Electrophosphorescent organic light emitting concentrator

Embodiments of the disclosed subject matter provide a device with a base having an opening, and a plurality of organic light emitting devices (OLEDs) disposed on a plurality of substrates and arranged in a light directing structure onto the base, where the opening of the base is a light exit aperture of light output by the plurality of OLEDs.

PARTIES TO A JOINT RESEARCH AGREEMENT

FIELD OF THE INVENTION

The present invention relates to luminaire devices having organic light emitting diodes disposed on substrates and arranged in a light directing structure and other devices, including the same.

BACKGROUND

Phosphorescent organic light emitting diodes (PHOLEDs) have been used commercially in flat panel displays. More recently, PHOLEDs are finding applications in solid-state lighting due to their color tunability and potentially low cost. For use in general lighting, however, PHOLEDs must operate at a higher luminance (i.e., greater than 3,000 nits) than in displays. To obtain this level of brightness, current densities of greater than 1 mA/cm2are required, which can lead to a reduced device lifetime and efficiency. Moreover, to obtain a desirable light distribution profile for uniform surface illumination, additional optical lighting source solutions are required that often increase the cost and complexity of the fixture.

SUMMARY OF THE INVENTION

An embodiment of the disclosed subject matter provides a device including a base having an opening, and a plurality of organic light emitting devices (OLEDs) disposed on a plurality of substrates and arranged in a light directing structure onto the base, where the opening of the base is a light exit aperture of light output by the plurality of OLEDs.

According to another embodiment, a first device comprising a first organic light emitting device is also provided. The first organic light emitting device can include an anode, a cathode, and an organic layer, disposed between the anode and the cathode. The first organic light emitting device can be arranged in a light directing structure, where an opening of a base of the structure is a light exit aperture of light output by the first organic light emitting device. The first device can be a consumer product, an organic light-emitting device, and/or a lighting panel.

DETAILED DESCRIPTION

Embodiments of the disclosed subject matter provide increased directional light concentration from an emissive device such as an organic light-emitting diode (OLED) luminaire, for use in spot lighting and other applications for high intensity illumination.

As disclosed herein, a luminaire device may include a base having an opening, and a plurality of organic light emitting devices (OLEDs) disposed on a plurality of substrates and arranged in a light directing structure onto the base, where the opening of the base is a light exit aperture of light output by the plurality of OLEDs. Each OLED can include a reflective surface that is disposed to direct light output by each OLED towards the light exit aperture, independent of its original emission position within the light directing structure. The reflective surface of opposing sides of the light directing structure may concentrate light emitted into the structure from the OLEDs and directs the light towards the light exit aperture.

The light directing structure may be a polyhedral structure (e.g., discussed below in connection withFIGS. 3(a)-3(d)) or a parabolic structure (e.g., as shown inFIG. 9and discussed below). As used herein, a polyhedral structure refers to a structure having planes, meeting in pairs along the edges which are straight-line segments, and with the edges meeting in vertex points. The polyhedral structure may be, for example, a triangular structure, a tetragonal structure, a pentagonal structure, a hexagonal structure, a heptagonal structure, an octagonal structure, a nonagonal structure, a decagonal structure, a hendecagonal structure, or a dodecagonal structure. As used herein, the parabolic structure may be a three-dimensional structure having symmetrical curves, which are approximately U-shaped. The parabolic structure may be, for example, a simple paraboloid, a circular paraboloid, an elliptic paraboloid, a hyperbolic paraboloid, or a compound paraboloid.

The device disclosed herein may output red, green, blue, and/or white light, and the device may be controlled so as to adjust the color temperature of the outputted light.

In some embodiments, the concentrating luminaire device can include multiple triangular, large-area OLEDs, such as electrophosphorescent light emitting devices (PHOLEDs) deposited onto plastic substrates and assembled into a structure whose open base serves as the light exit aperture, such as four such devices arranged in a pyramid. In such an embodiment, the pyramidal structure may be the light directing structure. The OLED surfaces may be highly reflective. The emission from the devices may be directed toward the aperture independent of its original emission position within the pyramid. The reflectance inherent to the OLED architecture concentrates light emitted into the structure by the opposing pyramid sides, ultimately directing the emission toward the aperture.

A total emissive area of the OLEDs may larger than that of the light exit aperture so as to increase luminance. Since the emissive area may be larger than that of the aperture, the luminance may be increased by approximately a factor of three compared to a conventional device with the same area as the aperture. Light output from the light exit aperture of the device may be in a pattern that provides uniform surface illuminance. The far-field intensity profile of the concentrator may have a “batwing” distribution that meets requirements and/or desired features of general lighting for uniform illumination of planar surfaces. The directionality of the emission from the OLEDs determines the radiation pattern of the concentrator, and also may affect the degree of concentration. An emission profile of the device may be adjustable according to a profile of the OLEDs. A directionality of light emitted from the OLEDs may determine a radiation pattern and the concentration of the light output.

FIGS. 3(a)-3(d)shows a concentrator that includes four OLEDs according to an embodiment of the disclosed subject matter. Four OLEDs may be grown on triangular substrates, such as indium tin oxide (ITO)-coated polyethylene terephthalate (PET) substrates, and may be attached to metal plates having the same shape and size as the devices. Each section, combining the device and the plate as shown inFIG. 3(c), may be assembled into a pyramidal structure (e.g., a structure having an apex angle of 15.5°, or the like), and fixed in place. The emissive (or substrate) side of the OLED may face inwards so that the light emission from one segment is reflected by adjacent devices, and is directed towards the exit aperture, as shown inFIG. 3(d).

The OLEDs of the device, such as that shown inFIGS. 3(a)-3(d)may be flexible OLEDs, fluorescent OLEDs, or phosphorescent OLEDs. The OLEDs may emit red light, green light, blue light, and/or white light. A controller may control a color temperature of the emitted light from the plurality of OLEDs. In some embodiments, a surface of the plurality of OLEDs is reflective to visible light. OLEDs used with embodiments disclosed herein may be top-emitting and/or bottom-emitting when the individual OLED structure is considered. That is, OLEDs used in embodiments disclosed herein may emit through the substrate on which they are fabricated, or through the opposite surface of the OLED. Thus, each individual OLED may be arranged such that the substrate is on the interior surface of the OLED relative to the concentrator, or on the outermost surface of the OLED relative to the interior of the concentrator, depending upon whether each OLED is top- or bottom-emitting.

In some embodiments, the concentrator can include a microlens array or a grating that is embedded into each of the substrates, so that the light output from a light exit aperture has a directed illumination profile. The light exit aperture of the device including the concentrator may be adjustable, where a larger aperture produces a higher luminous flux at a lower exit angle than that with a smaller aperture, since light emitted by the OLEDs at a vertex of the light directing structure has fewer reflections with the larger aperture.

One or more of the substrates of the concentrator, such as the concentrator shown inFIGS. 3(a)-3(d), may be disposed with respect to one another so as to form apex angles of 15.5°-55.5°. The apex angles decrease the exit angle of light output from the light exit aperture. The apex angles may provide a concentration factor of 3.0 to 1.4 and an extraction efficiency of 40%-70% of the light output by the OLEDs. The apex angles at which the substrates are disposed with respect to one another may be adjustable so as to enable emission from any location from the OLEDs to be directed toward the light exit aperture.

A concentration factor (CF) may be defined as the ratio of the luminous flux of the luminaire measured at the exit aperture to that of the conventional planar device as a reference with the same area as the aperture:

Here, Lside,iand Lrefthe luminances from the single panel concentrator device placed within the luminaire, and the reference (e.g., areas Asideand Aref), respectively, at current density, J. Further,

Leff=∑i=14⁢⁢Lside,i·(Aside/Aref)
may be defined as the effective luminance (Leff) of the concentrator emitted at the aperture compared with the reference.

FIG. 4(a)shows the effective luminance (Leff) versus current density (J) characteristics of a reference device, a single panel device with the other panels turned off, and from four panels forming an example concentrator. The current density (J) versus voltage (V) characteristics (as shown in the inset portion ofFIG. 4(a)) indicate that the panel device operates at a higher voltage than the reference, which is primarily a result of increased lateral resistance of ITO (indium tin oxide) with a device area. Although the single panel device has a lower Leffthan the reference device, likely due to losses from reflections inside the concentrator, the integrated Lefffrom the concentrator substantially exceeds that from the reference device. As a result, the CF for the device is in the range of 2.5 to 3.1, at current densities from 0.01 to 1 mA/cm2, as shown inFIG. 4(b). Given that the area ratio is 7.4, the loss in the concentrator is approximately 60%, yet this is partially compensated by the higher brightness at the aperture.

To demonstrate the effect of geometry on CF, equation (1) may be rewritten as:
CF(J)=4·G(θapex)·ηext(J,G(θapex))  (2)
where G(θapex)=¼·csc(θapex/2) is the geometric area ratio between the single concentrator panel and the aperture as a function of apex angle, θapex. Also, ηext(J,G(θappex)) is the geometric extraction efficiency measured by comparing the luminance of the single panel concentrator device versus the reference at J.

The geometric extraction efficiency (ηext(J,G(θapex)) may be determined by:

ηext⁡(J,G⁡(θapex))=∫S⁢I⁡(s)·R⁡(θapex)Nds·⁢ds/∫S⁢I⁡(s)·⁢ds,(3)
where G is the geometric area ratio, J is the current density, ηextis the extraction efficiency, θapexis an apex angle, I(s) is the initial luminance emitted by an area segment, ds, of the single panel device with a total area of S (that is, S is the total area of the single device including the concentrator), R(θapex) is the reflectance of the OLED, and Ndsis the number of reflections for a ray from ds to reach the aperture as discussed below.

FIGS. 5(a)-5(b)show G, ηextand CF at J=1.0 mA/cm−2as functions of four different θapexand a fixed aperture area of 1.0 cm2. In particular,FIG. 5(a)shows a geometric area ratio (G) and an extraction efficiency (ηext), andFIG. 5(b)shows the CF versus the apex angle, θapex, at J=1.0 mA/cm2for concentrators with θapexof 15.5, 25.5, 35.5 and 55.5°. The CF may increase monotonically as θapexdecreases due to the increased number of reflections compared to concentrators with large θapex. At the same time, ηextmay be decreased due to increased propagation losses. As θapexis decreased from 55.5° to 15.5°, ηextmay decrease from 68.1±1.5% to 38.9±1.3% due to the increased number of reflections. That is, utilization of the effective area that contributes to the output luminance may decrease with θapex. Nonetheless, CF increases from 1.46±0.03 to 2.92±0.10 due to the increase of G. Table 1 gives values for CF and ηext, at J=1.0 mA cm−2for these devices.

In Table 1, the concentration CF is calculated based on the effective luminance from a single panel, and assuming that all four panels have identical luminous characteristics. Errors for CF and ηextmay be standard deviations from at least three single panel concentrator devices.

FIG. 6(a)shows the normalized luminous intensity of the concentrator with respect to the reference as a function of viewing angle, φ, measured in the direction parallel to the side (denoted as horizontal) and along the diagonal of the aperture. While the reference device is approximately a Lambertian source, the concentrator according to embodiments of the disclosed subject matter may exhibit a batwing intensity profile where the intensity at viewing angles from φ=40° to 50° relative to the aperture normal is larger than along the central axis of the concentrator. The resultant illuminance distribution is given by:

I⁡(ϕ)=L⁡(ϕ)h2·cos3⁢ϕ(4)
at a viewing angle φ and distance, h. For arbitrary h, the concentrator may produce a nearly uniform surface illumination over Δφ=±40°, while the reference device may have peak illuminance at φ=0° and decreases dramatically with φ, as shown inFIG. 6(b). When installed overhead, the profile of the concentrator, unlike the reference device, may reduce and/or avoid strong veiling reflections from the illuminated surface that results from intense downward emission at low φ.

A ray-tracing algorithm may be used to model the angular distribution profile of the luminaire, and to determine Nds in Eq. (3). The simulation generates the extraction efficiency, ηext, of the rays emitted at distance, x, from the vertex of the concentrator, the intensity-weighted average number of reflections,N, required to reach the aperture, and their intensity-weighted-average exit angles,αexit, relative to the concentrator central axis. Each property for two different OLED reflectances, ROLED, is provided in Table 2. Details of the algorithm and assumptions used are described below in connection withFIG. 12.

TABLE 2Simulated extraction efficiency, average intensity-weighted reflections and exit angles(ηext.x,Nreflection,αexit, respectively) of the exiting rays for two values of OLED reflectance,ROLED, versus the relative position of emission, x, from the apex. Concentratorheight is assumed to be unity, and the device reflectance invariant to incident angle.Position xROLED(%)00.10.2. . .0.80.91.0ηext.x6614.2%15.7%17.7%. . .43.0%53.8%69.3%7118.7%20.3%22.5%. . .47.6%57.4%71.1%Nreflection663.633.443.20. . .1.330.840.31713.923.713.44. . .1.450.940.37αexit661.2°0.6°0.5°. . .29.4°39.1°51.2°711.1°0.6°0.5°. . .29.7°39.3°51.0°

Table 2 shows simulated (e.g., where concentrator height is assumed to be unity, and the device reflectance invariant to incident angle) extraction efficiency (ηext), average intensity-weighted reflections (N), and exit angles (αexit) of the exiting rays for two values of OLED reflectance, ROLED, versus the relative position of emission, x, from the apex.

Emission originating near the apex may be strongly attenuated due to the high Nds, and hence may not contribute significantly to the exit luminance. In addition,αexitof such rays are low, which is responsible for the relatively weak intensity along the central axis (e.g., as shown inFIGS. 6(a)-6(b)). On the other hand, rays emitted near the aperture escape with fewer reflections, and āexitis distributed across a range from only 30° to 50°, corresponding to the high intensity peak near 40° observed in the profile (e.g., as shown in the shaded area ofFIG. 6(b)). A primary factor that determinesαexit, and the resultant batwing distribution, is the Lambertian emission distribution of the panels. The reflectance of the device may determine ηext(see Table 2). The desired emission profile of the concentrator may be achieved by tailoring the profiles of its component OLEDs. For example, if the OLEDs in the concentrator have relatively intense emission at high angles by using, for example, microlens arrays or a grating embedded in the substrate, the emission can be extracted with a lowerNat smallerαexit, which results in directed or spot illumination profiles.

The geometry of the concentrator also affects its emission profile. A concentrator with a larger aperture (or θapex) may produce a higher luminous flux at lowαexitthan that with a smaller aperture, since the rays emitted near the vertex experience fewer reflections with an enlarged escape cone, as shown inFIG. 13and disclosed below. Additionally, if the side panel angle is large, its emission near the aperture exits at smallerαexit, while increasing the total ηextas shown in Table 3 below. This configuration has a correspondingly decreased geometric area ratio, leading to a reduced CF (seeFIGS. 5(a)-5(b)).

Both ηextand CF may be enhanced, independent of geometry, by increasing the OLED reflectance, ROLED. The OLED may form a weak microcavity, where ROLEDis determined by the reflection, transmission and interference occurring inside the organic thin films and the metal cathode.FIGS. 7(a)-7(b)show ROLEDas a function of incident angle, θincand wavelength, λ, calculated for OLEDs having an electron transport layer with an Al cathode (denoted as Device A) or with an Ag cathode (Device B), as shown inFIGS. 8(a)-8(b), and disclosed below. Since the OLED emission may be unpolarized, its total reflectance is obtained from the average of the transverse electric and magnetic mode reflectances at wavelengths from λ=460 to 600 nm, corresponding to 90% of the spectral emission from the green OLED, and at incident angles from θinc=0° to 80°. At θinc>80°, most emission for both devices is reflected by the PET substrate. The reflectance of Device A may vary from 64.2±1.3% to 76.3±1.2%, compared with that of the Device B, which may vary from 69.2±0.6% to 79.9±2.2%. The errors may be due to the 10% variation of the total thickness of the organic layers. Since Ag has a smaller extinction coefficient than Al, Device B may be correspondingly less absorbing and may have a higher RPHOLED, as shown inFIGS. 7(a)-7(b), leading to an increased ηextfrom the concentrator (Table 2). The high ROLEDcontours inFIGS. 7(a)-7(b)may be spectrally shifted to the OLED emission maximum by tuning the thickness of the electron transport layer (ETL) and/or the hole transport layer (HTL).

The outcoupling efficiency of the OLEDs, which may contribute to the total luminous flux of the concentrator, is also dependent on the properties of the microcavity formed between the emission zone and the cathode as shown inFIGS. 8(a)-8(b).

FIGS. 8(a)-8(b)shows calculated outcoupling efficiency of the OLEDs at wavelength (λ) of 522 nm at an emission angle θ=0°, normal to the layers. The thickness are varied for the (a) ETL, (b) HTL. The device structure used in the calculation is: ITO (100 nm)/15 wt % MoO3doped into CBP (tHTLnm)/CBP (10 nm)/Ir(ppy)2(acac) doped into CBP (15 nm)/TPBi (10 nm)/2 wt % Li doped into Bphen (tETLnm)/LiQ (1.5 nm)/Ag (150 nm). The refractive indices of the organic layers are measured by variable angle spectroscopic ellipsometer. Each fraction coupled to air modes (outcoupling), glass modes, waveguide modes (ITO and organics) and the cathode is calculated from the relative energy transferred from the dipoles. The dipole may be formed at the interface between the emissive layer (EML) and hole blocking layer (HBL).

As demonstrated by this example, ROLEDmay be modified by varying the HTL thickness without significantly changing the outcoupling efficiency of the device. The fraction of incident light that is not reflected may be primarily absorbed by the ITO and the cathode. For example, Device A may have the following characteristics: ITO 100 nm/15 wt % MoO3doped into CBP 60 nm/CBP 10 nm/8 wt % doped in Ir(ppy)2(acac) into CBP 15 nm/TPBi 65 nm/LiF 1.5 nm/Al 150 nm. Device B may have the following characteristics: ITO 100 nm/15 wt % MoO3doped into CBP 60 nm/CBP 10 nm/8 wt % doped into Ir(ppy)2(acac) in CBP 15 nm/TPBi 10 nm/2 wt % doped Li in Bphen 55 nm/8-hydroxyquinolinato lithium (LiQ) 1.5 nm/Ag 150 nm. At normal incidence at λ=522 nm where the OLED emission peaks, ITO and Al in Device A absorbs 20.0±1.2% and 10.1±0.8% of the light, while the ITO and Ag absorption in Device B are 19.7±1.7% and 5.1±0.2%, respectively, considering 10% variation in thickness of organic layers.

In the embodiments of the disclosed subject matter disclosed above, concentrated OLED emission may be from a pyramid-shaped luminaire device and/or other polyhedral luminaire device. By increasing the area of a side of the concentrator, a high concentration factor may be achieved at the expense of the geometric extraction efficiency due to increased reflections from the surfaces of the devices comprising the edge of the luminaire. To achieve efficient extraction and high CF, increasing the cathode reflectivity is an effective means to increase the device external luminance efficiency. The angular intensity profile of the luminaire follows a batwing distribution, making it suitable for uniform downward illumination of surfaces. While a pyramid shape is shown and described herein as an example concentrator structure, different concentration factors and emission profiles can be achieved employing other geometries, such as a triangular structure, a tetragonal structure, a pentagonal structure, a hexagonal structure, a heptagonal structure, an octagonal structure, a nonagonal structure, a decagonal structure, a hendecagonal structure, and a dodecagonal structure. The structure may be a parabolic structure, such as a simple paraboloid, a circular paraboloid, an elliptic paraboloid, a hyperbolic paraboloid, and a compound paraboloid.

For example, a parabolic or compound parabolic concentrator can potentially achieve a CF as high as 7, and may provide aesthetic advantages over the pyramidal-shaped design.FIG. 9(a)shows a parabolic concentrator (reflector) whose geometric areal ratio, G, is equal to 2.3.FIG. 9(b)its simulated angular distribution profile as a function of viewing angle in the arbitrary unit.

FIG. 10shows a Concentration Factor (CF) versus geometric areal ratio, G, of the parabolic concentrator (reflector) for two different PHOLED reflectance, RPHOLED, 80% and 95% invariant to the incident angle. At G=13.5, and RPHOLED=80% and 95%, the parabolic concentrator attains CF=4.0 and 6.8, respectively.

That is, concentrating the emission as disclosed herein can be advantageously realized in many practical, high intensity OLED-based luminaire configurations.

As disclosed above, a luminaire device may include a base having an opening, and a plurality of organic light emitting devices (OLEDs) disposed on a plurality of substrates and arranged in a light directing structure onto the base, where the opening of the base is a light exit aperture of light output by the plurality of OLEDs. Each OLED can include a reflective surface that is disposed to direct light output by each OLED towards the light exit aperture, independent of its original emission position within the light directing structure. The reflective surface of opposing sides of the light directing structure may concentrate light emitted into the structure from the OLEDs and directs the light towards the light exit aperture.

EXPERIMENTAL

Four PHOLEDs grown on triangular, ITO-coated substrates were attached to metal plates having the same shape and size as the devices, as shown inFIG. 3(a). Each section, combining the device and the plate is then assembled into a pyramidal structure with an apex angle of 15.5°, and fixed in place. The emissive (or substrate) side of the PHOLED faces inwards so that the light emission from one segment is reflected by adjacent devices, and is eventually directed towards the exit aperture.

In some embodiments, the PHOLEDs ofFIGS. 3(a)-3(b)may be grown by vacuum sublimation at a base pressure less than 5×10−7torr on the 60Ω/□ (i.e., 60 ohm-per-square) ITO-coated substrates with greater than 79% transmittance at a wavelength (λ) of 550 μm. The device structure is as follows: ITO (100 nm/MoO3doped at 15 vol. % in 4,4′-bis(carbazol-9-yl)biphenyl (CBP) as a hole injection layer8(HIL, 60 nm)/CBP as the hole transport layer (HTL, 10 nm)/bis(2-phenylpyridine) (acetylacetonate) iridium(III) (Ir(ppy)2(acac)) doped at 8 vol. % in CBP as the emissive layer (EML, 15 nm)/2,2′,2″-(1,3,5-benzenetriyl)-tris(J-phenyl-1-H-benzimidazole) (TPBi) as the hole blocking and electron transporting layer (HBL and ETL, 65 nm)/LiF (1.5 nm)/Al (cathode, 100 nm). The area of the reference PHOLED and one triangular side of the concentrator were 1 cm2and 1.85 cm2(resulting in a total concentrator interior area of 7.4 cm2), respectively. Prior to deposition, particulates remaining on the solvent-cleaned substrates were removed by CO2snow cleaning to minimize electrical shorts. PHOLED electroluminescence characteristics were measured by a parameter analyzer and a calibrated Si-photodiode whose area is larger than that of the concentrator aperture.

FIGS. 11(a)-11(c)show a ray-tracing algorithm for a single panel concentrator device according to embodiments of the disclosed subject matter.FIG. 11(a)shows decomposition of a ray with initial intensity, I, at the polar angle, φ, and the azimuthal angle, φ, with respect to the normal and the median of the triangular panel, respectively. The forward component is directed toward the aperture (arrow300), and the lateral component is confined within the pyramid (arrow302), being reflected (arrow304) by adjacent device panels and attenuated. Here, φ and φ are varied from −90 to 90° and 0 to 180°, respectively.

FIG. 11(b)shows ray tracing of the forward component at an initial emission angle, β, with respect to the normal of the concentrator panel. The original intensity I of the ray emitted at an arbitrary position x from the vertex of the concentrator satisfies the Lambertian distribution, and its forward component intensity (seeFIG. 6(a)-(c)as described above) and β are determined versus φ and φ. As the ray is reflected by the opposing panel, its intensity is attenuated by RPHOLED, and its reflected angle is increased by the apex angle, θ, of the concentrator. Then, the ray travels the length, lnuntil the next reflection. The height of the concentrator, L, may be set to unity. The exit angle, αexit, of the ray escaping through the aperture is defined with respect to the central axis of the concentrator, which determines the final angular distribution profile.

FIG. 11(c)shows a schematic of the ray-tracing algorithm. The ray can escape through the aperture only if it fulfills the exit condition: the total travel lengths added to the initial emission position x must be greater than L, or the initial or reflected emission angle is larger than π/2−θ so that it does not meet the opposing panel. Each traced ray contains information about its final intensity, exit angle, and the number of reflections up to extraction.

The simulation described above may be based on a single-wavelength and fixed reflectance RPHOLEDthat is independent of the incident angle, and does not include optical effects other than reflection.

In embodiments of the disclosed subject matter, there may be different ray-tracing simulation results for different concentrator geometries.FIG. 12shows a comparison of the exit angles, αexit, of emission normal to a single concentrator panel at apex angles, θapex=25.5 and 55.5°. Table 2 above shows the simulated properties of the concentrators with apex angle θapex=25.5 and 55.5°. Concentrators with larger apex angles have improved extraction efficiencies due to the reduced number of reflections relative to those with smaller θapex. Particularly, emission near the vertex is preferentially extracted at larger exit angles (αexit=39.0°), and the emission near the aperture (x=1) at smaller anglesαexit=1.10. This loss/emission position tradeoff may significantly affect the emission pattern of the concentrator.

The PHOLED reflectance may be calculated.FIG. 13shows PHOLED reflectance and transmittance with an incident angle θiand a refracted angle θi. The total reflectance of the PHOLED including the PET substrate may be calculated as follows:
RPHOLED(θi)=R1(θi)+T1(θi)·T2(θt)·R(θt)+T1(θi)·T2(θt)·R2(θt)·R2(θt)+  (S1)
where R1and R2are the fractions of the incident energy reflected back to the air and the PET by the air/PET interface, T1and T2are the transmitted fractions into the PET and air, respectively, and R is the reflectance of the PHOLED structure calculated using the transfer matrix method. Now, Eq. (S1) is rewritten as:

Referring again toFIG. 8(a)-8(b), the outcoupling efficiency may be calculated with varying the thicknesses of the hole transport (tHTL) and electron transport (tETL) layers.FIGS. 8(a)-8(b)show the calculated outcoupling efficiency of the PHOLEDs at wavelength (λ) of 522 nm at an emission angle θ=0°, normal to the layers. The thickness are varied for the ETL shown inFIG. 8(a)and the HTL shown inFIG. 8(b). The device structure used in the calculation is: ITO (100 nm)/15 wt % MoO3doped into CBP (tHTLnm)/CBP (10 nm)/Ir(ppy)2(acac) doped into CBP (15 nm)/TPBi (10 nm)/2 wt % Li doped into Bphen (tETLnm)/LiQ (1.5 nm)/Ag (150 nm). The refractive indices of the organic layers are measured by variable angle spectroscopic ellipsometer. Each fraction coupled to air modes (outcoupling), glass modes, waveguide modes (ITO and organics) and the cathode is calculated from the relative energy transferred from the dipoles. It is assumed that the dipole is formed at the interface between EML and HBL.

FIG. 14shows the scale-independency of the concentrator. The fraction of the extracted emission from the equally-sized segments of the single panel device, comprising the total extracted emission at the aperture, may be calculated. The segment closest to the vertex of the concentrator contributes least to the total emission due to the reflections, while the segment closest to the aperture does most. Thus, a pyramid structure may be truncated at certain height, and its top side may be replaced with the planar device, considering the relatively weak contribution of D1as identified inFIG. 14. However, such height may never exist, because the removed small pyramid is also the concentrator. It can attain the higher luminous flux than the planar device mounted on the top of a truncated pyramid. Therefore, regardless of the dimension of the concentrator and the origin of the emission, all rays generated within the structure may contribute to the light output.