Thermal properties of organic light-emitting diodes

1 LetterThermal properties of organic light - emitting diodesKevin J. Bergemanna, Robert Krasnyb, Stephen R. Forresta,c,d, aDepartment of Physics, University of Michigan, Ann Arbor, MI 48109, USAbDepartment of Mathematics, University of Michigan, Ann Arbor, MI 48109, USAcDepartment of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USAdDepartment of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109, USAarticle infoArticle history:Received 10 February 2012 Received in revised form 28 April 2012 Accepted 3 May 2012 Available online 18 May 2012 Keywords:LightingConvectionConductionRad iationabstractThermal management is important for the efficient operation of organic light -emittingdiodes (OLED, or PHOLED) at high brightness, with the device operating temperature influ-encing both lifetime and performance.

2 We apply a transmission-matrix approach to analyt-ically model the effects of Thermal conduction, convection and radiation on OLED temperature. The model predictions match experiment without requiring the use of fittingparameters. This allows for the simulation of the Thermal response of various device archi-tectures, materials combinations and environmental factors under a variety of operatingconditions. Using these simulations, we find that 87% of the heat is dissipated through theair space adjacent to the glass package cap. Furthermore, an air gap between the device cath-ode and cap provides a significant Thermal impedance. Minimizing the thickness ofthe inter-nal air gap can lead to nearly room temperature operation, even at very high brightness.

3 2012 Elsevier All rights high efficiency, large color gamut, and ease of man-ufacture of organic light - emitting diodes (OLEDs) have ledto their practical application in flat panel displays[1]. Morerecently, large-area white OLEDs have also been foundsuitable for lighting applications, with devices alreadyexceeding the efficiency of fluorescent panels[2,3].However, the lifetime of OLEDs operated at the surfaceluminance required for lighting (3000 cd/m2or higher) issensitive to temperature, with longer lifetime for adecrease of 10 K[4]. Accurate methods for modeling anddesigning temperature-tolerant device structures andluminaries, therefore, are , we apply a recently introduced matrix method toquantify one-dimensional heat-transfer from the active re-gion of a multi-layer, packaged OLED by fully describingthe effects of conduction, convection and radiation.

4 In anextension of previous work[5], we employ an analyticaltreatment for the effects of convection, allowing for anaccurate determination of the packaged device thermalproperties using no undetermined, free parameters. Withthis method, we describe approaches to minimizing thetemperature increase in high-brightness OLEDs that areof particular interest in solid-state lighting described previously[5,6], the transmission matrixapproach employs Laplace transforms of the heat transferequations. The solution to these equations through a singlelayer is represented using:bTi 1bQi 1"# cosh hi Zisinh hi sinh hi Zicosh hi "#bTibQi"# AiBiCiDi bTibQi"# T hi bTibQi"#; 1 wherebTi s andbQi s are the Laplace transforms of thetemperature and heat flux across theith layer.

5 Hi Liffiffiffiffiffiffiffiffiffiffiffiffiff iCis=Kipis the operational propagation constant,Kiis the Thermal conductivity of the film,Ciis its volumetricheat capacity,Liis the layer thickness,Zi ffiffiffiffiffiffiffiffiffiffiffiffiffif fiffiffiffiffiffiffi1= KiCis pisthe characteristic impedance, andAi,Bi,Ci, andDiare ma-trix elements that can be approximated by polynomial1566-1199/$ - see front matter 2012 Elsevier All rights Corresponding author at: Department of Electrical Engineering andComputer Science, University of Michigan, Ann Arbor, MI 48109, Forrest). organic Electronics 13 (2012) 1565 1568 Contents lists available atSciVerse ScienceDirectOrganic Electronicsjournal homepage: in the Laplace variable,s.

6 Multiple layers arehandled in one of two ways: a series of layers are treatedas the product of the transmission matrices for the severalfilms, while layers placed in parallel, or parallel heat chan-nels such as conduction and Thermal radiation, are treatedby assuming that the incident heat flux splits between thetwo independent channels with no flow between gives the final matrix as the sum of the channels:bQ1bQ2"# XibQ1ibQ2i"# XiAi=Bi 1=Bi1=Bi Ai=Bi bT1bT2"# 2 The parallel and series channels are then combined tomodel heat transfer through arbitrary, multilayer, one-dimensional systems. Full OLED modeling also requiresthe inclusion of interface resistance[7]and the treatmentof radiation and conduction as parallel heat transfer work treated convective transfer from thedevice surface as an additional conductive layer whosethickness was used as a free parameter to match the modelpredictions to the measured data, thereby limiting itspredictive capabilities.

7 Here, we model convection usingNewton s Law of Cooling[8,9],Qconv hDT, wherehisthe convective heat transfer coefficient of the ambient,andDTis the temperature difference between the surfaceand ambient. For forced convection,his a constant, whileit is temperature-dependent for natural convection[9].Now,Qconvis derived from the Nusselt number, Nu whoseform depends on the Thermal environment and experimen-tal geometry. For our analysis, we consider only the case ofconvection in the laminar flow regime from the upper sur-face of a heated, horizontally positioned packaged OLED. Inthis case[8],Nu hL=Kamb 0:54Ra1=4, whereLis thecharacteristic length of the system,Kambis the thermalconductivity of the convective medium, and Ra is the Ray-leigh number.

8 Other orientations and geometries may beconsidered by inserting the appropriate expression forNu. The Rayleigh number is then defined for a givenconvective medium, in our case air, as:Ra CPq2gb DT L3lKamb 3 whereCPis the heat capacity at constant pressure of theconvective medium,qis its density,lthe viscosity,gisthe acceleration due to gravity, andbis the gas volumeexpansion coefficient. From the foregoing, we find thatQ DT5/4, which renders the Laplace transform of thisequation mathematically intractable. However, the tem-perature rise for the devices studied is only 5 10 K evenunder the highest intensity operating conditions[4,5]. Thissmall temperature change allows us to set the Rayleighnumber to a constant, thereby linearizing Newton s Lawof Cooling and greatly simplifying the analysis.

9 The param-eters used to calculate this term and the values of Ra andNu are provided inTable 1. Applying this assumption fora simulated input power of 1 kW/m2, we find that thedevice reaches a steady-state temperature of approxi-mately 85 C. If we then change the Rayleigh number bytwo orders of magnitude in the model, the steady-statetemperature changes by only 2%, indicating that the modelis largely insensitive to these the analytical treatment of convection withthe matrix method allows us to derive an expression forthe device operating temperature,Tin, in terms of the inputheat flux,Qin, the heat transfer coefficienth, and the trans-mission matrix elements to yield:Tin B2Th ATBT Qin1 B2Th ATBT ABBB ATBT 4 whereAT,BandBT,Bdenote matrix elements correspondingto heat transfer through the top (T) and bottom (B) devicesurfaces (seeFig.)

10 1).We tested the model using a 25 cm2, glass-encapsu-lated, green phosphorescent OLED (Universal DisplayCorp., Ewing, NJ) whose structure is shown schematicallyinFig. 1. Its layer thicknesses and material thermalTable 1 Rayleigh and Nusselt numbers at (kg/m3)Volumeexpansion(1/K)Viscosity(kg/ ms)DT(K) 10 10 56 Rayleigh number 103 Nusselt number(horizontalplate) structure of an OLED. Heat,Qin, is input in the organicemission layer and then splits to flow toward the top,QTin, and bottom,QBin, device then the temperature of the active layer,TSandQSare the temperature and heat flow through the top device surface,Troomis the ambient temperature, andQTout,QBout, andQRadoutare the heatfluxes due to convection at the top surface, conduction at the bottomsurface, and radiation, Bergemann et Electronics 13 (2012) 1565 1568constants are given inTable 2.