半導體超晶格之電子表面態

Electronic surface states of semiconductor superlattices

陳星旗(Hsing-Chi Chen)

指導教授 ： 薛文証

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.10357

摘要

本論文的主要目的在於研究砷化鎵/砷化鋁鎵半導體超晶格結構之電子態。我們利用傳輸矩陣法去做分析，推導出超晶格結構之色散關係方程式與表面態方程式。同時藉著改變超晶格結構中之量子阱層厚度、能障層厚度與高度、還有表面層之能障高度等參數，比較出一系列的迷你能帶與表面態圖。由這些圖可以讓我們清楚的看出電子在不同超晶格結構下的傳遞情形。

研究超晶格表面態的部分，在一些特殊例子中，使用傳統方法分析不僅假根數目較多，且容易造成表面態的誤判，而本方法可避免以上缺點。在研究表面態與迷你能帶部分，對於表面對稱式的超晶格結構，我們發現二層的超晶格結構是無法找出表面態的，但在四層的超晶格結構中卻有表面態的出現，尤其是在雙能障基底的例子中，表面態會出現的更明顯。

關鍵字

超晶格 ； 砷化鎵/砷化鋁鎵 ； 傳輸矩陣 ； 表面態 ； 迷你能帶

並列摘要

The main purpose of this thesis is to study the electron surface states of GaAs/AlGaAs superlattices. In the study, transfer matrix method is used to derive the dispersion relation equation and the surface states equation of superlattices. In addition, the results of minibands and surface states by changing the parameters of superlattices, including quantum well layer width, barrier layer width and potential height, and surface layer potential height are studied. From these results, the electron transportation in different superlattices structures is presented.

In calculating surface states, it may obtain more spurious solutions and mistakes in some special cases by traditional method. But these problems can be avoided by the present method.When analyzing surface states and minibands, surface states do not appear in the two-layer symmetric termination superlattices, but they appear in the four-layer ones, especially for the two-barrier basis superlattices, surface states appear more obviously.

並列關鍵字

superlattices ； GaAs/AlGaAs ； transfer matrix method ； surface states ； miniband

參考文獻

[1] G. E. Moore, “Cramming more components onto integrated circuits,＂Electronics vol.38, 114 (1965).

[2] R. P. Feyman, “There’s plenty of room at the bottom,＂J. micro. sys vol.1,60 (1992).

[3] H. D. Jensen, J. M. Martinis, “Accuracy of the electron pump,＂Phys. Rev. B vol.46, 13407 (1992).

[4] J. B. Xia, “Quantum waveguide theory for mesoscopic structures,＂Phys. Rev. B vol.45, 3593 (1992).

[5] R. Martel, T. Schmidt, H. R. Shea, T. Hertel, Ph. Avouris, “Single- and multi-wall carbon nanotube field-effect transistors,＂Appl. Phys. Lett vol.73, 2447 (1998).