利用ＦＤＢＰＭ研究半導體Ｙ形分支在外加電場與磁場下的量子效應與多層膜化學蝕刻的模擬計算

Abstract

本論文的第一部分，我們利用有限差分束傳輸法(Finite-Difference Beam Propagation Method;FDBPM)計算在半導體Y 形分支結構中, 電子波 傳播的量子干涉效應, 並分別計算不同分支角度與入射動能之間的關係。 外加電場可使得電子偏向其中的一個分支，隨著電子入射動能的不同，所 加的偏向電場必須隨著入射電子動能的增加而變大，而與分支角度的變化 沒有太大的相關性。在有外加電場時，固定分支角度和入射動能，所獲得 的反射機率通量大於不加電場的情形，從分支角度20度到180度都得到相 同的趨向。同樣地，外加磁場也可使電子偏向，此偏向磁場的大小亦隨電 子入射動能增加而變大。但是在外加磁場時，進入分支的機率通量隨著分 支的角度的增大而變小。在第二部分中，我們用Wulff的假設，計算半導 體多層結構化學蝕刻，在不均向蝕刻速率與材料間不同厚薄變化，對蝕刻 後邊角的關係。我們得到改變材料間的厚度可以改變蝕刻後V形槽邊角的 大小。 This thesis consists of two parts. In the first part, we simulate the characteristics of an electron-wave Y-branch switch by using the finite-difference beam propagation method (FDBPM). The electron can be guided into one of the branches by applying an external electric field. The reflection flux of electron under an applied electric field is smaller than that without the electric field. This tendency is held for the branch angle ranged from 20 to 180 degrees. According to our simulation results, it requires higher electric field to guide the electrons with the larger incident kinetic energy. Similarly, the electron can also be guided by applying an external magnetic field. For the increasing electron incident kinetic energy, the magnetic field strength should be increased in order to keep guiding the electron into one of the branches. Under the same magnetic field strength, the larger branch angle offers the smaller the flux into the branch. In the second part of this thesis, we use the Wulff's construction to simulate the chemical etching on semiconductor multilayers. By changing the layer absolute thickness and the relative ratio of multiple layers, we can get the different V-groove sidewall angles.