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Journals >Chinese Optics Letters >Volume 21 >Issue 2 >Page 022601 > Article

Chinese Optics Letters
Vol. 21, Issue 2, 022601 (2023)

Full description of dipole orientation in organic light-emitting diodes

Lingjie Fan^1、2, Maoxiong Zhao^1、2, Jiao Chu¹, Tangyao Shen^1、2, Minjia Zheng¹, Fang Guan³, Haiwei Yin², Lei Shi^{1、2、3、4、*}, and Jian Zi^{1、2、3、4、**}

Author Affiliations

¹Department of Physics, Key Laboratory of Micro- and Nano-Photonic Structures (Ministry of Education), and State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China

²Shanghai Engineering Research Center of Optical Metrology for Nano-fabrication (SERCOM), Shanghai 200433, China

³Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai 200438, China

⁴Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

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DOI: 10.3788/COL202321.022601 Cite this Article Set citation alerts

Lingjie Fan, Maoxiong Zhao, Jiao Chu, Tangyao Shen, Minjia Zheng, Fang Guan, Haiwei Yin, Lei Shi, Jian Zi. Full description of dipole orientation in organic light-emitting diodes[J]. Chinese Optics Letters, 2023, 21(2): 022601 Copy Citation Text

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Abstract

Considerable progress has been made in organic light-emitting diodes (OLEDs) to achieve high external quantum efficiency, among which dipole orientation has a remarkable effect. In most cases, the radiation of the dipoles in OLEDs is theoretically predicted with only one orientation parameter to match with corresponding experiments. Here, we develop a new theory with three orientation parameters to fully describe the relationship between dipole orientation and power density. Furthermore, we design an optimal test structure for measuring all three orientation parameters. All three orientation parameters could be retrieved from non-polarized spectra. Our theory provides a universal plot of dipole orientations in OLEDs, paving the way for designing more complicated OLED devices.

Keywords

dipole orientation Fourier series expansion organic light-emitting diodes

\begin{array}{l} R_{\pm}^{s, p} = {| r_{\pm}^{s, p} |}^{2} & for all cases, \\ T_{\pm}^{s} = {| t_{\pm}^{s} |}^{2} \frac{k_{z, \pm}}{| k_{z, 0} |} & for Im (k_{z, \pm}) = 0, \\ T_{\pm}^{p} = {| t_{\pm}^{p} |}^{2} \frac{n_{0}^{2}}{n_{\pm}^{2}} \frac{k_{z, \pm}}{| k_{z, 0} |} & for Im (k_{z, \pm}) = 0, \\ T_{\pm}^{s, p} = 0 & for Im (k_{z, \pm}) \neq 0 . \end{array}

(1)

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W_{\pm} = \int_{0}^{+ \infty} K_{\pm} d k_{∥}^{2},

(2)

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K_{\pm} = K_{\pm}^{s} + K_{\pm}^{p} .

(3)

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K_{\pm}^{s} = \frac{3}{8} \frac{1}{k_{0} k_{z, 0}} \frac{{| 1 + r_{\mp}^{s} \exp (2 j k_{z, 0} h_{0 \mp}) |}^{2}}{{| 1 - r_{+}^{s} r_{-}^{s} \exp (2 j k_{z, 0} h_{0}) |}^{2}} T_{\pm}^{s} \sin^{2} (θ) \sin^{2} (ϕ), K_{\pm}^{p} = \frac{3}{8} \frac{k_{∥}^{2}}{k_{0}^{3} k_{z, 0}} \frac{{| 1 + r_{\mp}^{p} \exp (2 j k_{z, 0} h_{0 \mp}) |}^{2}}{{| 1 - r_{+}^{p} r_{-}^{p} \exp (2 j k_{z, 0} h_{0}) |}^{2}} T_{\pm}^{p} \cos^{2} (θ) + \frac{3}{8} \frac{k_{z, 0}}{k_{0}^{3}} \frac{{| 1 - r_{\mp}^{p} \exp (2 j k_{z, 0} h_{0 \mp}) |}^{2}}{{| 1 - r_{+}^{p} r_{-}^{p} \exp (2 j k_{z, 0} h_{0}) |}^{2}} T_{\pm}^{p} \sin^{2} (θ) \cos^{2} (ϕ) - \frac{3}{8} \frac{k_{∥}}{k_{0}^{3}} \frac{1}{{| 1 - r_{+}^{p} r_{-}^{p} \exp (2 j k_{z, 0} h_{0}) |}^{2}} T_{\mp}^{p} T_{\pm}^{p} \sin (2 θ) \cos (ϕ) .

(4)

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P_{\pm} = \frac{k_{\pm}^{2} \cos (α)}{π} K_{\pm} .

(5)

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{\tilde{P}}_{\pm} = \int_{0}^{2 π} d ϕ \int_{0}^{π} d θ P_{\pm} \times F (θ, ϕ),

(6)

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F (θ, ϕ) = \sum_{l, m = 1}^{\infty} λ_{l, m} [a_{l, m} \cos (2 l θ) \cos (m ϕ) + b_{l, m} \cos (2 l θ) \sin (m ϕ) + c_{l, m} \sin (2 l θ) \cos (m ϕ) + d_{l, m} \sin (2 l θ) \sin (m ϕ)],

(7)

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\begin{array}{l} λ_{l, m} = \frac{1}{4} & for l = 0, m = 0, \\ λ_{l, m} = \frac{1}{2} & for l = 0, m \neq 0 or l \neq 0, m = 0, \\ λ_{l, m} = 1 & for l \neq 0, m \neq 0 . \end{array}

(8)

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a_{l, m} = \frac{2}{π^{2}} \int_{0}^{2 π} \int_{0}^{π} F (θ, ϕ) \cos (2 l θ) \cos (m ϕ) d θ d ϕ, b_{l, m} = \frac{2}{π^{2}} \int_{0}^{2 π} \int_{0}^{π} F (θ, ϕ) \cos (2 l θ) \sin (m ϕ) d θ d ϕ, c_{l, m} = \frac{2}{π^{2}} \int_{0}^{2 π} \int_{0}^{π} F (θ, ϕ) \sin (2 l θ) \cos (m ϕ) d θ d ϕ, d_{l, m} = \frac{2}{π^{2}} \int_{0}^{2 π} \int_{0}^{π} F (θ, ϕ) \sin (2 l θ) \sin (m ϕ) d θ d ϕ .

(9)

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F (θ, ϕ) = \frac{1}{2 π^{2}} + \frac{1}{2} a_{1, 0} \cos (2 θ) + \frac{1}{2} a_{0, 2} \cos (2 ϕ) + c_{1, 1} \sin (2 θ) \cos (ϕ) + a_{1, 2} \cos (2 θ) \cos (2 ϕ) .

(10)

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{\tilde{P}}_{\pm} = {\tilde{P}}_{\pm}^{s} \times \frac{π^{2}}{8} (\frac{2}{π^{2}} - a_{1, 0} - (a_{0, 2} - a_{1, 2})) + {\tilde{P}}_{\pm}^{p 1} \times \frac{π^{2}}{4} (\frac{2}{π^{2}} + a_{1, 0}) + {\tilde{P}}_{\pm}^{p 2} \times \frac{π^{2}}{8} (\frac{2}{π^{2}} - a_{1, 0} + (a_{0, 2} - a_{1, 2})) + {\tilde{P}}_{\pm}^{p 3} \times \frac{π^{2}}{2} c_{1, 1},

(11)

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{\tilde{P}}_{\pm}^{s} = \frac{k_{\pm}^{2} \cos (α)}{π} \times \frac{3}{8} \frac{1}{k_{0} k_{z, 0}} \frac{{| 1 + r_{\mp}^{s} \exp (2 j k_{z, 0} h_{0 \mp}) |}^{2}}{{| 1 - r_{+}^{s} r_{-}^{s} \exp (2 j k_{z, 0} h_{0}) |}^{2}} T_{\pm}^{s}, {\tilde{P}}_{\pm}^{p 1} = \frac{k_{\pm}^{2} \cos (α)}{π} \times \frac{3}{8} \frac{k_{∥}^{2}}{k_{0}^{3} k_{z, 0}} \frac{{| 1 + r_{\mp}^{p} \exp (2 j k_{z, 0} h_{0 \mp}) |}^{2}}{{| 1 - r_{+}^{p} r_{-}^{p} \exp (2 j k_{z, 0} h_{0}) |}^{2}} T_{\pm}^{p}, {\tilde{P}}_{\pm}^{p 2} = \frac{k_{\pm}^{2} \cos (α)}{π} \times \frac{3}{8} \frac{k_{z, 0}}{k_{0}^{3}} \frac{{| 1 - r_{\mp}^{p} \exp (2 j k_{z, 0} h_{0 \mp}) |}^{2}}{{| 1 - r_{+}^{p} r_{-}^{p} \exp (2 j k_{z, 0} h_{0}) |}^{2}} T_{\pm}^{p}, {\tilde{P}}_{\pm}^{p 3} = - \frac{k_{\pm}^{2} \cos (α)}{π} \times \frac{3}{8} \frac{k_{∥}}{k_{0}^{3}} \frac{1}{{| 1 - r_{+}^{p} r_{-}^{p} \exp (2 j k_{z, 0} h_{0}) |}^{2}} T_{\mp}^{p} T_{\pm}^{p} .

(12)

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v_{x} = \frac{π^{2}}{8} (\frac{2}{π^{2}} - a_{1, 0} + (a_{0, 2} - a_{1, 2})), v_{z} = \frac{π^{2}}{4} (\frac{2}{π^{2}} + a_{1, 0}), v_{x, z} = \frac{π^{2}}{2} c_{1, 1} .

(13)

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{\tilde{P}}_{\pm} = {\tilde{P}}_{\pm}^{s} \times (1 - v_{x} - v_{z}) + {\tilde{P}}_{\pm}^{p 1} \times v_{z} + {\tilde{P}}_{\pm}^{p 2} \times v_{x} + {\tilde{P}}_{\pm}^{p 3} \times v_{x, z},

(14)

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F (θ, ϕ) = \frac{1}{N} \times \sum_{i = 1}^{N} δ (v - v_{i}) \sin (θ) = \frac{1}{N} \times \sum_{i = 1}^{N} δ (θ - θ_{i}) δ (ϕ - ϕ_{i}) .

(15)

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v_{x} = \frac{1}{N} \sum_{i = 1}^{N} \sin^{2} (θ_{i}) \cos^{2} (ϕ_{i}), v_{z} = \frac{1}{N} \sum_{i = 1}^{N} \cos^{2} (θ_{i}), v_{x, z} = \frac{1}{N} \sum_{i = 1}^{N} \sin (2 θ_{i}) \cos (ϕ_{i}) .

(16)

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Lingjie Fan, Maoxiong Zhao, Jiao Chu, Tangyao Shen, Minjia Zheng, Fang Guan, Haiwei Yin, Lei Shi, Jian Zi. Full description of dipole orientation in organic light-emitting diodes[J]. Chinese Optics Letters, 2023, 21(2): 022601

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