成長於矽基版之矽鍺磊晶層受子能態之理論研究

Abstract

本論文提出了一套受子能階的理論計算方法，適用於受應力(strained)及非受應力(unstrained)之半導體材料，並以含變形(strain)磊晶層的異質接面結構SiGe/Si為理論研究的對象。採用Luttinger-Kohn 的等效質量理論(effective mass theory)及Bir-Pikus 的應力理論為基礎，將受子波函數 (acceptor wave function) 表示成未受應力之反晶格空間價帶六個 Γ 點Bloch functions 的線性組合，組合中的係數稱之為envelope functions，為6×6 Luttinger-Kohn Hamiltonian 的解。 在SiGe/Si異質接面結構中，由於壓縮應力的存在，使得SiGe之晶格點群自 Td 群下降成其子群 D2d 群，而原本簡併的輕電洞與重電洞能帶頂點因此應力而分開，受子能階也跟著分裂。我們針對此內生應力之Si1-xGex磊晶層，以群論中之投影運算子(projection operator)，求出符合D2d group對稱性之受子波函數，並以摻雜B之Si1-xGex/Si為例，實際計算不同對稱性能態之束縛能對應Ge比例x之變化圖，以了解壓縮應力對受子能階的影響。 本研究中的特例，x = 0 的塊材Si，其受子能階的計算結果與實驗文獻比較起來，相當一致，因此，我們的計算結果具有相當的可靠性。故本論文針對受應力之Si1-xGex (摻雜B) 的計算數據可信度很高，對於未來相關的實驗或理論研究，極具參考價值。

Recently, strained SiGe/Si has attracted a great research interest because of its potential applications in high-speed and optical devices. There has nevertheless been no thorough investigation on the acceptor levels in Si and strained SiGe. In the present research, a theoretical method has been developed based on the effective mass theory and the variation method with group-theoretical consideration for acceptor states in strained SiGe. Energy levels for bound states in B-doped SiGe/Si are computed using this approach. We construct the acceptor wave functions for the bound states from linear combinations of the and Bloch functions of the unstrained structure. The coefficients of the combinations are the so-called envelope functions which are the solutions of the 6×6 effective mass Hamiltonian. The angular part of the hydrogen-like envelopes are found precisely by using the technique of projection operators, while the radial ones are chosen to be the superpositions of a set of exponential functions times the lowest possible polynomials which give a correct asymptotic behavior in the vicinity of the origin (the impurity site). The coefficients of the superpositions are taken as variational parameters and obtained by minimizing the expectation energy. The calculations for group-III acceptor states in bulk Si is just the special case of strained Si1-xGex/Si for zero stress. The results are obtained straightforward by setting x equal to zero. A more complete series of acceptor states in B-doped Si associated with both the p3/2 and p1/2 valence bands has been obtained as well. We conclude that our approach is appropriate for the calculations of acceptor levels in both strained and unstrained semiconductors.