Analysis of heat diffusion considering driving images on 6-inch flexible AMOLED display

We report the heat diffusion on flexible active-matrix organic light-emitting diode (AMOLED) displays. Two-dimensional heat diffusion is used for the heat conduction and convection analysis, generated on the surface of a flexible AMOLED display. The heat diffusion parameters and the time constant are studied in terms of the driving conditions of a 6-inch flexible AMOLED display. The temperature distribution on the screen is obtained by applying heat diffusion using the finite difference method (FDM) with an FPGA driving board. We can predict temperature more precisely by calculating temperature changes according to the images. The proposed method improves the accuracy of predicting the temperature. The average and standard deviation of the temperature error (TER) are ∼0.5°C and ∼0.5°C for the proposed method, respectively. For the conventional method, the values are ∼4.5°C and ∼0.7°C, respectively, neglecting the increase in temperature based on the images. This method can be used in compensation technology for OLEDs and thin film transistors (TFTs) that require accurate temperature distribution on the screen.


Introduction
Flexible active-matrix organic light-emitting diode (AMOLED) displays offer various benefits such as pure black, fast response, wide viewing angle, rich color and flexibility [1]. However, unlike liquid crystal display (LCD), it is difficult to avoid the burn-in phenomenon because of the short lifetime of AMOLED displays [2]. The burn-in behavior is a key issue in AMOLED displays, especially in blue OLEDs. Note that the red and green OLEDs with phosphorescence materials have a relatively long lifetime [3]. In addition, out-coupling technology has been developed to reduce current density by extracting the light dissipating inside AMOLED displays [4,5].
The OLED degradation can be compensated by correcting input data using the data driver IC for OLED driving [6]. By sensing the TFTs and OLEDs performances periodically, OLED degradation can be compensated at a pixel level [6]. In this case, the number of data lines is too many and the same number of ADC (analog to digital converter) is needed for sensing. This can be used for OLED TVs, but it is difficult to apply it to mobile products that are sensitive to electronic components and power consumption [7].
Therefore, the prediction of OLED degradation without sensing the currents can be possible using accumulated data in mobile products. It is necessary to store the data for the current density and temperature that affect the OLED lifetime [8]. The current density of a pixel can be decided from the data based on input images. However, the temperature of a flexible AMOLED display is affected by various factors such as environmental temperature, heat from electronic components, and driving images. These influences should be reflected in storing data. Note that the environmental temperature can be easily obtained by the sensors built into the product. Note also that the temperature increase due to heating of the component and wire resistance can be checked through preliminary evaluations. The images could be affected by the current flow through the thin film transistors (TFTs) and OLEDs. Therefore, the temperature on the surface of an AMOLED display needs to be predicted.
In this paper, the surface temperature is studied considering the images using the heat diffusion equation in a flexible AMOLED display. The two-dimensional equation for the surface temperature is obtained to determine the heat conduction and convection on the surface of a flexible AMOLED display. The heat diffusion parameters and the time constant required for utilizing the equation are extracted according to the driving conditions of the AMOLED display. The temperature distribution is predicted by applying the heat diffusion to the finite difference method (FDM) using FPGA (field programmable gate array) driving board. Note that FDM is widely used to analyze heat diffusion because it is used to solve differential equations that are included in the heat diffusion equation [9,10]. Compared to the conventional method that does not consider the change in temperature by images, the proposed method can predict a more accurate temperature on the display surface. This method can be used for the compensation algorithms for OLEDs and TFTs that need accurate temperature in a pixel.

Fabrication and equipment
We fabricated a 6-inch flexible AMOLED display using low-temperature poly-Si oxide (LTPO) TFT on a polyimide (PI) substrate with the 7 TFTs and 1 capacitance (7T1C) pixel architecture with the conventional RGB structure [11,12]. The AMOLED display resolution is 1228 × 2700, and the OLED efficiencies of red, green, and blue are ∼ 49, ∼ 150, and ∼ 8 cd/A, and the subpixel currents of red, green, and blue are ∼ 24, ∼ 25, and ∼ 53 nA at 650 nits, respectively. The cross-sectional view is shown in Figure 1(a), consisting of cover glass, acrylic OCA, polarizer, AMOLED panel, back-plate, and heat dissipation sheet, a 0.23 mm thick composite material containing copper to enhance the heat diffusion. Thermal imaging camera FLIR ONE PRO was used to measure the surface temperature distribution. When monitoring the temperature at a specific location for a long time, GRAPHITEC's midi LOGGER GL800, a contact-type thermometer, was used. The FPGA (Xilinx Kintex-7) was used to count and store input data and perform FDM calculations. Figure 1(b) shows a unit cell where a cluster of pixels array has TFTs and OLEDs in FDM calculation. Note that on the surface of a flexible AMOLED display, heat diffuses horizontally by conduction and vertically by convection, and the influence of convection in contact with air is much smaller than that of conduction. The accuracy of calculation can be improved by decreasing the unit cell size for calculating FDM, but the hardware burden will increase. Therefore, an appropriate unit cell area should be selected.

Results and discussion
Figure 2(a) shows the relationship between the changes in average temperature and normalized current increase compared to black (G0) image when driving 650 nits in a 6-inch flexible AMOLED display. It is noted that the average temperature difference between G0 and white (G255) is ∼ 8°C. In addition, the increase in the average temperature in the case of G186 and WB images is similar Here, T refers to temperature and x, y represent the position of the unit cell. Note that a cluster of pixel array has TFTs and OLEDs, which is used for FDM calculation. Note that on the surface of the flexible AMOLED display, heat diffuses horizontally by conduction and vertically by convection, and the influence of convection in contact with air is much smaller than that of conduction. since the current increase is almost the same. However, the temperature distribution is significantly different as shown in Figure 2(b,c): Figure 2(b) shows better uniformity compared to Figure 2(c). Note that the bright parts show high temperatures while the dark ones show relatively low temperatures. Note also that the bottom area of the display has a relatively higher temperature due to the heat from the driver IC regardless of input image. This can be ignored because all driving images have the same influence. Figure 2(c) shows a large temperature difference between the upper region (G255) and the lower region (G0). Unlike the input image, the interface between the upper and the lower regions shows a gradual change due to heat diffusion. Therefore, heat diffusion should be considered in predicting the temperature. The previous image can also affect the temperature. Therefore, to predict temperature accurately, heat diffusion and temperature change over time should be considered.
In this paper, the heat diffusion equation is used for the diffusion over the pixels and time. Using the energy conservation law, Equation (1) can be written by subtracting the output energy (E out ) from the input energy (E in ) and adding the generated energy (E gen ) equals to the storage energy (E st ) [13]: Assuming a two-dimensional AMOLED display, the energy conservation law is modified as follows. On the surface of the flexible AMOLED display, heat diffusion takes place horizontally by conduction and vertically by convection. In an arbitrary area A with circumference S, adding an input heat for t is equal to the heat increase for the area A. The heat diffusion equation can be expressed as Equation (2) [13]: where , da is the differential area, and d s is the vertical heat differential. The environmental temperature T env is set to 0 to easily define the increase in temperature.
The t is converged to 0, so the right term is converted into an integral form over time. Using the relationship between the rate of energy generation per unit volume and temperature, the equation can be changed as follows [13,14]: where x and y represent coordinates, k and h are redefined as k and h using the relationship between the rate of energy generation per unit volume and temperature. This form makes heat diffusion analysis easy because the temperature is a more convenient value for display engineering. In other words, the physical values such as weight, specific heat, mass density, etc. of each component of the AMOLED display do not need to be considered. Temperature increase T from driving images can be defined using display current, which can be calculated using the relationship between the OLED efficiencies of red, green, and blue and input data for each sub-pixel [8]. The relationship between the display current and the temperature increase used in this paper is shown in Figure 2(a). It can be expressed by the following equation, T = −0.85I 2 + 9.44I, where I is the average current increase compared to that of the driving G0 image.
To calculate the temperature using this equation, it is necessary to extract parameters (k , h , ρ ) suitable for the display evaluation. As described in Figure 1(a), a flexible AMOLED display consists of various components. The general method is to use parameters suitable for each component. However, this approach increases the inaccuracy due to the complexity of integrating the influence of each component. In this paper, we introduce a simple method to have integrated parameters suitable for a flexible AMOLED display.
To obtain horizontal and vertical diffusion parameters k and h , the steady state condition was used without time dependence. Then, Equation (3) can be expressed as Equation (4) below [13]: When the image shown in Figure 3(a) is driven in flexible AMOLED, heat diffusion takes place with no change over time. The heat diffusion takes place only in the x-axis when G0 and G255 are respectively arranged on both half sides of the display. When Figure 3(a) image is driven in the flexible AMOLED display, Figure 3(b) shows the photograph of temperature distribution and Figure 3(c) shows the measured result and its regression of temperature distribution according to the x-axis. Note that the temperature increase is zero at x = 0. From comparing the regression curve of temperature distribution and the solution of Equation (4), we can find h and k regarding the AMOLED display. In this work, h is 1.056 and k is 120,915 L 2 P , where L P represents one pixel length. The h has no unit, the unit of k is m 2 and pixel size can be achieved with pixel length L P [14].
The time constant, indicating the degree of change over time, can be extracted using the temperature profile observed while transitioning from G0 to G255 image, as shown in Figure 4(a). In this case, it is possible to simplify the heat diffusion equation using a solid image that does not cause heat diffusion. The simple form removing the diffusion parameters is as follows [13]: The measured temperature change over time when driving Figure 4(a) images and sequence is shown in Figure 4(b). Figure 4(c) shows the measured result and its regression curve of the temperature change. In the same way as the diffusion parameters, we can find that ρ is 195 sec in this work [14] from comparing the regression and the solution of Equation (5). Note that in Figure 4(b) the equilibrium time is relatively large. If images vary dynamically, it is difficult to properly reflect the temperature change when the images change. On the other hand, fixed images mainly used in mobile and IT applications are considered in this article to assess the temperature effect.
For FDM application, the heat diffusion equation (3) is modified using the Taylor series [14]: Here, i represents the peripheral positions (up, down, left, and right) of the unit cell area when the flexible AMOLED display is divided as shown in Figure 1(b). The length ( x) of unit cell is selected as 64 pixels to minimize the error and capacity of the FPGA used. The time interval ( t) is selected as 1/100 level of the time constant to minimize the error in this work.  Note that the scale bar shows the temperature. The temperature error, TER, is defined as the measured temperature minus the simulated temperature. The TER distribution between the conventional and the proposed method for (e) 1 min and (f) 15 min driving. Figure 5(a-f) shows the comparison between the conventional and current method using the heat diffusion equation (6). Note that the conventional method does not take into account the changes according to driving images. The maximum brightness is 650 nits, and the evaluation is carried out at room temperature.
The temperature increase caused by electronic components and wire resistance is reflected in the display through pre-evaluation. In order to determine the difference in the driving time, the evaluations are conducted respectively for 1 and 15 min. Figure 5(a) shows the driving image selected as a complex image so that various heat diffusions take place inside the image. Figure 5(b,c) shows the simulation result of the conventional method and the proposed method, respectively, while Figure 5(d) indicates the measured result for driving 15 min after the transition from G0 to the evaluation image. It can be seen that the simulation result in Figure 5(c) is consistent with the measured result in Figure 5(d). Note that the lower regions of Figure 5(b,c,d) are relatively brighter because of the driver IC at the bottom.
The simulation and measurement results are compared as follows. First, the screen of the flexible AMOLED display is equally divided into 737 regions. Note that a unit cell has 64 × 64 pixels and a whole screen has 737 regions. The difference between measurement and simulation for each region is defined as temperature error (TER, measured minus the simulated temperature). Figure 5(e) shows the TER comparison between the conventional and proposed method for driving 1 min after the transition from G0 to the evaluation image. Note that 1 min driving is not enough time to reflect the temperature change. But the conventional method has an average TER of ∼ 1.0°C and standard deviation TER of ∼ 0.4°C. Since the conventional method does not consider the temperature effect of images, it can be seen that TER consists of all positive values and can be ∼ 2.0°C in bright areas. However, the proposed method has an average TER of ∼ −0.3°C and a standard deviation TER of ∼ 0.3°C. It reflects the heat diffusion depending on the image. This lowers the TER average to the extent that a negative value is possible. Figure 5(f) shows the TER comparison between the conventional and the proposed method when driving 15 min after the transition from G0 to the evaluation image. The conventional method has an average TER of ∼ 4.5°C and standard deviation TER of ∼ 0.7°C, but the proposed method yields average TER of ∼ 0.5°C and standard deviation TER of ∼ 0.5°C.
It can be seen that the average and standard deviation of TER increase when the driving time increases to 15 min compared to 1 min. For the conventional method, the driving time, temperature and TER also increase. The maximum TER is ∼ 8°C, which increases significantly compared to the average TER. In the proposed method, the time constant is reflected in the heat diffusion so that the temperature change over time can be considered, indicating that the TER is more accurate.
The proposed method can reflect the temperature change caused by heat diffusion and time variance according to the driving images. This can significantly improve the accuracy of temperature prediction. This method can be used in compensation technology for TFTs and OLEDs that require accurate temperature information.

Conclusion
We study the surface temperature of AMOLED displays in terms of driving images using heat diffusion. It is modified in two-dimension to reduce prediction errors caused by the complex AMOLED display structure. The heat diffusion parameters and the time constant required for utilizing the diffusion equation are extracted using the driving conditions of a 6-inch flexible AMOLED display. The parameters are extracted based on temperature for display engineering. To obtain horizontal and vertical diffusion parameters k and h , the diffusion condition in the steady state is used without time dependence. In the case of time constant, no diffusion condition is used with a solid image that does not cause heat diffusion.
The temperature distribution is predicted by applying heat diffusion to FDM using the FPGA driving board. The average and standard deviation of TER are improved to ∼ 0.5°C and ∼ 0.5°C for the proposed method, while for the conventional method the values are ∼ 4.5°C and ∼ 0.7°C. The proposed method can reflect the temperature change according to driving images, which can significantly improve the temperature accuracy. This method can accurately predict the surface temperature of flexible AMOLED displays according to the images.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Notes on contributors
Chang Hoon Jeon received his B.S. and M.S. degrees in radio wave engineering at Hanyang University in South Korea in 1999 and 2001, respectively. He is now a candidate for a Ph.D. degree at the Department of Information Display of Kyung Hee University and is working as Research Fellow in LG Display Co., Ltd. His main