The rapid advancement of technology in recent years has driven the demand for photothermal (PT) and electrothermal devices with ultra-large arrays. These devices find applications in a wide range of fields, including optics, electronics, and materials science. Accurate prediction of their thermal performance is crucial for optimizing their design and functionality. Traditional methods of modeling and simulation, such as the finite element method (FEM), have been instrumental in solving complex thermophysics issues. However, when dealing with ultra-large arrays, building an equal-scale three-dimensional (3D) FEM model becomes extremely memory and time-consuming. Moreover, the use of periodic boundary conditions (PBCs), a common simplification method in FEM, can lead to considerable errors when applied to ultra-large arrays irradiated with a local heating source. In a new study published in Journal Optics Express and led by Prof. Jinying Zhang and Dr. Defang Li from the School of Optics and Photonics at the Beijing Institute of Technology, in collaboration with Dr. Jiushuai Xu and Dr. Erwin Peiner from the Technical University of Braunschweig developed a novel approach called the Linear Extrapolation Method based on Multiple Equipropotional Models (LEM-MEM), which addresses the challenges of predicting thermal performance in ultra-large pixel arrays.
Photothermal and electrothermal devices have become integral in various applications due to their ability to convert light or electrical energy into heat, which can be precisely controlled and utilized for numerous purposes. As these devices evolve and scale up in size and complexity, accurately predicting their thermal behavior becomes increasingly challenging. The flow field and temperature distribution in ultra-large arrays can vary significantly and are governed by intricate thermophysical phenomena. FEM has been a powerful tool in the thermal modeling and simulation of these devices. However, it becomes impractical when dealing with ultra-large arrays due to the immense computational resources required to create 3D models that accurately represent the physical system. This limitation necessitates the development of alternative methods that strike a balance between computational efficiency and accuracy. PBCs a commonly used simplification technique in FEM, can be applied to periodic structures with a uniform temperature distribution in the periodic direction. However, for ultra-large arrays subjected to local heating, PBCs fail to meet these conditions, leading to inaccuracies in the simulation results.
The authors proposed the LEM-MEM method which offers a promising solution to the challenges associated with predicting the thermal performance of ultra-large pixel arrays. Rather than attempting to model the entire array at once, LEM-MEM adopts a more efficient approach. It builds several reduced-size FEM models, each with a finite array size (typically within 50×50 arrays), to conduct simulations and extrapolations. By using appropriate structural simplifications and linear extrapolation, LEM-MEM allows the prediction of steady-state temperature characteristics on wafer-level substrates with tens of millions of pixels while minimizing computational consumption. The LEM-MEM methodology is grounded in the principle that, for the same heating energy and heat conduction, the steady-state temperature remains proportional to the irradiated area and the dimensions of the heat-conducting material. By constructing models with varying array sizes and extrapolating the results, the study achieves highly accurate predictions of the thermal behavior of ultra-large pixel arrays.
To validate the accuracy of LEM-MEM, the researchers designed and fabricated photothermal transducers with array sizes exceeding 4000×4000 pixels. These transducers incorporated repetitive and periodic microstructures, making them an ideal testbed for assessing the predictive capabilities of the new methodology. They designed and fabricated four different pixel patterns on a 4-inch silicon substrate, each with specific dimensions and radiation areas. These patterns were used to test the steady thermal properties of the PT transducers. The experimental results demonstrated the remarkable predictability of LEM-MEM, with the maximum percentage error of the average temperature falling within 5.22% for all four pixel patterns. Furthermore, the measured response time of the proposed PT transducer was found to be within 2 ms, meeting the requirements for real-time applications.
The research team also explored the impact of microstructure design on the thermal performance of photothermal transducers. The choice of microstructure, including the area of SiO2, the contact area between Si and SiO2, the thickness of SiO2, and the spacing of adjacent pixels, was systematically studied. Their results revealed that these microstructural parameters play crucial roles in determining the steady thermal performance of the transducers. For instance, increasing the area of SiO2 resulted in higher average pixel temperatures, while larger contact areas between Si and SiO2 led to lower temperatures due to reduced contact thermal resistance. The thickness of SiO2 was also found to be a significant factor, with thinner films leading to higher temperatures.
In a nutshell, the study led by Prof. Jinying Zhang and colleagues introduced the innovative Linear Extrapolation Method based on Multiple Equipropotional Models (LEM-MEM) as a an important advancement in predicting the thermal performance of ultra-large pixel arrays in photothermal and electrothermal devices. This method offers a balance between computational efficiency and accuracy, allowing for efficient simulations and predictions. The experimental validation of LEM-MEM on photothermal transducers demonstrates its high predictability and provides insights into the impact of microstructure design on thermal performance. The implications of this research extend to various thermal engineering applications, making LEM-MEM a valuable tool for optimizing the design of thermal devices in diverse fields.
Li D, Zhang J, Xu J, Peiner E. Linear extrapolation method based on multiple equiproportional models for thermal performance prediction of ultra-large array. Opt Express. 2023 ;31(9):15118-15130. doi: 10.1364/OE.486394.