^{1}and Stephen R. Forrest

^{1,2,a)}

### Abstract

We use a general transmission matrix formalism to determine the thermal response of organic light-emitting diodes(OLEDs) under high currents normally encountered in ultra-bright illumination conditions. This approach, based on Laplace transforms, facilitates the calculation of transient coupled heat transfer in a multi-layer composite characteristic of OLEDs.Model calculations are compared with experimental data on 5 cm × 5 cm green and red-emitting electrophosphorescent OLEDs under various current drive conditions. This model can be extended to study other complex optoelectronic structures under a wide variety of conditions that include heat removal via conduction,radiation, and convection. We apply the model to understand the effects of using high-thermal-conductivity substrates, and the transient thermal response under pulsed-current operation.

The authors thank Mr. Kevin Bergmann for helpful discussions. We are grateful to the U.S. Department of Energy, Energy Frontier Center at the University of Southern California (Award No. DE-SC0001011, XQ, experiment, analysis) and the Universal Display Corp. (SRF, analysis) for financial support of this work. We also thank a Small Business Innovation Research program subcontract funded by the U.S. Department of Energy through the Universal Display Corporation (SRF, experimental methods) for partial financial support.

I. INTRODUCTION

II. THEORY

III. EXPERIMENT

IV. RESULTS

V. DISCUSSION

VI. CONCLUSIONS

### Key Topics

- Organic light emitting diodes
- 19.0
- Convection
- 15.0
- Thermal convection
- 14.0
- Multilayers
- 13.0
- Thermal models
- 13.0

##### H01L27/15

##### H01L27/28

##### H01L33/00

##### H01L51/50

## Figures

(a) Heat flow for layers in series. Here, *T* _{1} and *T* _{2} denote the Laplace transformation of ambient temperatures on both sides of the composite; and are the thermal input and outflow of material *i*(*j*). Here, is based on the continuity of the interface heat flux between adjacent layers. (b) Heat flow for layers in parallel, where denote input heat flux carried by two thermal dissipation modes, and is the total heat flux into material, *i*.

(a) Heat flow for layers in series. Here, *T* _{1} and *T* _{2} denote the Laplace transformation of ambient temperatures on both sides of the composite; and are the thermal input and outflow of material *i*(*j*). Here, is based on the continuity of the interface heat flux between adjacent layers. (b) Heat flow for layers in parallel, where denote input heat flux carried by two thermal dissipation modes, and is the total heat flux into material, *i*.

(a) Illustration of the series and parallel heat pathways for an OLED used in setting up the matrix product. The matrix product describing the thermal flux to the left is , and is composed of transport in air, glass substrate, and ITO anode in sequence, and is the product for thermal transport to the right, composed of the organic layer, metal cathode, air gap, encapsulation, and air in sequence. (b) The construction of , where and are the source and ambient temperatures, respectively, and are the heat fluxes dissipated through the left and right surfaces, and is the total thermal power flow. The conduction matrices for the organic, metal cathode, and air layers are multiplied in sequence while radiation is incorporated as a parallel pathway.

(a) Illustration of the series and parallel heat pathways for an OLED used in setting up the matrix product. The matrix product describing the thermal flux to the left is , and is composed of transport in air, glass substrate, and ITO anode in sequence, and is the product for thermal transport to the right, composed of the organic layer, metal cathode, air gap, encapsulation, and air in sequence. (b) The construction of , where and are the source and ambient temperatures, respectively, and are the heat fluxes dissipated through the left and right surfaces, and is the total thermal power flow. The conduction matrices for the organic, metal cathode, and air layers are multiplied in sequence while radiation is incorporated as a parallel pathway.

(Color) (a) Schematic structure of small-area Ir(ppy)_{3} devices: glass (1 mm)/ITO (120 nm)/organic layers (105 nm)/Al cathode (100 nm). (b) Patterning of the ITO and Al anode and cathode stripes, each 1 mm wide. (c) Thermal images of the Ir(ppy)_{3} device under a fixed voltage of 10 V (corresponding to a current density of 1 A/cm^{2}) after 10, 20, and 30 s operation following the onset of the voltage ramp. The dashed square indicates the device location.

(Color) (a) Schematic structure of small-area Ir(ppy)_{3} devices: glass (1 mm)/ITO (120 nm)/organic layers (105 nm)/Al cathode (100 nm). (b) Patterning of the ITO and Al anode and cathode stripes, each 1 mm wide. (c) Thermal images of the Ir(ppy)_{3} device under a fixed voltage of 10 V (corresponding to a current density of 1 A/cm^{2}) after 10, 20, and 30 s operation following the onset of the voltage ramp. The dashed square indicates the device location.

(Color) (a) Schematic structure of large-area devices: glass (0.7 mm)/indium tin oxide (120 nm)/organic layers (120 nm)/Al cathode (100 nm)/air gap (30 μm)/glass encapsulation (0.7 mm). (b) Illustration of the patterns used for the ITO and Al anode and cathode contacts, both 5 cm wide. (c) Thermal images of the large-area green device under a fixed voltage of 7 V (or a current density of 3.4 mA/cm^{2}) after 60, 120, 180, and 240 s operation following the onset of the voltage ramp. The dashed square indicates the device location.

(Color) (a) Schematic structure of large-area devices: glass (0.7 mm)/indium tin oxide (120 nm)/organic layers (120 nm)/Al cathode (100 nm)/air gap (30 μm)/glass encapsulation (0.7 mm). (b) Illustration of the patterns used for the ITO and Al anode and cathode contacts, both 5 cm wide. (c) Thermal images of the large-area green device under a fixed voltage of 7 V (or a current density of 3.4 mA/cm^{2}) after 60, 120, 180, and 240 s operation following the onset of the voltage ramp. The dashed square indicates the device location.

The external quantum (*EQE*) and power efficiencies (*PE*) vs the drive current density of large-area (a) green, and (b) red electrophosphorescent OLEDs (PHOLEDs).

The external quantum (*EQE*) and power efficiencies (*PE*) vs the drive current density of large-area (a) green, and (b) red electrophosphorescent OLEDs (PHOLEDs).

(a) Current density vs voltage (*J-V*), and (b) luminance vs current density (*L-J*) characteristics of large-area green (squares) and red (dots) PHOLEDs.

(a) Current density vs voltage (*J-V*), and (b) luminance vs current density (*L-J*) characteristics of large-area green (squares) and red (dots) PHOLEDs.

Transient temperature response (open symbols) measured using infrared imaging at different voltages for large-area (a) green, and (b) red PHOLEDs following the onset of the voltage step. The results are compared with transmission matrix model calculations (solid lines). The corresponding drive currents and other operating parameters for these conditions are provided in Tables I and II, with the parameters used for the calculations provided in Table III.

Transient temperature response (open symbols) measured using infrared imaging at different voltages for large-area (a) green, and (b) red PHOLEDs following the onset of the voltage step. The results are compared with transmission matrix model calculations (solid lines). The corresponding drive currents and other operating parameters for these conditions are provided in Tables I and II, with the parameters used for the calculations provided in Table III.

Calculated temperature gradient across the ITO and glass layers for heat fluxes of Q_{1} = 197 W/m^{2}, Q_{2} = 270 W/m^{2}, Q_{3} = 353 W/m^{2}, and Q_{4} = 447 W/m^{2} generated in the PHOLED light emitting layer (EML). The surface temperatures at each heat flux are obtained from measurements using infrared imaging. The small thermal gradient suggests that the thermal measurements made at the glass surface are an accurate determination of the temperature of the EML.

Calculated temperature gradient across the ITO and glass layers for heat fluxes of Q_{1} = 197 W/m^{2}, Q_{2} = 270 W/m^{2}, Q_{3} = 353 W/m^{2}, and Q_{4} = 447 W/m^{2} generated in the PHOLED light emitting layer (EML). The surface temperatures at each heat flux are obtained from measurements using infrared imaging. The small thermal gradient suggests that the thermal measurements made at the glass surface are an accurate determination of the temperature of the EML.

Transient temperature response (open symbols) measured using infrared imaging at different voltages for large-area (a) green, and (b) red PHOLEDs following the end of the drive voltage step at time, *t* = 0. The devices were operated at a fixed voltage until temperature equilibrium was reached. The results are compared with transmission matrix model calculations (solid lines). The corresponding drive currents and other operating parameters for these conditions are provided in Tables I and II, with the parameters used for the calculations provided in Table III.

Transient temperature response (open symbols) measured using infrared imaging at different voltages for large-area (a) green, and (b) red PHOLEDs following the end of the drive voltage step at time, *t* = 0. The devices were operated at a fixed voltage until temperature equilibrium was reached. The results are compared with transmission matrix model calculations (solid lines). The corresponding drive currents and other operating parameters for these conditions are provided in Tables I and II, with the parameters used for the calculations provided in Table III.

Calculated PHOLED temperature due to convective losses as a function of air conductivity at input heat fluxes of 100, 200, 500, and 1000 W/m^{2}.

Calculated PHOLED temperature due to convective losses as a function of air conductivity at input heat fluxes of 100, 200, 500, and 1000 W/m^{2}.

Calculated PHOLED temperature (open dots) as a function of thermal input power for devices using glass, sapphire, and silicon substrates. The results are compared with the finite element analysis (solid dots). Where only matrix results are shown (open symbols), the differences with FEA calculations are negligible on the scale of the plot.

Calculated PHOLED temperature (open dots) as a function of thermal input power for devices using glass, sapphire, and silicon substrates. The results are compared with the finite element analysis (solid dots). Where only matrix results are shown (open symbols), the differences with FEA calculations are negligible on the scale of the plot.

Temporal response of the PHOLED temperature (solid dots) at various pulse widths of 1, 5, and 10 ms under a fixed, ultrahigh thermal input power of 10^{6} W/m^{2}. Linear fits are displayed as solid lines. The physical and thermal parameters are the same as for the large-area devices. Now, , whereas is used here compared to that of the large-area devices due to the short pulse duration.

Temporal response of the PHOLED temperature (solid dots) at various pulse widths of 1, 5, and 10 ms under a fixed, ultrahigh thermal input power of 10^{6} W/m^{2}. Linear fits are displayed as solid lines. The physical and thermal parameters are the same as for the large-area devices. Now, , whereas is used here compared to that of the large-area devices due to the short pulse duration.

Heat transfer for the multilayer composite PHOLED is calculated using different polynomial expansion orders (*n* = 6, 7, and 8). Note the convergence of the solutions for *n* = 6 and *n* = 7, whereas the solution becomes unstable at *n* = 8.

Heat transfer for the multilayer composite PHOLED is calculated using different polynomial expansion orders (*n* = 6, 7, and 8). Note the convergence of the solutions for *n* = 6 and *n* = 7, whereas the solution becomes unstable at *n* = 8.

## Tables

Summary of efficiency and thermal parameters of the large-area green PHOLED.

Summary of efficiency and thermal parameters of the large-area green PHOLED.

Summary of efficiency and thermal parameters of the large-area red PHOLED.

Summary of efficiency and thermal parameters of the large-area red PHOLED.

Summary of the thermal parameters used in modeling.

Summary of the thermal parameters used in modeling.

Roots of the truncated denominator polynomial.

Roots of the truncated denominator polynomial.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content