JP2006277987A - Simulation method and device of organic electroluminescent element - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To simulate luminescent characteristics of an organic electroluminescent element with accuracy. <P>SOLUTION: In the simulation method for finding luminescent characteristics of light taken out of the organic electroluminescent element with a light reflecting layer, an amplitude ratio or a phase difference of direct light irradiated from a light-emitting face toward an observation side at a certain angle θ with a normal line direction of the light-emitting face to reflection light reflected at the light reflecting layer once or more after being emitted from the light-emitting face and directed toward the observation side at the same angle as the direct light is found with consideration of anisotropy of an amplitude of light emitted from light-emitting molecules as a fourth factor, in addition to reflection, an amplitude at transmission, and change of phases (a first factor), light absorption (a second factor), and a light-path difference (a third factor) at each layer interface constituting organic electroluminescent element introduced from Fresnel equations with the use of a complex index of refraction. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a simulation method and apparatus for predicting the light emission characteristics of an organic electroluminescent element that can be used in fields such as display elements, backlights, lighting, interiors, signs, signboards, electrophotographic machines, and optical signal generators. It is.

  Organic phosphor or organic phosphorescent material in which holes injected from the first electrode (generally anode) formed on the substrate and electrons injected from the second electrode (generally cathode) are sandwiched between the two electrodes In recent years, researches on organic electroluminescent devices using the principle of light emission upon recombination in the body have been actively conducted. This element can be reduced in thickness, can emit light with high luminance under a low driving voltage, and has a feature that multicolor light emission is possible by selecting a fluorescent material.

The organic electroluminescence device emits light with high brightness, which is a C.D. W. First shown by Tang et al. (See Non-Patent Document 1, for example). A typical configuration of the organic electroluminescent device presented by Kodak Company is a tris (8-quinolinolato) aluminum having a hole transporting diamine compound, a light emitting layer and an electron transporting property on an ITO glass substrate, and Mg: Ag as a cathode was sequentially provided, and green light emission of 1000 Cd / m ² was possible with a driving voltage of about 10V. The current organic electroluminescent device basically follows the above-mentioned configuration of Kodak Company, and has a structure in which a first electrode, a thin film layer including a light emitting layer, and a second electrode are sequentially laminated on a substrate. Have. The thin film layer may have a single-layer structure including only the light-emitting layer, but in many cases, it has a laminated structure including a plurality of layers provided with a hole transport layer and an electron transport layer.

  By the way, in an organic electroluminescent element, light interferes inside the element, and it is known that even if an element is manufactured using the same material, emission characteristics such as emission spectrum, chromaticity, and luminance change depending on the element structure. It has been. And the method of simulating the change of the light emission characteristic by this optical interference is proposed (refer patent document 1).

In the method of Patent Document 1, the direct light emitted from the light emitting surface to the observation side at a certain angle θ with respect to the normal direction of the light emitting surface, and after being emitted from the light emitting surface and reflected by the light reflecting layer one or more times. , Reflection and transmission at the interface of each layer constituting the organic electroluminescence device derived from the Fresnel equation using the complex refractive index, the amplitude ratio or phase difference with the reflected light directed to the observation side at the same angle θ as the direct light In addition to changes in time and amplitude, phase absorption, light absorption, and optical path difference, scattered light produced by scattering at angles other than regular reflection when light emitted from the light emitting surface is reflected by the light reflection layer This is a simulation method that is taken into consideration and is assumed that the amplitude of the light emitted from the luminescent molecule is isotropic and is isotropic, and is scattered at an angle other than regular reflection when reflected by the light reflecting layer. Light emission in any angle direction considering the presence of scattered light It is to predict the characteristics.
JP 2005-38659 A Appl. Phys. Lett. 51 (12) 21, 913 (1987)

  However, in the simulation method of Patent Document 1 that also considers scattered light as described above, there is a large difference between the viewing angle dependency of luminance obtained by simulation and the viewing angle dependency of luminance obtained by an actual light emitting element. There was a difference, and the simulation accuracy was not necessarily high.

  In particular, when an organic EL (Electro Luminescence) display is manufactured using an organic electroluminescent element, and the viewing angle dependency of the luminance of a pixel is different for each emission color, a simulation was performed by the method of Patent Document 1. As a result, as described above, even if a simulation result indicating that each emission color is balanced not only in the front direction but also in a state viewed from a direction angled with respect to the normal direction of the screen, Due to the fact that the accuracy of the simulation is not high, an actual organic EL display, for example, shows a correct emission color when viewed from the front, and each emission color when viewed from a direction angled with respect to the normal direction of the screen. There is a possibility that inconvenience may occur that the visibility of the display cannot be secured.

  In addition, this disadvantage is not known until an organic EL display with insufficient quality is manufactured and the light emission characteristics are actually measured. Therefore, only the inconvenience and simulation that the organic EL display is wasted. Then, there arises a disadvantage that there is no guarantee that an element design for an organic EL display of sufficient quality can be achieved.

  The present invention performs element design in consideration of the viewing angle dependency of light emission characteristics, and produces light emitting elements for organic EL displays with a wide viewing angle and good visibility. Another object of the present invention is to provide a simulation method and apparatus capable of obtaining an accurate simulation result that matches an actual measurement value.

  The object is solved by using the following simulation method or simulation apparatus.

  That is, when obtaining the light emission characteristics of the extracted light of an organic electroluminescence device having a light reflection layer and a known configuration, the light was emitted from the light emitting surface to the observation side at a certain angle θ with respect to the normal direction of the light emitting surface. The amplitude ratio or phase difference between the direct light and the reflected light emitted from the light emitting surface and reflected by the light reflection layer at least once and then toward the observation side at the same angle θ as the direct light is expressed as (1) complex refraction. The reflection at the interface of each layer constituting the organic electroluminescence device derived from the Fresnel equation using the rate, the change in amplitude and phase during transmission, (2) light absorption, (3) optical path difference, and (4) luminescent molecule This is a simulation method for an organic electroluminescent element, which is obtained in consideration of the anisotropy of the amplitude of light emitted from the organic electroluminescent element.

  In addition, in order to obtain the emission characteristics of the extracted light of an organic electroluminescence device having a light reflection layer and a known configuration, it is emitted from the light emitting surface to the observation side at an angle θ with respect to the normal direction of the light emitting surface. The amplitude ratio or phase difference between the direct light and the reflected light emitted from the light emitting surface and reflected by the light reflecting layer at least once and then directed to the observation side at the same angle θ as the direct light is expressed as (1) complex Reflection at the interface of each layer constituting the organic electroluminescence device derived from the Fresnel equation using the refractive index, change in amplitude and phase during transmission, (2) light absorption, (3) optical path difference, and (4) light emission An organic electroluminescent device simulation apparatus comprising means for determining anisotropy of amplitude of light emitted from a molecule.

  The simulation method of the present invention has a specific effect that a simulation result that matches the emission characteristics of the organic electroluminescence element actually obtained with high accuracy can be obtained.

  The simulation apparatus of the present invention also has a unique effect that it can obtain a simulation result that matches the emission characteristics of the organic electroluminescence element actually obtained with high accuracy.

  Hereinafter, embodiments of a simulation method and apparatus for an organic electroluminescent element according to the present invention will be described in detail with reference to the accompanying drawings.

  The light reflecting layer as used in the present invention is a layer having a function of reflecting visible light, and as a material, a simple metal, an alloy, or other inorganic compound that can reflect visible light, an organic compound that can reflect visible light, etc. Can be illustrated. Further, it may have a function as an electrode.

  In addition, the emission characteristic of extracted light in the present invention is a concept including at least one of emission spectrum, chromaticity, and luminance of light emitted from the element to the outside at an arbitrary angle with respect to the normal direction of the light emitting surface. Used as. In other words, the emission characteristic of the extracted light is at least one angle dependency of the emission spectrum, chromaticity, and luminance of the light emitted to the outside.

  Direct light (see 4 in FIG. 1) emitted from the light emitting surface to the viewing side (see 5 in FIG. 1) at an angle θ with respect to the normal direction of the light emitting surface (see 2 in FIG. 1). ) And reflected light (see 3 in FIG. 1) that is emitted from the light emitting surface and reflected at least once by the light reflecting layer (see 1 in FIG. 1) and then directed to the observation side at the same angle θ as the direct light. ) Generally differs in amplitude and phase, but this is due to the following three factors.

  The first element in the present invention is a change in the amplitude and phase at the time of reflection and transmission at the interface of each layer constituting the organic electroluminescent element, which is derived from the Fresnel equation using the complex refractive index. It is represented by (1) to (4) (see Equation 1).

  Light is incident at an angle θ0 from a medium 0 having a complex refractive index N0 (see 6 in FIGS. 2 and 3) to a medium 1 having a complex refractive index N1 (see 7 in FIGS. 2 and 3). (See FIGS. 2 and 3. Note that the arrow indicates a vector, and the black circle symbol in the circle indicates a vector that is directed perpendicularly to the page. The symbol of represents a vector that goes to the other side of the page perpendicularly to the page.These conventions apply to other figures as well in the following.) (Also, in FIG. Represents incident light, 9 represents reflected light, and 10 represents transmitted light. The subscripts s and p represent a component perpendicular to the incident surface of the light electric field (S-polarized light) and a component parallel to (P-polarized light). Respectively, the amplitude reflectance and the amplitude transmittance are expressed by the following formulas (1) to (4). Note that rs is the amplitude reflectance of S-polarized light, ts is the amplitude transmittance of S-polarized light, rp is the amplitude reflectance of P-polarized light, and tp is the amplitude transmittance of P-polarized light. In the figure, E represents an electric field, and H represents a magnetic field. The positive direction of the electromagnetic field in the S-polarized light is defined as shown in FIG. 2, and the positive direction of the electromagnetic field in the P-polarized light is defined as shown in FIG. Equation (5) (see Equation 1) is Snell's law.

The complex refractive index is expressed by N _j = n _j −i · k _j . Here, n _j is a refractive index, k _j is an extinction coefficient, and i is an imaginary unit. The refractive index and extinction coefficient are collectively called an optical constant. Since the extinction coefficient of each layer constituting the organic electroluminescent element as well as the light reflecting layer is generally not 0, the complex refractive index N _j is generally a complex number. Therefore, the amplitude reflectance and the amplitude transmittance are also complex numbers, and include information on the phase shift during reflection and transmission. The ratio of the amplitude of the reflected light to the amplitude of the incident light and the ratio of the amplitude of the transmitted light are the absolute values of the amplitude reflectance and the amplitude transmittance, respectively. Further, if the deflection angle of the amplitude reflectance and the amplitude transmittance is obtained, the value of the phase shift at the time of reflection and transmission can be obtained. In order to obtain changes in the reflection and transmission amplitude and phase at the interface of each layer of the organic electroluminescent element, the values of the optical constants of the respective layers constituting the organic electroluminescent element are necessary. (Metric) or the like.

  The second element is light absorption. Since the extinction coefficient of each layer constituting the organic electroluminescence element is generally not 0, light is absorbed as the light wave travels. When a light wave having a wavelength λ travels a distance d through a medium having an extinction coefficient k, the amplitude becomes exp (−2πkd / λ) times. Further, at the time of reflection by the light reflecting layer, a part of the light is absorbed without being reflected. The energy reflectivity during reflection is the square of the absolute value of the amplitude reflectivity, and the energy absorption rate can be obtained by subtracting the energy reflectivity from 1. As a result of these light absorptions, the light amplitude decreases.

  The third factor is the optical path difference. The phase is different by the optical path difference. For example, as shown in FIG. 4, the viewing side (see 15 in FIG. 4) from the light emitting surface at an angle θ with respect to the normal direction of the light emitting surface (see 12 in FIG. 4) in the medium of refractive index n. Direct light (see 14 in FIG. 4) radiated from the light-emitting surface, reflected light emitted from the light emitting surface and reflected by the light reflecting layer (see 11 in FIG. 4), and then reflected toward the observation side at an angle θ (Refer to 13 in FIG. 4) has an optical path difference of 2nd · cos θ (where d is a distance from the light emitting surface to the light reflecting layer). Therefore, the direct light and the reflected light have a phase difference of 4πnd · cos θ / λ (where λ is the wavelength of the light).

  In the present invention, in addition to the above three elements, anisotropy of the amplitude of light emitted from the light emitting molecule is considered as a fourth element. According to previous studies, it has been found that the amplitude of the light emitted from the luminescent molecule is not isotropic but anisotropic. Therefore, the present invention considers the anisotropy of the amplitude of the light emitted from the light emitting molecule in order to obtain a simulation result that is similar or consistent with the actual result. In the simulation method using each formula described below based on this concept, direct light emitted from the light emitting surface to the observation side at a certain angle θ with respect to the normal direction of the light emitting surface, and emitted from the light emitting surface. The amplitude ratio with the light traveling to the light reflecting layer (the light traveling toward the observation side at the same angle θ as that of the direct light after being reflected by the light reflecting layer) is generally not 1 and is radiated according to the emission angle. The light amplitude value will be different. In the conventional simulation technology considering scattered light, direct light emitted from the light emitting surface to the observation side at a certain angle θ with respect to the normal direction of the light emitting surface, and light emitted from the light emitting surface toward the light reflecting layer. The amplitude ratio is always 1, and the value of the amplitude of the emitted light is always constant according to the emission angle, but this can be considered physically if the phenomenon that light is emitted from the light emitting molecule is considered. Could not give the correct results.

  The thickness of each layer constituting the organic electroluminescence device, optical constants, emission intensity distribution in the film thickness direction in the light emitting layer, light spectrum emitted from the light emitting layer, and direction distribution of the number of light emitting molecules are used as design data. In actuality, it is held in a memory (not shown), read from the memory as needed, and supplied to the processing unit for simulation). An internal light emission interference model considering reflection and transmission at all interfaces can be configured, and the emission characteristics of extracted light can be obtained. In the calculation, the S-polarized light and the P-polarized light can be calculated independently and may be added together at the end. The electric field amplitude of the light emitted from the light emitting molecule is generally anisotropic, and the present invention will explain the case of light emission by electric dipole transition. In this case, except for the case where the transition dipole moment of the light emitting molecule is perpendicular to the normal direction of the light emitting surface, light is emitted at an angle θ with respect to the normal direction of the light emitting surface (see 18 in FIG. 5). Direct light (see 20 in FIG. 5) radiated from the surface to the observation side (see 21 in FIG. 5) and a light reflection layer (see 17 in FIG. 5) radiated from the light emitting surface The amplitude ratio with the light that goes is not 1, but changes depending on the direction of the transition dipole moment (see 22 in FIG. 5) (FIG. 5).

  In order to obtain the emission spectrum, the emission energy of each wavelength is calculated. At this time, first, the product of the refractive index of the light emitting layer (generally having wavelength dependence) and the square of the electric field amplitude of the light emitted from the light emitting interface. The emission energy of each wavelength is obtained so as to have a magnitude determined according to the angle formed by the direction of the light that springs out with respect to the direction of the transition dipole moment of the luminescent molecule. Next, an emission spectrum is obtained by multiplying this value by a spectrum value (energy of a wavelength of interest) emitted from the light emitting layer. As a spectrum emitted from the light emitting layer, a photoexcitation emission spectrum of a film made of the same material as the light emitting layer may be used. In addition, since luminescent molecules generally face various directions, the following is performed.

  First, the two declinations (directions) of the transition dipole moment are each divided into several, and the emission spectra when the transition dipole moment is directed to each angular direction are obtained independently by the above method. Next, after multiplying each emission spectrum by the number of light emitting molecules facing the angle direction, this value is integrated over the angle direction, and the total emission spectrum is obtained by adding the contributions from all directions.

  The emission intensity distribution may be handled as follows. First, the light emitting layer is divided into several layers, and the emission spectra when only the interface of each layer emits light are obtained independently by the above method. Next, after multiplying each emission spectrum by the emission intensity at the interface, this value is integrated over the thickness direction, and the total emission spectrum is obtained by adding the contributions from all the interfaces. From this spectrum, chromaticity and luminance can be obtained.

  Hereinafter, the internal light emission interference model will be described in detail.

  First, when the transition dipole moment of a light emitting molecule is directed in a certain direction, there is no light emission distribution in the thickness direction, and the light emission is concentrated at an interface, that is, there is only one light emitting molecule directed in a certain direction. The case will be described, and then this will be used to expand the case where there are luminescent molecules in various directions and the luminescence distribution spreads in the thickness direction.

In an organic electroluminescent device having m thin film layers and a cathode on a substrate, layer numbers are given as shown in FIGS. For j = 1 to _m , the film thickness of the jth layer is set to dj. Similarly, for j = 0 to m + 1, the refractive index at wavelength λ is n _j (λ), the extinction coefficient is k _j (λ), and the complex refractive index is N _j (λ) = n _j (λ) −i.・ K _j (λ). (Here, i is an imaginary unit.) The refractive index at the wavelength λ outside the device is n (λ). (Normally air, approximating attenuation factor (k (λ)) = 0, and approximating to be the same as the refractive index of vacuum, N (λ) = N (λ) = 1. )
First, considering the case where light emission is concentrated at the (h-1) th layer / hth layer interface, the light emitting surface is defined as the (h-1) th layer / hth layer interface. The (h−1) th layer and the hth layer are made of the same material, and N (h−1) (λ) = Nh (λ). {When the light emitting layer is composed of the (h-1) th layer and the hth layer and the light emission intensity is concentrated at the (h-2) layer / (h-1) layer interface, d (h-1) = 0. } The electric field at each interface of the light of wavelength λ contributing to the extracted light in the θ direction is expressed as Es _j ^α (λ) and Ep _j ^α (λ) {where s and p are s-polarized light and p-polarized light, respectively. (S-polarized light is light whose electric field is perpendicular to the yz plane, and p-polarized light is light whose magnetic field is perpendicular to the yz plane). The subscript j represents the layer number. The superscript α has a value of 0 or 1, where 0 indicates light directed in the negative z-axis direction and 1 indicates light directed in the positive z-axis direction}. The sin θ _j (λ) and cos θ _j (λ) are obtained using the equations 2 and 3 with respect to the direction θ _j (λ) in each layer of the light contributing to the extracted light of the wavelength λ in the θ direction.

Formula 2 is derived from Snell's law, and then the conjugate complex number of the complex number N _j (λ) is multiplied by the numerator denominator to convert the denominator into a real number.

Equation (3a) in Equation 3 is transformed into a trigonometric relational equation and an equation represented by sin in the equation derived from Snell's formula in sin, and then Equations (3b) and (3c) in Equation 3 Street real part, imaginary part p
_{In j} (λ) and q _j (λ), the square root of a complex number is converted into the form of the sum of a real number and an imaginary number.

Next, the amplitude of the light emitted from the luminescent molecule is determined. Consider a case where the transition dipole moment of the luminescent molecule is oriented in the M direction as shown in FIG. (Bold characters in the figure indicate vectors. The same applies hereinafter.) The light focused on the kh0 direction and the kh1 direction. Here, the unit vector in the electric field direction of the S-polarized light traveling in the kh0 direction is es0, and the unit vector in the electric field direction of the P-polarized light is ep0. In addition, the unit vector in the electric field direction of the S-polarized light toward the kh1 direction is es1, and the unit vector in the electric field direction of the P-polarized light is ep1. The xyz component of each vector is as shown in Equation 4.

  The transition dipole moment M is an amount that appears when calculating the transition probability of a transition involving light emission in quantum mechanics, and is defined as a matrix element between the start state and the end state of the dipole moment operator. Which is given by equation (5).

Here, ek and xk represent the charge and position vector of the kth particle. Ψf and ψi represent the wave functions of the final state and the initial state of the system, respectively. θ _TM and φ _TM are declinations of M. kh0 and kh1 are wave vector.

  In the present invention, the anisotropy of the amplitude of light emitted from the light emitting molecule is considered as a fourth element. This element is expressed by the following equation (Equation 6) and is included as an element of the simulation.

The deactivation rate of photon emission in a certain angular direction of the excited molecule is proportional to | e · M | ² when the unit vector in the electric field direction of the emitted photon is e, so the amplitude of the emitted light is | It can be considered that it is proportional to e · M |. That, m0 = 1 and when, S polarized light of the electric field amplitude of the light vs0, P v _p 0 the electric field amplitude of the polarization of light, kh1 S-polarized v _s 1 the electric field amplitude of the light directed in a direction toward the kh0 direction, When the electric field amplitude of the P-polarized light is v _p 1, Equation 6 is obtained.

Next, the actual simulation including the procedure will be described below. As (λ) and ap (λ) satisfying the equations (Equation 7, Equation 8, Equation 9, Equation 10) in the following cases (1) to (4) are obtained, and Es ₀ ⁰ (λ), Ep _o at that time are obtained. ⁰ (λ) is obtained. These are the electric fields of light emitted from the multilayer film and reaching the substrate.
(1) When j = 0

(2) When j = h

(3) When j = m + 1

(4) When j ≠ 0, j ≠ h and j ≠ m + 1

  Next, using the formula (11a) to the formula (11d) (see Expression 11), the s-polarized light having the wavelength λ in the negative direction of the z-axis at the angle θ0 (λ) is transmitted from the substrate to the outside. The transmittance Ts (λ), the reflectance Rs (λ), the transmittance Tp (λ) of the p-polarized light from the substrate to the outside, and the reflectance Rp (λ) are obtained.

Next, the multilayer film reflectance when the light that reaches the external / substrate interface and is reflected again is reflected by the multilayer film is obtained. 9 and 10 show a case where light having a wavelength λ is incident on the multilayer film from the substrate at an angle θ0 (λ). The electric field at each interface is represented by E ⁽¹⁾ s _j ^α (λ) and E ⁽¹⁾ p _j ^α (λ).

Next, E ⁽¹⁾ s ₀ ⁰ (λ), E ⁽¹⁾ s ₀ ¹ (λ), E ⁽¹⁾ p ₀ satisfying the equations (Equation 12, Equation 13) in the cases of (5) and (6) below ⁰ (λ), E ⁽¹⁾ Find p ₀ ¹ (λ). E ⁽¹⁾ s ₀ ¹ (λ), E ⁽¹⁾ p ₀ ¹ (λ) represents the electric field of the incident light on the multilayer film, and E ⁽¹⁾ s ₀ ⁰ (λ), E ⁽¹⁾ p ₀ ⁰ (λ) represents the electric field of the reflected light reflected by the multilayer film.
(5) When j = m + 1

(6) When j ≠ m + 1

  Reflectance rs (λ) at the multilayer film of s-polarized light of wavelength λ directed in the positive direction of the z-axis in the substrate at an angle θ0 (λ), and reflectivity rp (λ at the multilayer film of p-polarized light ) Is as shown in Equation 14.

Since the thickness of the substrate is much larger than the wavelength of normal light, it may be considered that the light reflected once or more at the external / substrate interface loses coherence with other light. The light sequentially reflected by the external / substrate interface and the multilayer film can be added incoherently, and when all paths are added, the emission spectrum I _EL (λ) in the θ direction can be expressed by Equation 15.

Here, I _EM (λ) is a spectrum of light emitted from the light emitting layer.
The reason why the term N (λ) / nh (λ) is included will be described below.
In Equation (8a) to Equation (8e) (see Equation 8), the magnitude of the transition dipole moment for each of the S-polarized light and P-polarized light in the light source is as follows when m ₀ in Equation (4a) (see Equation 4) is 1. The calculation was performed as a dipole transition. When the (h-1) th layer and the hth layer are infinitely thick and there is no return light, for example, at an angle θ (h-1), the (h-1) th layer is S with a wavelength λ directed in the negative z-axis direction. The light energy of polarized light is expressed by Equation 16.

When nh (λ) has wavelength dependence, the value of light energy directed toward the θ (h−1) direction varies depending on the wavelength.
At this time, the energy of light having a wavelength λ emitted in the θ direction is expressed by Equation 17.

  In order to remove the wavelength dependency of the energy of the light source, the equation 17 may be divided by nh (λ) / 2 (see equation 18).

Here, the light emission spectrum I _EL (λ) in the θ direction can be obtained by multiplying the light spectrum I _EM (λ) emitted from the light emitting layer as the wavelength dependence of the energy of the light source. From the same consideration, even in a general element configuration, a term of n (λ) / nh (λ) is entered as in Expression 18. Since the external refractive index n (λ) = 1 is normal, the term n (λ) / nh (λ) may be omitted when the wavelength dependency of nh (λ) is small.

Further, when the transmittances Ts (λ) and Tp (λ) from the substrate to the outside are large and the reflectances Rs (λ) and Rp (λ) are small, or the reflectance of the multilayer film is small, the calculation is simplified. Therefore, the calculation of equations in the cases of (5) and (6) may be omitted by setting the reflectance of the multilayer film to 0. At this time, the emission spectrum I _EL (λ) in the θ direction can be expressed by Equation 19.

  The tristimulus values X, Y, and Z in the CIE1931 color system can be obtained from the emission spectrum using Equation 20, and the chromaticity coordinates (x, y) in the θ direction and the relative luminance L can be obtained.

  When the direction of the luminescent molecule is various and the transition dipole moment is in various directions, the following is performed.

First, let g (θ, φ) be the number of luminescent molecules facing the direction M (θ, φ) of an arbitrary transition dipole moment. When the direction of the transition dipole moment is M (θ, φ), the emission spectrum in the θ direction is obtained using Equation 15 and is set as IEL (λ, θ, φ). Further, integration is performed in the angular direction using Equation 21, and an emission spectrum I _EL (λ) in the θ direction is obtained.

  When the light emitting molecules are not oriented and the orientation is random, g (θ, φ) may be set as a constant. In the case where the light emitting region has a spread in the thickness direction (Z-axis direction), the following is performed.

The (h-2) th layer, the (h-1) th layer, and the hth layer are made of the same material. It is assumed that the light emitting region extends from the (h-2) layer / (h-1) layer interface to the (h-1) layer / h layer interface, and light emission at an arbitrary plane z in this region. Let intensity be f (z). The case where the light emitting surface {the (h-1) layer / h layer interface when the light emitting region is limited to the (h-1) layer / h layer interface} is the surface z in the region of Formula 22 , The emission spectrum in the θ direction is obtained using Equation 21, and is set as I _EL (λ, z).

Further, integration is performed within the light emission region using Equation 23 to obtain a light emission spectrum I _EL (λ) in the θ direction.

The integration of the direction of the transition dipole moment and the integration of the emission region is summarized as follows. That is, the emission spectrum from the light emitting molecule of the transition dipole moment M (θ, φ) on the surface z is obtained using Equation 15 and is set as I _EL (λ, θ, φ, z). Further, integration is performed in the angular direction and in the light emission region using Equation 24, and the light emission spectrum I _EL (λ) in the θ direction is obtained.

 Tristimulus values X, Y, and Z in the CIE 1931 color system are obtained from the emission spectrum using the equations (20a) to (20d) (see Equation 20), the chromaticity coordinates (x, y) in the θ direction, and the relative luminance. L can be obtained.

  The present invention is effective in a device having a structure in which a transparent first electrode, a thin film layer made of an organic compound, and a light reflecting layer are laminated on a transparent substrate, but the light reflecting layer and the thin film layer made of an organic compound are formed on the substrate. It is also effective for an organic electroluminescence device having a top emission structure in which a transparent second electrode is laminated.

  To actually simulate using the above model, a program reflecting the simulation method of the present invention may be executed using a computer. Specifically, for example, it is carried out as follows. First, the thickness of each layer constituting the organic electroluminescence device, the optical constant, the light emission intensity distribution in the film thickness direction in the light emitting layer, the light spectrum emitted from the light emitting layer, the direction distribution of the number of light emitting molecules, and the viewing angle of interest The numerical data is stored in the hard disk of the computer by an input means such as.

  Next, a program reflecting the simulation of the present invention stored in advance in the hard disk is started, and calculation processing is executed using the data stored in the hard disk. The calculation process is performed using a hard disk, a memory, and a CPU in the computer, and the contents are roughly as follows. First, an emission spectrum in a viewing angle direction of interest by a luminescent molecule directed in a certain direction at a certain position in the luminescent layer is obtained, and the presence of the luminescent molecule is multiplied there. By sequentially obtaining the light emitting molecules in various positions and in various directions, and finally adding all of the obtained ones, an emission spectrum in the viewing angle direction of interest of the device can be obtained. Further, luminance and chromaticity can be obtained from the emission spectrum. The obtained result can be confirmed by displaying it on output means such as a monitor.

  In addition, the present invention is effective for simulation of light emission characteristics in an oblique direction with respect to the normal direction of the light emitting surface, and is particularly effective for simulation of viewing angle dependence of light emission luminance. In addition, the present invention can be used particularly when the light spectrum emitted from the light emitting layer is broad, specifically when the half width is 50 nm or more.

  EXAMPLES Hereinafter, although an Example and a comparative example are given and this invention is demonstrated, this invention is not limited by these examples.

  A glass substrate on which a ITO transparent conductive film having a thickness of 106 nm was laminated by sputtering was cut into 38 × 46 mm, and then unnecessary portions of ITO were removed by etching. The obtained substrate was ultrasonically cleaned with an alkaline cleaning liquid for 10 minutes and then cleaned with ultrapure water. This substrate was subjected to UV / ozone treatment for 1 hour immediately before producing the device, placed in a vacuum apparatus, and evacuated until the degree of vacuum in the apparatus became 5 × 10 −4 Pa or less. First, copper phthalocyanine (CuPc) was vapor-deposited by 6 nm by resistance heating, and then N, N′-di- (naphthalen-1-yl) -N, N′-diphenyl-benzidine (NPD) was used as a hole transport material. Subsequently, 62 nm was vapor-deposited, and subsequently, tris (8-quinolinolato) aluminum (Alq) was vapor-deposited as a light-emitting layer at 54 nm. A cathode mask was attached, and after doping by exposure to lithium vapor, aluminum was deposited to a thickness of 150 nm to form a cathode.

The organic electroluminescence device thus fabricated was made to emit light at a current density of 10 mA / cm ² , and the luminance in the direction of 0 °, 30 °, 60 ° with respect to the normal direction of the substrate surface was measured. It was like 11 (1). The luminance is normalized with 1 in the 0 ° direction.

Example 1
The organic electroluminescence device having the above-described configuration is simulated using the model of the present invention, and the luminance in the direction of 0 °, 15 °, 30 °, 45 °, 60 °, and 75 ° with respect to the normal direction of the substrate surface is obtained. As a result, as shown in (2) of FIG. 11, almost the same numerical value as that of an actual light emitting element was obtained. The luminance is normalized with 1 in the 0 ° direction.

  Here, the direction of the luminescent molecule is random, g (θ, φ) = 1 in Equation 24, and θ = 0, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180 °. The cases were calculated and added independently. φ was set to 0 to 2π. Here, the emission intensity distribution f (d) in the light emitting layer is strongly reduced at the NPD / Alq interface as it approaches the Alq / electron transport layer interface as shown in FIG. It was assumed that

(Where α is a constant, and d is a number in nm of the distance measured toward the Alq / electron transport layer interface with the NPD / Alq interface as 0. Note that the emission spectrum is finally normalized. Α can be any value, but here it is 1. The value of 10 in the denominator of the exponential function was determined by analyzing the emission spectrum in the normal direction of the element plane.)
That is, the emission intensity was reduced to 1 / e at a point advanced 10 nm from the NPD / Alq interface toward the Alq / electron transport layer interface. In the calculation, the light emitting layer was divided into six at equal intervals, and the cases where a total of seven surfaces were light emitting interfaces were independently calculated and added.

That is, the calculation was performed as shown in Equation 26. Here, I _EL on the right side is a function of λ, θ, φ, z, and is I _EL (λ, θ, φ, z).

Note that the wavelength was calculated every 5 nm for 400 to 800 nm. Further, as a light spectrum emitted from the light emitting surface, a spectrum (FIG. 13) obtained by laminating 25 nm of Alq on a quartz plate and measuring a photoexcitation spectrum was used. Moreover, as an optical constant of each layer which comprises an organic electroluminescent element, each layer was each laminated | stacked 100 nm on the glass substrate, and the value obtained by measuring an optical constant by polarization analysis was used.

Comparative Example 1
About the organic electroluminescent element of this structure, it simulates by the method of paragraphs 0066-0103 of patent document 1, and 0 degree | times, 15 degrees, 30 degrees, 45 degrees, 60 degrees with respect to the normal line direction of a substrate surface, When the luminance in the direction of 75 ° was obtained, it was as shown in (3) of FIG. Note that the ratio r ² of the area where regular reflection occurs with respect to the entire area of the light reflecting layer interface was 0.87 described in Patent Document 1. The luminance is normalized with 1 in the 0 ° direction. Compared with the present embodiment, the difference from the actual measurement is large.

It is the schematic which shows the direct light and reflected light of angle (theta). It is the schematic which shows reflection and permeation | transmission of S polarization | polarized-light. It is the schematic which shows reflection and permeation | transmission of P polarized light. It is the schematic which shows the optical path difference of the direct light and reflected light of angle (theta). It is the schematic which shows the direct light and reflected light of angle (theta) by a dipole transition. It is an internal emission interference model diagram of S-polarized light from a single luminescent molecule directed in a certain direction. It is an internal emission interference model diagram of P-polarized light from a single luminescent molecule directed in a certain direction. It is the schematic which shows the direction of the unit vector of a transition dipole moment, a wave vector, and each electric field. It is a schematic diagram showing an electric field when S-polarized light is incident on a multilayer film from a substrate. It is the schematic which shows an electric field when the light of P polarization enters into a multilayer film from a substrate. It is the schematic which shows the viewing angle dependence of the brightness | luminance of an Alq element. It is the schematic which shows the emitted light intensity distribution in a light emitting layer. It is the schematic which shows the photoexcitation spectrum of an Alq thin film.

Explanation of symbols

1, 11, 17 Light reflecting layer 2, 12, 18 Light emitting surface 3, 19 Reflected light 4, 20 Direct light 5, 15, 21 Observation side 6 Medium 0: Complex refractive index N0
7 Medium 1: Complex refractive index N1
8 Incident 9 Reflected 10 Transmitted 13 Reflected light B
14 Direct light A
16 Refractive index n
22 Transition dipole moment

Claims (2)

A simulation method for obtaining light emission characteristics of extracted light of an organic electroluminescence device having a light reflection layer and a known configuration, and emitting from the light emitting surface to the observation side at an angle θ with respect to the normal direction of the light emitting surface. The amplitude ratio or phase difference between the reflected direct light and the reflected light emitted from the light emitting surface and reflected by the light reflection layer at least once and then directed to the observation side at the same angle θ as the direct light is (1) Reflection at the interface of each layer constituting the organic electroluminescent element derived from the Fresnel equation using the complex refractive index, change in amplitude and phase during transmission, (2) light absorption, (3) optical path difference, and (4) A method for simulating an organic electroluminescent device, wherein the method is obtained in consideration of anisotropy of amplitude of light emitted from a light emitting molecule. A simulation apparatus for obtaining the light emission characteristics of extracted light of an organic electroluminescence device having a light reflection layer and a known configuration, and emitting from the light emitting surface to the observation side at an angle θ with respect to the normal direction of the light emitting surface The amplitude ratio or phase difference between the reflected direct light and the reflected light emitted from the light emitting surface and reflected by the light reflection layer at least once and then toward the observation side at the same angle θ as the direct light is (1) Reflection at the interface of each layer constituting the organic electroluminescent element derived from the Fresnel equation using the complex refractive index, change in amplitude and phase during transmission, (2) light absorption, (3) optical path difference, and (4 ) A simulation apparatus for an organic electroluminescent device, comprising means for obtaining anisotropy of amplitude of light emitted from a luminescent molecule.

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