PHYSICAL REVIEW APPLIED 10, 014023 (2018) Full Electrothermal OLED Model Including Nonlinear Self-heating Effects Axel Fischer, 1, * Manuel Pfalz, 1 Koen Vandewal, 1 Simone Lenk, 1 Matthias Liero, 2 Annegret Glitzky, 2 and Sebastian Reineke 1 1 Dresden Integrated Center for Applied Physics and Photonic Materials and Institute for Applied Physics, Technische Universität Dresden, Nöthnitzer Straße 61, 01187 Dresden, Germany 2 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin, Germany (Received 15 December 2017; revised manuscript received 2 May 2018; published 24 July 2018) Organic light-emitting diodes (OLEDs) are widely studied semiconductor devices for which a simple description by a diode equation typically fails. In particular, a full description of the current-voltage rela- tion, including temperature effects, has to take the low electrical conductivity of organic semiconductors into account. Here, we present a temperature-dependent resistive network, incorporating recombination as well as electron and hole conduction to describe the current-voltage characteristics of an OLED over the entire operation range. The approach also reproduces the measured nonlinear electrothermal feed- back upon Joule self-heating in a self-consistent way. Our model further enables us to learn more about internal voltage losses caused by the charge transport from the contacts to the emission layer which is characterized by a strong temperature-activated electrical conductivity, finally determining the strength of the electrothermal feedback. In general, our results provide a comprehensive picture to understand the electrothermal operation of an OLED which will be essential to ensure and predict especially long-term stability and reliability in superbright OLED applications. DOI: 10.1103/PhysRevApplied.10.014023 I. INTRODUCTION Organic light-emitting diodes (OLEDs) have become the standard technology for smartphone displays and will also take the lead in the TV market soon [1,2]. New appli- cations requiring considerably higher brightnesses than displays (>100 cd/m 2 ) or lighting (>1000 cd/m 2 ) are envi- sioned. In particular, signaling in the automobile sector is attractive, as new design possibilities allow clearly visible elements to be incorporated, helping to make cars more distinguishable and appealing. However, the use of OLEDs as tail lights, turn lights, or even break lights involves super-bright operation (>10 000 cd/m 2 ) in order to fulfill international regulations. OLEDs are highly attractive as desired red-orange devices have become very efficient. The required level of luminance is achieved and at the same time they are much more stable than, for example, blue OLEDs since red OLEDs do not suffer from high triplet energies [3]. Another issue accompanying high brightness is the strongly enhanced power dissipation, leading to Joule self- heating [4,5]. Apart from a possible degradation of the OLED due to warming, self-heating has the negative effect that the lateral brightness becomes very inhomogeneous, canceling out the benefits of the OLED technology being a * Corresponding author: axel.fischer@iapp.de; www.iapp.de truly scalable area light source [6]. Furthermore, OLEDs tend to show a very strong electrothermal feedback, which involves a positive feedback loop between cur- rent flow, power dissipation, and temperature increase [7]. This behavior is due to the widely observed temperature- activated conductivity in organic semiconductor devices which is also the case for OLEDs [8–10]. If self-heating comes into play, the steady increase of the current flow and the power dissipation, when driven at a constant volt- age, can even lead to an abrupt destruction of a device by thermal runaway [11]. The use of a constant current operation, or a series resistor, can prevent the underly- ing thermal-switching process, but not the fact that OLED emission becomes inhomogeneous at high injection cur- rents. Besides that, strong electrothermal feedback eventu- ally leads to a current-voltage regime of S-shaped negative differential resistance (S NDR) [7,11], which increases the complexity of predicting the device’s behavior [12]. Another difficulty OLED technology faces for super- bright applications, besides internal Joule heating, is the external variation of the ambient temperature, which can change the driving current and the light output as well. Thus, an accurate and reliable model to understand the current-voltage-temperature relation of an OLED is essen- tial for further progress in this field. Here, we will introduce a physics-motivated explicit description of OLED current-voltage curves at various 2331-7019/18/10(1)/014023(12) 014023-1 © 2018 American Physical Society