- 學位論文
矽基材上壓電薄膜極子特性研究
Polariton properties of piezoelectric film on the silicon half-space
摘要
將壓電超晶格薄層覆蓋在半無窮域材料之上，當壓電材料極化軸具有週期性變化時，光子與聲子特性將會耦合使此結構成為極子晶體，探討此種在半無窮域材料上覆蓋壓電超晶格薄層結構的頻散曲線是本研究的目的。 將半無窮域中垂直薄層方向的行為做Laplace轉換，如此處理可降低邊界條件的數目，使特徵值問題的維度減少，如此可大為減低數值計算的複雜度，對求取頻散曲線有相當大的助益。 為證明此法的適用性，首先以前述的方法求取等向性材料半無窮域覆蓋他種等向性材質薄層的頻散曲線，其結果與利用其他方法所解得的頻散關係完全相同。再將此法用於求取非等向性半無窮域覆蓋壓電薄層的頻散曲線，顯示利用Laplace轉換法也適用於電磁波方程式及應力波方程式耦合的系統。最後再求取半無窮域覆蓋壓電超晶格薄層的頻散曲線，顯示本研究所開發的方法確實能有效降低求取數值解的複雜度，而在同樣的運算量之下可獲得較傳統方法為高的精確度。
並列摘要
A half-space substrate is covered with a thin layer of piezoelectric superlattice that is polarized oppositely at regular intervals. In this structure phonon and photon will couple together results in quantized behavior of polariton. To study the dispersion curves of polariton in this structure is the goal of this research. In the half-space, the Laplace transform is applied to the coordinate normal to the thin layer. This treatment reduces the number of boundary conditions and decreases the complexity of eigenvalue problems as a consequence. Therefore, it can reduce the computation load significantly and is very helpful in finding dispersion curves. In order to verify the proposed method, dispersion relation for a structure consists of an isotropic layer topped on another isotropic half-space is derived with the aforementioned method. The result is identical with that obtained by an established method. For an anisotropic half-space covered with piezoelectric layer, the electromagnetic and acoustic waves are coupled together. The proposed method can also find its dispersion curves without difficulty. Finally, the method is employed to study the dispersion behavior of polariton in the structure of an anisotropic half-space substrate covered with a thin layer of piezoelectric superlattice. Comparing to the conventional method, the advantage of the proposed method is obvious and higher accuracy is achieved with the same computational load.