Online proceedings - EDA Publishing Association

24-26 September 2008, Rome, ItalyxN’yW’ E’S’W’Gx’N’Gy’Gx’CGyS’E’N’W’ WE’NCSES’a) b) c)Fig 3. Models in 2D a) Finite differences grid b) Finite differences model c) Vector SUNRED modelThe description of the successive node reduction method can be found in our earlier publications such as [3] and [10].Transport equations (without Seebeck and Peltier terms):For the thermal field:j = σ e E(1)p = −σ ⋅ grad T(2)Continuity equations:div j = 0(3)∂Tdiv p = jE − c , (4)∂twhere j and p are the current and power density, E is theelectric field strength, T is the temperature, σ e and σ denotethe electric and thermal conductance, c is the volumetric heatcapacitance density. In this model the electrical capacity isdiscarded, because the electrical time-constants are muchsmaller than the thermal time-constants.SUNRED is using a Finite Differences Method (FDM)model [9], the FDM equations are the following (for steadystatesituation, neglecting capacitances) shown by Eq. (5)and (6).For the electrical field:UW'−UCUE'−UCUS '−UCσe+ σ ++2eσ2e 2xxyUN '−UCUB'−UCUT'−UC+ σe+ σ +2eσ2e 2yzz= 0(5)( UE'−Uσe24xTW'−TC+ σ2xTN'−TC+ σ2y22') ( UN '−US ') ( U+ σe+ σ2e4yTE'−TCTS'−TC+ σ + σ +22x yTB'−TCTT'−TC+ σ + σ = 022z zWT '−U24zwhere x, y, and z denote the size of a cell of the model grid(Fig. 3.a); E’, W’, S’, N’, T’, B’ are the East, West etc.neighboring nodes. After multiplication by the cell volumex×y×z and substitution of conductance we obtain for theelectrical field:112Gex( UW'−UC) +2Gex( UE'−UC) +11+2Gey( US '−UC) +2Gey( UN '−UC) +11+ G ( U −U) + G ( U −U) = 02ezB'and or the thermal field:G ( U12 ex1+21+2 y1+2 zE'Gx( TG ( TG ( TW 'S 'B'−U)C−TC) +−T) +−T+2Gez( UT '−U2 12C 2 ey N ' C1G ( )2 xTE'−TC+1CG ('− ) +2 yTNTC1C) + G ('− ) = 02 zTTTCC)+12G ( UezT 'B'−UC))22++(6)(7)(8)Mounting screwsComputerCoolant inletOLEDThermostatCold-plateCoolant outletFig 4. Measurement setup for measuring the I-V characteristics of OLEDsV. MEASUREMENT OPTIONSThermal and electrical measurements: Usual electricalcharacteristics of OLEDs (I-V characteristics) can be measuredwith conventional laboratory equipment. At our laboratorysuch measurements can be carried out in temperaturecontrolled environment, the device under test is attached to athermostated cold-plate. Our measurement setup is outlinedin Fig. 4.©EDA Publishing/THERMINIC 2008 237ISBN: 978-2-35500-008-9