Angle- and Thickness-Dependent Response Characteristics of YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7−δ</sub>-Based Atomic-Layer Thermopile Heat Flux Sensors
Xi Chen, Bowan Tao, Ruipeng Zhao, Kai Yang, Yudong Xia, Qichen Wang, Zhenzhe Li, Tian Xie
Abstract
The atomic layer thermopile (ALTP) heat flux sensor has played an important role in the study of boundary layer transition. However, the response characteristics of the sensors still have not yet been clarified sufficiently. Herein, the angle- and thickness-dependent response characteristics of the ALTP heat flux sensors are investigated. Based on a 1-D thermal conductivity model, the anisotropic thermal conductivity ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa _{\textit {ab}}$ </tex-math></inline-formula> = 4.28 W/m <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula> K, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa _{c}$ </tex-math></inline-formula> = 0.53 W/m <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula> K) and anisotropic Seebeck coefficient ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta {S}$ </tex-math></inline-formula> = <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$16.72 \mu \text{V}$ </tex-math></inline-formula> /K) of YBa2Cu3O7-δ (YBCO) thin films are obtained by fitting the angle-dependent sensitivities. As the inclined angle increases, the increased thermal conductivity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa _{z}$ </tex-math></inline-formula> along the normal direction of the thin film leads to a decrease in temperature difference <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta {T}$ </tex-math></inline-formula> . Therefore, the sensitivity of the ALTP heat flux sensor only reaches the maximum value <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 24.16 \mu \text{V}$ </tex-math></inline-formula> /(kW/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}^{{2}}$ </tex-math></inline-formula> ) at 18° even if the inclined angle continues to increase. The increased thermal conductivity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\kappa _{z}$ </tex-math></inline-formula> results in a decrease in the response time of the ALTP heat flux sensor as the inclined angle increases. The results of static calibration experiments and simulations indicate that the sensitivity of the ALTP heat flux sensor is almost independent of the thickness of the thin film, but their response time gradually decreases with increasing thickness based on heat conduction theory. This work may provide a good design basis for the application of ALTP heat flux sensor.