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Analysis of the emission profile in organic light-emitting devices

B. Perucco, N. A. Reinke, D. Rezzonico, M. Moos, and B. Ruhstaller

Open Access Open Access

Abstract

In this paper, numerical algorithms for extraction of opto-electronic material and device parameters in organic light-emitting devices (OLEDs) are presented and tested for their practical use. Of particular interest is the extraction of the emission profile and the source spectrum. A linear and a nonlinear fitting method are presented and applied to emission spectra from OLEDs in order to determine the shape of the emission profile and source spectrum. The motivation of the work is that despite the existence of advanced numerical models for optical and electronic simulation of OLEDs, their practical use is limited if methods for the extraction of model parameters are not well established. Two fitting methods are presented and compared to each other and validated on the basis of consistency checks. Our investigations show the impact of the algorithms on the analysis of realistic OLED structures. It is shown that both fitting methods perform reasonably well, even if the emission spectra to be analyzed are noisy. In some cases the nonlinear method performs slightly better and can achieve a perfect resolution of the emission profile. However, the linear method provides the advantage that no assumption on the mathematical shape of the emission profile has to be made.

© 2010 Optical Society of America

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Figures (13)
Fig. 1
Fig. 1 Open cavity organic LED (a) and cavity organic LED (b) with semi-sphere glass lens. θ stands for the observation angle.

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Fig. 2
Fig. 2 (a) Calculated emission spectra from an open cavity OLED and fitted emission spectra. The values in parenthesis show the combination of parameters used for the assumed emission profile to calculate the emission spectrum. The first value indicates the relative position, the second value stands for the width of the profile. (b) Comparison between the assumed and extracted emission profiles. The linear method was used here without incorporation of angular information.

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Fig. 3
Fig. 3 (a) Calculated emission spectra from a cavity OLED and fitted emission spectra. (b) Comparison between the assumed and extracted emission profiles. The linear method was used here and no angular information is considered.

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Fig. 4
Fig. 4 (a) Calculated emission spectra from a cavity OLED assuming delta-shaped emission profiles represented by the points. The lines represent the fitted emission spectra. (b) Comparison between the assumed and extracted emission profiles. The vertical points stand for the assumed positions of the delta-shaped emission profile. The linear method was used here and no angular information is considered.

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Fig. 5
Fig. 5 (a) Difference between the extracted emission profile for analyzed spectral data with and without angular information. The method used is the linear fit algorithm. (b) Radiance obtained by integration over the emission spectrum for each angle. Calculated emission intensities using the dipole model in combination with the assumed (c) and extracted emission profile (d).

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Fig. 6
Fig. 6 (a) Comparison between the extracted emission profiles where a priori one knows the shape of the source spectrum and where this information is left as another degree of freedom. (b) The extracted source spectrum by the linear fitting method in comparison to the assumed. The method used is the linear fitting algorithm and angular information is incorporated.

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Fig. 7
Fig. 7 (a) Fitted emission spectrum compared to the emission spectrum calculated by the assumed emission profiles. (b) Comparison between the assumed and extracted emission profiles of two emitters. The method used is the linear algorithm and no angular information is incorporated.

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Fig. 8
Fig. 8 (a) Extracted emission profiles where different signal to noise ratios (s/n) have been assumed compared to the assumed emission profile. The method used is the linear fitting method. (b) Relative error between the extracted and assumed emission profile as a function of the signal-to-noise ratio. The signal-to-noise ratio is defined as the maximum emission intensity value divided by the standard deviation of the noise.

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Fig. 9
Fig. 9 (a) Emission spectra resulting from the extracted emission profile and assumed. (b) Comparison between the assumed and extracted emission profiles of a cavity OLED where the nonlinear fitting algorithm is used and no angular information is considered.

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Fig. 10
Fig. 10 (a) The difference between the extracted emission profile and assumed. The method used is the nonlinear fit algorithm with incorporation of angular information. (b) The radiance obtained by integration over the emission spectrum for each angle. Calculated emission intensities using the dipole model in combination with the assumed (c) and extracted emission profile (d).

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Fig. 11
Fig. 11 (a) Assumed and extracted emission profile. (b) Comparison between the a priori known source spectrum and the extracted source spectrum by the nonlinear optimization method with incorporation of angular information.

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Fig. 12
Fig. 12 (a) Comparison between the assumed and extracted emission profiles for two emitters. The method used in this case is the nonlinear optimization method without incorporation of angular information. (b) Fitted emission spectrum compared to the emission spectrum used as data for the analysis and calculated by the assumed emission profiles.

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Fig. 13
Fig. 13 (a) Extracted emission profiles where different signal to noise ratios (s/n) have been assumed compared to the assumed emission profile. The method used is the nonlinear fitting method. (b) Relative error between the extracted and assumed emission profile as a function of the signal to noise ratio. The signal to noise ratio is defined as the maximum emission intensity value divided by the standard deviation of the noise.

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Equations (9)

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I f ( λ i )   =   ∑ j = 1 N I c ( λ i ,   δ j )   ⋅   P e ( δ j ) ,
I c   ( λ i ,   δ j )   =   I ( λ i ,   δ j )   ⋅   S ( λ i ) ,
r 1   ( λ i )   =   I f ( λ i )   −   I m   ( λ i ) .
r 1   ( λ i )   =   ∑ j = 1 N I c   ( λ i ,   δ j )   ⋅   P e ( δ j )   −   I m ( λ i ) .
A   =   ( I c   ( λ 1 ,   δ 1 ) I c   ( λ 1 ,   δ 2 ) … I c   ( λ 1 ,   δ N ) I c   ( λ 2 ,   δ 1 ) I c   ( λ 2 ,   δ 2 ) … I c   ( λ 2 ,   δ N ) … … … … I c   ( λ M ,   δ 1 ) I c   ( λ M ,   δ 2 ) … I c   ( λ M ,   δ N ) ) ,
r 2 s , p   ( λ i ,   θ l )   =   ∑ j = 1 N I c s , p   ( λ i ,   δ j k ,   θ l )   ⋅   P e ( δ j k )   −   I m s , p   ( λ i ,   θ l ) .
r 3 s , p   ( λ i ,   x ,   θ l )   =   I c s , p   ( λ i ,   x ,   θ l )   −   I m s , p   ( λ i ,   θ l ) .
f ( x )   =   1 2 Q M   ( ∑ s , p ∑ l = 1 Q ∑ i = 1 M r 3 s , p   ( λ i ,   x ,   θ l ) 2 ) 1 2 .
s / n   =   m a x ( I c ( λ i ,   θ l ) ) σ ,
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