本文提出奈米流道曲線加工到預定寬度及深度之模擬模式，本文先利用自行設定的控制點所取得的三次曲線方程式(Cubic Spline curve equation)，進而計算出近似曲線的多個整數之微小線段，來進行AFM的直線段與曲線加工實驗。本文先利用加工直線梯型凹槽到預定深度及寬度的方法，算出加工直線梯型凹槽到預定深度及寬度所需的偏移量以及切削道次數，並利用自行設定的控制點取得欲加工路徑的曲線方程式。本文亦創新提出，利用第一條曲線所設立的控制點，再利用偏移公式以及上述所求出的偏移量，求出同一切削層其他道次的曲線方程式的控制點的計算方法，進而計算出同一切削層其他切削道次的曲線方程式。由於AFM機台無法進行曲線加工，故本文提出應用曲線與微小線段的弦誤差的計算公式，進而用直線近似曲線的方法算出由許多微小線段連結而成的近似曲線之直線。又因為AFM機台精度只到1nm，故我們將微小線段的各個交點取整數來進行加工，而為縮小誤差，我們在進行量測時取近似理想曲線位置的斷面進行量測。最後進行本文所建立的曲線加工到預定寬度及深度之模擬模式的模擬結果與實驗結果相比較，驗證本文所建立之模擬模式為合理可接受的。
而一般在做AFM奈米流道直線段梯形凹槽切削時，通常都會在快切到接近目標深度時，再改變一次下壓力來使得最後一切削層之深度接近目標深度。然而因實際AFM機台在改變下壓力時，改變下壓力的時間約為7分鐘左右，因此此方法會多了一次需要改變下壓力的時間。為了在實際應用上取得最少加工前置時間，本文利用加工奈米流道直線段梯形凹槽到預定深度及寬度的較少加工道次及改變下壓力次數的加工方法及其目標函數和限制條件。一開始先定探針加工最大下壓力的安全係數，在安全係數下的下壓力開始模擬加工梯型凹槽之深度，然後逐步調整下壓力，模擬加工梯型凹槽之加工深度，使其逐漸逼近梯型凹槽之目標深度。而確定接近梯型凹槽目標深度之後，則在每一切削層第一切削道次皆設定此下壓力值，第二切削道次則改變下壓力取得與第一切削道次之相同切削深度，最後應用比下壓能理論模式進一步估算出可達到預定奈米流道直線段梯形凹槽深度的切削層數及第一切削道次之下壓力，進而能達到最少改變下壓力的次數。
　　在這裡為了防止探針在切削多次時造成探針因疲勞而產生斷裂，因此我們設了安全係數，得出了在安全係數下之最大下壓力，再利用此下壓力逐步慢慢調整下壓力大小，使其下壓力能夠加工逼近到所預定之深度。然而本文第一切削層之預定切削深度可以用比下壓能之方法來直接得出所預定之切削深度，故可略過逐步逼近之步驟。而本文之第二切削層與第三切削層切削之後的加工預定深度，則無法直接利用比下壓能公式來預估此深度，故這時須利用最佳化之逐步逼近法來反覆模擬調整下壓力，進行第二切削層切削或第三切削層切削使其在設定之下壓力加工奈米流道之直線段梯型凹槽深度能剛好逼近所預定深度。加工到預定深度確定了之後再來利用上述之方法調整偏移量，來達到加工直線段梯型凹槽到預定寬度。本文提出針對整合直線段加工及曲線加工之奈米流道梯型凹槽到不同預定深度與寬度，依照上述方法先模擬出直線段不同切削層的各切削道次的滿足較少的加工道次及較少改變下壓力次數的較佳下壓力，再將所獲得之較佳下壓力應用到整合直線段加工及曲線加工之奈米流道梯型凹槽的加工。

The paper proposes a simulation model for nanochannel curve machining to the preset width and depth. First of all, the paper uses a Cubic Spline curve equation acquired from the self-set control points .This study uses the obtained cubic spline curve equation to further calculate the multiple integers’ tiny line segments of a near-curve, and conducts AFM for machining a nanochannel which is a straight-line segment and a curve segment machining experiments. The paper firstly uses the method of machining a straight-line trapezium groove to the preset depth and width, and then calculates the offset amount and the number of cutting passes required for machining the straight-line trapezium groove up to the preset depth and width. The paper also uses the self-set control points to obtain the curve equation of the path for machining. Besides, the paper innovatively proposes using the control point set by the first curve, and then uses offset equation and the offset amount obtained above to find a method for calculating the control point of curve equation of other passes on the same cutting layer. Furthermore, the paper calculates the curve equation of other passes on the same cutting layer. Since the AFM machine is unable to carry out curve machining, the paper proposess applying the calculation equation of the chord error between curves and tiny line segments, and further using straight-lined near-curve method to calculate the near-curve straight line formed by connection of many tiny line segments. But the accuracy of AFM machine is 1nm only, so the various intersecting points of the tiny line segments are taken as integers to carry out machining. In order to reduce the error, we take, when carrying out measurement, the cross-section at a nearly ideal curve position for measurement. Finally, the paper carries out comparison between simulation results and experimental results of the simulation model of the self-established curve machining up to the preset width and depth. It is proved that the simulation model established by the paper is reasonable and acceptable.
When carrying out, in general, cutting of an nanochannel straight-line segment trapezium groove, by AFM machine it is usually found that as it is getting close to the target depth, down force has to be changed for one more time so as to make the depth of the last cutting layer approach to the target depth. Nonetheless, since the time required for the AFM machine to actually carry out change of down force is around 7 minutes, this method needs to spend more time for change of down force for one more time. In order to achieve the least preparation time for machining during application to experiments, the paper uses the machining of nanochannel straight-line segment trapezium groove up to the preset depth and width, which is a machining method requiring less cutting passes and less times of change of down force, as well as its target function and constraints. At the beginning, the paper firstly sets the safety coefficient of the greatest down force for probe cutting, and starts simulated cutting of the depth of trapezium groove at the down force under safety coefficient. After that, the paper step by step adjusts the down force and simulates cutting of the cutting depth of trapezium groove, making it step by step approach to the target depth of trapezium groove. After the paper confirms that it is close to the target depth of trapezium groove, the paper sets the down force value for the first cutting pass on each cutting layer. For the second cutting pass, down force is to be changed to acquire the same cutting depth as that of the first cutting pass. Finally, specific down force energy (SDFE) theoretical model is applied to further estimate the number of cutting layer and the down force of the first cutting pass of the achievable preset depth of the nanochannel straight-line segment trapezium groove. Furthermore, the least number of times of change of down force can be achieved.
Here, in order to prevent occurrence of broken probe due to probe fatigue after cutting for multiple times, safety coefficient is set to achieve the greatest down force under the safety coefficient. The paper also uses this down force to step by step adjust the down force size slowly, and makes cutting by the down force approach to the preset depth. Nevertheless, for the preset cutting depth on the first cutting layer, SDFE method can be used to directly obtain the preset cutting depth. Thus, the procedures of stepwise approach can be neglected. As to cut to the preset depth after cutting on the second cutting layer and the third cutting layer, SDFE equation cannot be directly used to estimate this depth. Hence, optimal stepwise approach method has to be used to repeatedly simulate and adjust the down force for carrying out cutting on the second cutting layer or cutting on the third cutting layer in order to make the depth of straight-line segment trapezium groove of the nanochannel cutted by the set down force, exactly approach to the preset depth. After cutting to the preset depth is confirmed, the above method is used to adjust the offset amount to achieve the preset width of the cutted straight-line segment trapezium groove. The paper proposes integration of straight-line segment machining and curve machining of nanochannel trapezium groove to different preset depths and widths. In accordance with the above method, the paper firstly simulates the better down force that satisfies less cutting passes and less times of change of down force for various cutting passes on different cutting layers of straight-line segments. The acquired better down force is further applied to the integrated straight-line segment machining and curve machining of nanochannel trapezium groove.

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