本文發展出分子靜力學三維準穩態奈米切削模式，進行模擬AFM探針切削單晶矽奈米流道梯形凹槽的偏移循環加工，其除可計算切削力、等效應力與等效應變外，亦可計算被切削單晶矽工件所提升之溫度；進而可進行被切削單晶矽工件的溫度分佈分析。本文假設切削模式，被切削單晶矽工件溫度的提升是由塑性變形熱與摩擦熱兩種熱源產生。本文以固定下壓力之偏移循環加工方法，加工單晶矽基板奈米流道梯形凹槽，其為設定每切削層在固定下壓力下切削一道次，然後將探針向右偏移再切削一道次，再將探針向左往回偏移至前述兩道次中間位置切削加工，做為一個偏移循環加工。本文先應用比下壓能理論公式計算出切削深度，以及估算各道次偏移某一距離再加工之下壓力及切削力。並運用分子靜力學三維準穩態奈米切削模擬模式，模擬第一切削層偏移循環加工法所得第一切削道次到第三切削道次之下壓力及切削力，再將兩者所得之切削力進行比較。本文亦假設AFM探針切削單晶矽奈米梯形凹槽第一切削道次及第二切削道次為相似的模擬條件，因其第一切削道次及偏移循環第二切削道次切削模擬過程皆為單一溝槽切削模擬。本文塑性變形熱可由被切削工件單晶矽，其等效應力與等效應變之乘積計算出。另發展出針對奈米切削單晶矽刀面上產生摩擦熱的方法，並計算因摩擦熱源產生的溫度提升之方法。本文再將兩種熱源所產生之溫度提升加總計算後，得到被切削單晶矽工件各原子提升之總溫度，再進行溫度場分析。此外本文亦進一步將前述所得被切削單晶矽工件各原子提升之總溫度帶入有限差分熱傳方程式，利用此方法計算出每一步階奈米級梯形凹槽偏移循環加工切削，被切削單晶矽工件溫度場，再進行分析。最後並與前述未考慮有限差分熱傳遞所計算的被切削單晶矽工件各原子之溫度提升之數值做比較。

The paper develops a three-dimensional quasi-steady molecular statics nanocutting model to carry out simulation of offset cycle cutting method by cutting nanochannel of trapezium groove on single-crystal silicon by AFM probe. It can calculate not only cutting force, down force, equivalent stress and equivalent stress, but also temperature rise of the cut workpiece, and furthermore, analyze the temperature distribution of the cut silicon workpiece. The paper supposes that in the cutting model, the temperature rise of the cut single-crystal silicon workpiece is caused by two heat sources: plastic deformation heat and friction heat. The paper uses an offset cycle cutting method under a fixed down force to cut a nanochannel of trapezium groove single-crystal silicon substrate. It is set that each cutting layer is cut for one pass under a fixed down force. After that, let the probe be offset rightwards to carry out cutting for one pass, and then leftwards to the middle position between the above two cutting passes to carry out cutting, completing one offset cycle cutting. First of all, the paper applies specific down force energy (SDFE) theoretical equation to calculate the cutting depth and estimate the down force and cutting force for each cutting pass of the offset cycle cutting. The paper also uses three-dimensional quasi-steady molecular statics nanocutting simulation model to simulate the down force and cutting force of the 1st to 3rd cutting passes acquired from implementation of offset cycle cutting method on the 1st cutting layer. And the two results of cutting force obtained by SDFE equation and the three-dimensional quasi-steady molecular statics nanocutting model are compared. The paper also supposes that the 1st and 2nd cutting passes during nanpcutting of trapezium groove on single-crystal silicon by AFM probe have similar simulation conditions since the simulated cutting process of the 1st cutting pass and the 2nd cutting pass with offset cycle are both simulated cutting of single groove. In the paper the plastic deformation heat can be calculated by multiplying the equivalent stress by equivalent strain of the cut single-crystal silicon workpiece. Besides, the paper develops a method for producing the friction heat between the silicon workpiece and tool face for nanocutting of single-crystal silicon, and develops a method for calculation of temperature rise caused by the friction heat on flank. The paper also adds up the temperature rise produced from two heat sources, acquiring the total temperature rise in each atom of the cut single-crystal silicon workpiece, and then carries out analysis of temperature field. Besides, the paper further substitutes the total temperature rise in each atom of the cut single-crystal silicon workpiece, as acquired above, in finite difference heat transfer equation. Using this finite difference method, the paper calculates the temperature field of the cut single-crystal silicon workpiece during each step of offset cycle cutting for cutting a nanoscale trapezium groove, and then carries out analysis. Finally, the result is compared with the numerical value of temperature rise in each atom of the cut single-crystal silicon workpiece previously calculated without consideration of finite difference heat transfer.

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