本研究使用有限單元法(Finite Element Method)分析軟體ANSYS，去探討孔洞（Void）對於半導體熱電材料碲化鉍(Bismuth Telluride)在其最大產能密度下時的局部熱應力的影響，由於熱電材料的溫差會產生電壓差，從而產生電流，而電流通過材料內部會因為電阻而產生熱，故吾人去分析熱應力值的變化時，除了溫差所產生的熱通量外，也要考慮電阻所產生的熱對於應力值的變化。
本文在邊界條件上不考慮外界對碲化鉍的應力影響，專注考慮上下側溫差對其孔洞的熱應力影響，並且將問題分為: (一)熱固耦合分析及(二)熱電固耦合分析兩種情況，來分析孔洞的熱應力變化，並且比較兩種的情況。
結果發現，應力主要集中在孔洞邊緣θ = 90°與270°處，分別為壓應力及張應力，而在熱電固耦合時會有額外的壓應力。熱固耦合時，溫度場為線性，而在熱電固耦合時溫度場為非線性。而且我們發現，含孔洞的立體塊狀，與含孔洞的平板的應力值有某些關聯。另外溫差不大時，可用熱固耦合分析代表熱電固耦合分析的結果。

In this study, the computer software ANSYS has been used to investigate the effect of the thermal stress of a void in Bismuth Telluride under its working conditions. Since the temperature difference in a semiconductor thermoelectric material is accompanied by an electric potential difference, and result in electric current, the heat will be generated by the electric resistance. Therefore, when we analyze the thermal stress in semiconductor thermoelectric material, in addition to the heat flux due to the temperature difference between the boundaries, the contribution from the Joule heating should also be considered.
In this paper, the influence of the external stress is not considered in the boundary conditions. We focus on the effect of the thermal stress due to the temperature difference between the upper and lower sides. The problem is studied by two approaches: Structure-thermal coupled analysis and Structure-thermoelectric coupled analysis. The thermal stress concentrations at the void are determined and compared by using these two approaches.
It is found that the local thermal stress is mainly concentrated at the edge of the void θ = 90° and 270°, which are compressive stress and tensile stress, respectively. And there is additional compressive stress in the Structure-thermoelectric coupled analysis. The temperature field of Structure-thermal coupled analysis is linear, and the Structure-thermoelectric coupled analysis is nonlinear. Moreover, we have found that the stress value of the three-dimensional block containing the void has some correlation with the plate containing the void. In addition, when the temperature difference is not large, Structure-thermal coupled analysis can be used to represent the results of the Structure-thermoelectric coupled analysis.

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