矽鍺磊晶成長於矽之淺受子能態之理論研究

Abstract

本論文主要是用一方法計算出矽鍺合金成長在矽基板上的受子能階，再判斷出其適當的束縛態及共振態。而此理論可推廣應用到各種受 應力作用的半導體材料。 在此我們使用Luttinger-Kohn 的等效質量理論以及Bir-Pikus的應力 理論出發；在受應力的矽鍺合金其點群由原來未受應力的Td群變成D2d群，使用ｋ.ｐ理論在處理此問題時，我們先對envelop functions角度部分以群論的投影算子選取適當的基底作為符合D2d群對稱性的波函數，以簡化計算，計算出隨著不同應力時的受子波函數之束縛態及共振態其變化的行為；而其中共振態的部分以各能帶所佔比例來判斷其合適與否。 在x=0的時，為此理論的一特殊狀況，經由與此一部分實驗結果的比較，可以確認此計算的可信度，故可預期在一般情形之下也是可信的；在束縛態的部分已可以的到相當可信的結果，此理論可對之後的相關半導體研究有所幫助。

A theoretical method has been developed and used for calculation of shallow acceptor levels of strained SiGe grown on Si substrate, and included the resonant states and bound states. The theory is based on the Lutting-Kohn 6-band model including the effect of deformation potential, and with group-theoretical consideration for acceptor states in strained SiGe. For the strained SiGe grown on (100)Si, the crystal symmetry change form Td to D2d. The angular part of envelope functions can well be found by using the technique of projection operators. We project the states to the band edge. Then we determine the resonant states by the ratio of the probability of heavy hole band, light hole band, and split of hole band. The calculation for group-III acceptor states in bulk is the special case of strained Si1-xGex/Si with x equal to zero which is the case of zero stress. Comparing to some experiment data in unstrained cases, the calculation of acceptor levels is concluded appropriate in both conditions of strained and unstrained semiconductors.