is not uniform. (b) SEM images of the surface and cross section of a film with 48:12 mg/mL PS:PEG. (c) The principle of the OLED outcoupling enhancement by the PS:PEG film.
As an example, the microporous structure formed by dropcasting 48:12 mg/mL PS:PEG in toluene is shown in the SEM images of Fig. 1(b). The size of the micropores ranges from ~1.5 μm to ~5 μm in diameter. They are densely packed at the surface and randomly distributed at a lower density within the bulk of the film. As shown next, the pores enhance light extraction through the glass substrate of an OLED.
In a regular OLED, only those light rays with an incident angle smaller than the critical angle (Ray 1, Fig. 1(c)) can escape at the substrate/air interface. However, with the index-matching PS film and the surface micropores, the light rays that were previously waveguided within the substrate (Ray 2) are now extracted due to the change of the substrate/air interface geometry. Additionally, some of the light rays may also be scattered by the pores within the bulk of the PS:PEG film (Ray 3), and hence change to directions that are forward-extracted.
Figure 2(a) shows the actual outcoupling enhancement by a 54:6 mg/mL PS:PEG film, for a conventional tris(8-hydroxyquinolinato) Al (Alq3)-based OLED with the structure ITO/5 nm MoO3/56 nm N,N'-bis(naphthalen-1-yl)-N,N'-bis(phenyl)benzidine (α-NPB)/64 nm Alq3/1 nm LiF/100 nm Al. The emission from an OLED with the same structure, but without the PS:PEG film is also shown. Both devices were lit under the same conditions. As seen, the light emitted from the pixel with the PS:PEG film is brighter and diffuse in comparison to the emission from the pixel without the microporous film. Additionally, the rim of the device (an epoxy sealant used for device encapsulation, sealing the gap between the OLED’s glass substrate and an additional glass cover) without the PS:PEG film is much brighter, indicating that a largefraction of the light is waveguided to the edge of the glass substrate. In contrast, the dark rim of the device with the PS:PEG film (left image) clearly demonstrates the enhanced forward light extraction by the PS:PEG film.
Fig. 2 Effect of 200 μL PS:PEG 54:6 mg/mL in toluene that were dropcast on the backside of the OLED’s ITO/glass substrate. (a) Images of two pixels with and without the PS:PEG film, each biased at 6 V. The dropcast area is 1 × 1 in.2 (b) Overall emission spectra of the devices with (red open circles) and without (black solid squares) the PS:PEG film. The current density in each device was J = 55 mA/cm2 (c) Angular emission intensity profile of the device with (red open circles) and without (black solid squares) the PS:PEG film. In each device J = 5.5 mA/cm2 The solid lines are the Lambertian emission profiles. The dashed purple line is the simulated emission profile. We note that the enhancement was essentially independent of J and consequently, of course, the brightness L, in agreement with other studies [16].
In order to quantify the outcoupling enhancement of the PS:PEG film, we measured the overall emission spectra of the devices using an integrating sphere, as shown in Fig. 2(b). The peak emission of the device with the PS:PEG film was slightly blue shifted to 516 nm from the 525 nm peak of the conventional device. This is attributed to the scattering effect of the micropores. The integration of the spectra yields an enhancement of ~61%. Furthermore, Fig. 2(c) shows the angular emission-intensity profile of the devices. As clearly seen, the emission profile of the device with the PS:PEG film was enhanced at all angles, but it deviates from a Lambertian profile, with increased intensity at higher angles. Assuming the emission profile has azimuthal symmetry, the integrated enhancement is ~57%, which is consistent with the spectral measurement. Figure 2(c) also shows the simulation results (discussed next) of the PS:PEG effect, which are in good agreement with the experimental results. We note that the enhancement was essentially independent of the current density J and consequently, of course, brightness L, in agreement with other studies [16].
The physical interpretation of the enhancement of the light extraction and the consequential angular emission profile lies in the geometrical change of the substrate/air interface morphology and the scattering effect of the embedded voids. Let I 0(θ 0) and I 1(θ 1) be the angular energy distribution in the emitting layer and in the PS:PEG film, respectively. In the absence of pores, due to energy conservation, I 0(θ 0)sinθ 0 dθ 0 = I 1(θ 1)sinθ 1 dθ 1, and with Snell’s law norgsinθ 0 = nPS:PEGsinθ 1 we get [31],
Similarly, the external luminous energy distribution is given by
where θ 2 is the viewing angle in the far field. Assuming isotropic emission, I 0(θ 0) = 1/(2π), Eq. (2) yieldswhich approximately resembles a Lambertian profile when norg >> nair.In the presence of micropores in the PS:PEG film, we assume the incoming light undergoes two processes: (i) scattering by the voids embedded within the film to uniformly distributed random directions, and (ii) refraction by the micropores at the top surface of PS:PEG, where part of light originally trapped in PS:PEG is extracted. The above assumptions may not be accurate for a real device, yet they can provide a qualitative analysis. Under these assumptions, the modified angular distribution in PS:PEG is given by
where C 1 and C 2 are constant, and θc = sin−1(nair/nPS:PEG) is the critical angle at the PS:PEG/air interface. If we don’t consider process (ii), the uniformly random scattering in process (i) gives C 1 = C 2. However, the refraction by surface micropores in process (ii) changes the incident angle for each ray, and helps part of the PS:PEG guided light to outcouple (changing θ 1 > θc to θ 1 < θc), which results in C 2 < C 1. In an ideal case where all PS:PEG guided light is extracted via surface micropores and there is no absorption in the device, C 2 = 0 and C 1 ideal = 0.359 can be calculated from energy conservation.After determining the expression for I 1’(θ 1), the external luminous energy distribution in the presence of micropores can be obtained from
Comparing Eqs. (3) and (5), we see that I 2’(θ 2) deviates from a Lambertian profile more than I 2(θ 2), since nair/nPS:PEG > nair/norg. Assuming nPS:PEG ≈1.58 we obtain excellent agreement between the calculated emission profile and the experimental profile (Fig. 2(c)). We note that the n of the matrix is not as crucial as the scattering factor C 1 in the model for determining the enhancement and emission profile. The use of nPEG = 1.48 (not shown) resulted in a nearly identical emission profile.
In Fig. 3 , we further demonstrate the ability to control the size and fill factor of the micropores. PS:PEG films with the same total concentration (60 mg/mL) but different weight ratios (ranging from 1:0 to 1:1 PS:PEG ratio) were fabricated and imaged using SEM. Although there is macroscopic domain formation caused by heat convection [29], Fig. 3 can adequately represent the microscopic structures formed in these films. Starting from the undoped PS film, as the concentration of PEG increases, the fill factor of the surface micropores increases until they fully cover the surface of the film (PS:PEG 4:1 ratio). This behavior is in accordance with the earlier interpretation of the micropores’ formation process (Fig. 1a). The device with the pure PS film barely shows any outcoupling enhancement, which confirms the role of the microstructure in enhancing light extraction. The increasing density of pores increases the scattering probability and at an optimal pore size and distribution, it maximizes the forward light extraction at the substrate/air interface. Indeed, as clearly shown in Table 1 , the enhancement factor relative to conventional OLEDs increases from 3% for undoped to ~60% for 10 wt.% PEG-doped PS. As the concentration of PEG further increases, the closely packed PEG-rich droplets formed during the drying process coalesce to form larger concave structures (Fig. 3). These structures, with a relatively smaller curvature but increased size, reduce the outcoupling enhancement.
Fig. 3 The surface SEM images of the PS:PEG films with different weight ratios, but constant total concentration of 60 mg/mL. The scale bar in the insets is 10 μm.
Table 1. Comparison of Outcoupling Enhancement Factor by PS:PEG Films with Different Weight Ratios Total Concentration: 60 mg/mL)a
Table 1 also summarizes the values of C 1 (see Eq. (5)) calculated from the experimental enhancement factor. These values are much smaller than the calculated ideal value of 0.359 which indicates only partial extraction of the trapped light by the PS:PEG film. The increaseof C 1 from a device with undoped PS to a device with a 9:1 PS:PEG film is due to the change of the interface geometry and the increased density of scattering centers within the film. The decrease of C 1 when the PEG concentration is further increased is attributed to the reduced light extraction caused by the smaller curvature of the larger PEG-coated micropores on the surface (Fig. 3).
To demonstrate the potential generality of this method, 48:12 mg/mL of PS: poly(vinyl pyrrolidone) (PVP) in chloroform were also applied on the backside of the substrate of an OLED, as a similar microporous structure was demonstrated earlier for this blend [30]. Such structures also resulted in ηout enhancement, but only by ~32%.
Finally, we note that we recently showed that if the conventional ITO anode is replaced by several layers of high conductivity poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate) (PEDOT:PSS), the OLED power efficiency can increase by up to 80% [32]. This modification of the anode can be combined with the technique shown in this paper to generate an even higher device efficiency.
4. Conclusions
We successfully fabricated controlled microporous structures by dropcasting toluene solutions of various PS:PEG ratios on the blank glass side opposite to the glass/ITO OLED structures. The microstructures of these films enhance the forward light extraction by scattering the light that is otherwise trapped in the OLED’s glass substrate. An enhancement of ~60% was achieved by optimizing the size and filling factor of the micropores formed in the PS:PEG film; the optimal PS:PEG weight ratio was found to be 9:1 – 4:1. The agreement between a theoretical analysis of the non-Lambertian angular intensity profile and the experiments is excellent, clearly showing that this enhancement originates from scattering by both surface and bulk micropores. Additionally, the non-Lambertian distribution provides increased emission intensity at larger angles. Hence, this approach provides an extremely simple and economical means for outcoupling enhancement in OLEDs and potential applications in OLED-based luminaires.
Acknowledgments
This work was supported by the US Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract No. DE-AC 02-07CH11358.
References and Links
1. S. R. Forrest, “The path to ubiquitous and low-cost organic electronic appliances on plastic,” Nature 428(6986), 911–918 (2004). [CrossRef] [PubMed]
2. Organic Electronics: Materials, Processing, Devices and Applications, F. So, ed. (CRC, 2010)
3. Organic Electronics in Sensors and Biotechnology, R. Shinar and J. Shinar, eds., (McGraw-Hill, 2009)
4. J. Shinar and R. Shinar, “Organic light-emitting devices (OLEDs) and OLED-based chemical and biological sensors: an overview,” J. Phys. D Appl. Phys. 41(13), 133001 (2008). [CrossRef]
5. Y. Sun and S. R. Forrest, “Enhanced light out-coupling of organic light-emitting devices using embedded low-index grids,” Nat. Photonics 2(8), 483–487 (2008). [CrossRef]
6. J. Frischeisen, D. Yokoyama, A. Endo, C. Adachi, and W. Brütting, “Increased light outcoupling efficiency in dye-doped small molecule organic light-emitting diodes with horizontally oriented emitters,” Org. Electron. 12(5), 809–817 (2011). [CrossRef]
7. M. Slootsky and S. R. Forrest, “Enhancing waveguided light extraction in organic LEDs using an ultra-low-index grid,” Opt. Lett. 35(7), 1052–1054 (2010). [CrossRef] [PubMed]
8. W. H. Koo, S. M. Jeong, F. Araoka, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, “Light extraction from organic light-emitting diodes enhanced by spontaneously formed buckles,” Nat. Photonics 4(4), 222–226 (2010). [CrossRef]
9. A. O. Altun, S. Jeon, J. Shim, J.-H. Jeong, D.-G. Choi, K.-D. Kim, J.-H. Choi, S.-W. Lee, E.-S. Lee, H.-D. Park, J. R. Youn, J.-J. Kim, Y.-H. Lee, and J.-W. Kang, “Corrugated organic light emitting diodes for enhanced light extraction,” Org. Electron. 11(5), 711–716 (2010). [CrossRef]
10. H. J. Peng, Y. L. Ho, X. J. Yu, and H. S. Kwok, “Enhanced coupling of light from organic light emitting diodes using nanoporous films,” J. Appl. Phys. 96(3), 1649–1654 (2004). [CrossRef]
11. S. Mladenovski, K. Neyts, D. Pavicic, A. Werner, and C. Rothe, “Exceptionally efficient organic light emitting devices using high refractive index substrates,” Opt. Express 17(9), 7562–7570 (2009). [CrossRef] [PubMed]
12. B. W. D’Andrade and J. J. Brown, “Organic light-emitting device luminaire for illumination applications,” Appl. Phys. Lett. 88(19), 192908 (2006). [CrossRef]
13. L. Lu, F. Zhang, Z. Xu, S. Zhao, Z. Zhuo, D. Song, J. Li, and Y. Wang, “Characteristics of ZnS nanocolumn arrays and their effect on the light outcoupling of OLEDs,” Physica B 405(17), 3728–3731 (2010). [CrossRef]
14. S. Reineke, F. Lindner, G. Schwartz, N. Seidler, K. Walzer, B. Lüssem, and K. Leo, “White organic light-emitting diodes with fluorescent tube efficiency,” Nature 459(7244), 234–238 (2009). [CrossRef] [PubMed]
15. J.-M. Park, Z. Gan, W. Y. Leung, R. Liu, Z. Ye, K. Constant, J. Shinar, R. Shinar, and K.-M. Ho, “Soft holographic interference lithography microlens for enhanced organic light emitting diode light extraction,” Opt. Express 19(S4Suppl 4), A786–A792 (2011). [CrossRef] [PubMed]
16. Y. Sun and S. R. Forrest, “Organic light emitting devices with enhanced outcoupling via microlenses fabricated by imprint lithography,” J. Appl. Phys. 100(7), 073106 (2006). [CrossRef]
17. J. Lim, S. S. Oh, D. Y. Kim, S. H. Cho, I. T. Kim, S. H. Han, H. Takezoe, E. H. Choi, G. S. Cho, Y. H. Seo, S. O. Kang, and B. Park, “Enhanced out-coupling factor of microcavity organic light-emitting devices with irregular microlens array,” Opt. Express 14(14), 6564–6571 (2006). [CrossRef] [PubMed]
18. H. Y. Lin, Y. H. Ho, J. H. Lee, K. Y. Chen, J. H. Fang, S. C. Hsu, M. K. Wei, H. Y. Lin, J. H. Tsai, and T. C. Wu, “Patterned microlens array for efficiency improvement of small-pixelated organic light-emitting devices,” Opt. Express 16(15), 11044–11051 (2008). [CrossRef] [PubMed]
19. S.-H. Eom, E. Wrzesniewski, and J. Xue, “Close-packed hemispherical microlens arrays for light extraction enhancement in organic light-emitting devices,” Org. Electron. 12(3), 472–476 (2011). [CrossRef]
20. W.-K. Huang, W.-S. Wang, H.-C. Kan, and F.-C. Chen, “Enhanced light out-coupling efficiency of organic light-emitting diodes with self-organized microlens arrays,” Jpn. J. Appl. Phys. 45(41), L1100–L1102 (2006). [CrossRef]
21. J. A. Zimberlin, P. Wadsworth, and A. J. Crosby, “Living microlens arrays,” Cell Motil. Cytoskeleton 65(9), 762–767 (2008). [CrossRef] [PubMed]
22. P. Ruffieux, T. Scharf, I. Philipoussis, H. P. Herzig, R. Voelkel, and K. J. Weible, “Two step process for the fabrication of diffraction limited concave microlens arrays,” Opt. Express 16(24), 19541–19549 (2008). [CrossRef] [PubMed]
23. J. S. Kim, D. S. Kim, J. J. Kang, J. D. Kim, and C. J. Hwang, “Replication and comparison of concave and convex microlens arrays of light guide plate for liquid crystal display in injection molding,” Polym. Eng. Sci. 50(8), 1696–1704 (2010). [CrossRef]
24. S. Walheim, M. Böltau, J. Mlynek, G. Krausch, and U. Steiner, “Structure formation via polymer demixing in spin-cast films,” Macromolecules 30(17), 4995–5003 (1997). [CrossRef]
25. J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281(5378), 802–804 (1998). [CrossRef] [PubMed]
26. M. Ulbricht, “Advanced functional polymer membranes,” Polymer (Guildf.) 47(7), 2217–2262 (2006). [CrossRef]
27. G. K. Stylios, P. V. Giannoudis, and T. Wan, “Applications of nanotechnologies in medical practice,” Injury 36(4Suppl 4), S6–S13 (2005). [CrossRef] [PubMed]
28. J.-K. Kim, K. Taki, and M. Ohshima, “Preparation of a unique microporous structure via two step phase separation in the course of drying a ternary polymer solution,” Langmuir 23(24), 12397–12405 (2007). [CrossRef] [PubMed]
29. J.-K. Kim, K. Taki, S. Nagamine, and M. Ohshima, “Periodic porous stripe patterning in a polymer blend film induced by phase separation during spin-casting,” Langmuir 24(16), 8898–8903 (2008). [CrossRef] [PubMed]
30. K.-H. Wu, S.-Y. Lu, and H.-L. Chen, “Formation of parallel strips in thin films of polystyrene/poly(vinyl pyrrolidone) blends via spin coating on unpatterned substrates,” Langmuir 22(19), 8029–8035 (2006). [CrossRef] [PubMed]
31. C. F. Madigan, M.-H. Lu, and J. C. Sturm, “Improvement of output coupling efficiency of organic light-emitting diodes by backside substrate modification,” Appl. Phys. Lett. 76(13), 1650–1652 (2000). [CrossRef]
32. M. Cai, T. Xiao, R. Liu, Y. Chen, R. Shinar, and J. Shinar, “Indium tin oxide-free tris(8-hydroxyquinoline) Al OLEDs with 80% enhanced power efficiency,” Appl. Phys. Lett. (in press).
