本文利用比下壓能觀念，建立兩種最佳化之逐步逼近到預定之奈米流道梯形凹槽深度之目標收斂函數的最少切削道次之估算方法。第一種為三切削道次偏移循環加工方法，每一切削道次皆為固定下壓力進行加工，進而估算出達到預定之奈米流道梯形凹槽深度之最少切削道次。而第二種方法為兩切削道次偏移循環加工方法，此方法在每一切削層第一切削道次皆設定一固定下壓力，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，而實際AFM機台在改變下壓力時，需額外耗費工時來改變下壓力，而本文為了在實際應用上取得最少加工前置時間，則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梯形凹槽深度之最少切削道次估算方法，在估算出最少切削道次之外，也使得變換下壓力次數達到最少，進而可使加工前置時間最少。
本文先利用三切削道次偏移循環加工方法加工單晶矽基板奈米流道梯形凹槽，其為設定每加工層在固定下壓力下加工一道次，然後將探針向右偏移再加工一道次，再將探針向左往回偏移至{前述兩切削道次中間位置加工；此時偏移量大小，需滿足奈米流道梯形凹槽的上凸及下凹值要在設定的收斂值範圍內，做為一個偏移循環。若要增加奈米流道凹槽之寬度，則為增加偏移循環次數，如此即可使奈米流道凹槽之凹槽寬度增加。但此方法因使用較小下壓力，深度會有所限制，所以在初始進行偏移循環加工時，優先調整偏移量取得較佳的上凸值，若底部突起高度仍大於設定之突起高度收斂值，則重複調整偏移量直到底部突起高度收斂至設定值內。本文使用三切削道次偏移循環加工方法加工，並建立最佳化之逐步逼近到預定之奈米流道梯形凹槽之深度之目標收斂函數的最少切削道次之估算方法。本研究經由反覆調整下壓力及偏移量，直到能以適當的下壓作用力及最少切削道次來達到預定之奈米流道梯形凹槽之深度，並將估算結果與實際實驗結果作驗證。
本文再利用兩切削道次偏移循環加工方法加工單晶矽基板奈米流道梯形凹槽，其為本文先設定為每一切削層之第一切削道次為一固定下壓力，在第二切削道次中則改變下壓力，使其能達到與第一切削道次之相同切削深度。在模擬過程中發現兩切削道次偏移循環加工方法如任意調整兩切削道次的相同切削深度，都能以固定之偏移量取得固定凸起高度。所以本文推出利用較大之下壓力，滿足凸起高度小於設定之收斂值，並建立以最少切削道次及最少加工時間達到預定奈米流道梯形凹槽之深度的估算方法。而為避免在多道次切削下造成探針破壞，因此，本文先設定一探針下壓力之加工安全係數下取得較大下壓力值進行奈米流道切削加工。本文先設定為每一切削層之第一切削道次為一固定下壓力，在第二切削道次中則改變下壓力，使其能達到與第一切削道次之相同切削深度。而在達到預定奈米流道梯形凹槽深度之前一層，則改變最後一層第一切削道次之下壓力，進而達到預定加工的奈米流道梯形凹槽深度。但實際機台在改變下壓力時，需額外耗費設定下壓力的時間，而本文為了以較少的加工前置時間達到預定加工的奈米流道梯形凹槽深度，則必須減少改變下壓力之次數，而經由模擬改變偏移量使凸起高度小於設定之收斂值後再反覆調整下壓力，計算出第一切削層至最後一切削層之第一切削道次都能以固定下壓力逐漸加深，到最後一切削層之第一切削道次達到預定加工的奈米流道梯形凹槽深度。在上述之步驟中每一切削層的第二切削道次亦都再改變下壓力，使其切削深度和第一切削道次有相同深度。而此方法能減少一次調整下壓力之加工前置時間。本文經由反覆調整下壓力，直到能以適當的下壓力及最少切削道次和最少加工前置時間來達到預定之奈米流道梯形凹槽深度，並將估算結果與實際實驗結果作驗證。

Employing specific down force energy (SDFE) concept, the paper establishes two methods for estimating the least cutting paths of target convergence function for optimal successive approximation of the expected depth of nanochannel trapezium groove. The first method is three-cutting-path offset cycle cutting method. Each path of cutting is made at a fixed down force. Furthermore, the least cutting paths to achieve the expected depth of nanochannel trapezium groove can be estimated. The second method is two-cutting-path offset cycle cutting method. For this method, the first cutting path of each cutting layer is set to use a fixed down force. In the second path, down force is changed to achieve the same cutting depth as in the first cutting path. When down force is to be changed on the AFM apparatus, additional effort and time have to be spent for such change of down force. In order to achieve the least fabricating lead time in practical application, SDFE theoretical model is adopted to further find out the estimation method that estimates the least cutting paths to achieve the expected depth of nanochannel trapezium groove. Not only the least cutting paths are estimated, the number of times for change of down force is also decreased to the least, making the fabricating lead time decreased to the least as well.
First of all, the paper uses three-cutting-path offset cycle cutting method to fabricate nanochannel trapezium groove of single-crystal silicon (Si) substrate. It is set that cutting is made for one path at a fixed down force on each cutting layer. After that, the probe is offset rightwards for cutting for one more path, and then offset leftwards to the middle position between the previous two cutting paths for cutting. During this time the offset amount should meet the condition that the upward and downward values of the nanochannel trapezium groove have to be within the set range of convergence values. Then this is considered an offset cycle cutting. If it is required to increase the width of nanochannel groove, the number of offset cycles has to be increased. In this way, the width of nanochannel groove can be increased. But this method uses a smaller down force and the depth is limited, so that when offset cycle cutting is carried out at the very beginning, offset amount adjustment should be a prioritized task to achieve a better upward value. If the upward height at the bottom of nanochannel trapezium groove is still greater than the set convergence value of upward height, offset amount should be adjusted repeatedly until the bulge height at the bottom is converged as below the set value. The paper uses three-cutting-path offset cycle cutting method for cutting, and establishes an estimation method of the least cutting paths of target convergence function for optimal successive approximation of the expected depth of nanochannel trapezium groove. The study repeatedly adjusts the down force and offset amount until a suitable down force and the least cutting paths are found to achieve the expected depth of nanochannel trapezium groove. The estimated results are compared with the actual experimental results for verification.
The paper also adopts two-cutting-path offset cycle cutting method to fabricate nanochannel trapezium groove of single-crystal Si substrate. The paper firstly sets a fixed down force for the first cutting path on each cutting layer, and then changes the down force in the second cutting path, making it achieve the same cutting depth as in the first cutting path. In the simulation process, it is found that in the two-path offset cycle cutting method, if the same cutting depth for the two cutting paths is arbitrarily adjusted, a fixed offset amount can be used to achieve the fixed upward height at the bottom of nanochannel trapezium groove. Therefore, the paper proposes using a greater down force to achieve a upward height that is smaller than the set convergence value, and establishes an estimation method of the least cutting paths and the shortest fabricating lead time to achieve the expected depth of nanochannel trapezium groove. In order to avoid damage of probe caused during cutting for multiple paths, the paper firstly sets a greater down force value to be acquired under a safe cutting coefficient of down force of probe, to conduct cutting of nanochannel. The paper firstly sets a fixed down force for the first cutting path on each cutting layer, and then changes the down force for the second cutting path, making it achieve the same cutting depth as in the first cutting path. On the layer before achieving the expected depth of nanochannel trapezium groove, the paper changes the down force for the first cutting path on the last layer, and further achieves the expected depth of the machined nanochannel trapezium groove. However, when down force is to be changed on the AFM apparatus, the time for setting of down force is additionally consumed. In order to use less fabricating lead time to achieve the expected depth of the cut nanochannel trapezium groove, the paper has to decrease the number of times for change of down force. Through simulation of the change of offset amount, the upward height at the bottom of nanochannel trapezium groove becomes smaller than the set convergence value, and then down force is adjusted repeatedly. After calculation, for the first cutting path from the first cutting layer to the last cutting layer, the depth can be gradually deepened at a fixed down force. In the first cutting path on the last cutting layer, the expected depth of the cutting nanochannel trapezium groove can be achieved. In the above steps, the down force for the second cutting path on each cutting layer is changed, making the cutting depth the same as the one in the first cutting path. This method can decrease the fabricating lead time for down force adjustment by one time. Through repeated adjustment of down force, the paper finally can use suitable down force, the least cutting paths and the least fabricating lead time to achieve he expected depth of nanochannel trapezium groove. The paper also compares the estimated results with the actual experimental results for verification.

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