於在半導體表面的金屬薄膜的系統，ARPE最近的實驗顯示出複雜的電子能帶結構在水平方向。這些複雜性是被歸因於在金屬及半導體這兩者的之間能帶混合的效應。被這些實驗激發，我們研究在半導體表面的金屬薄膜的受限的能階。

首先，這個系統是被一非對稱量子井所建立的模型—金屬薄膜被夾在真空(具有金屬的功函數作為能量障礙)及半導體(做為能量障礙的價帶補償)中間。我們數值地計算每一個受限的能階並且與ARPE在那些點做比較。這些結果與實驗觀測不一致。這只是能帶混合效應不能夠被金屬薄膜的受限給忽略掉。

為了要把能帶混合代入這個想法，我們得去更深入拋物線能帶及有效質量近似。我們採用了k.p方法建立半導體塊材的能帶結構的模型。兩個k.p漢米爾頓量是被檢查的：8x8的漢米爾頓量及4x4的Luttinger漢米爾頓量。我們重新定義k.p漢米爾頓量有一組無維度的參數，並且重新產生塊材的半導體砷化鎵的能帶。但是仍留下一些困難在連接在跨越金屬及半導體兩者之間界面的k.p波函數。
在未來的研究中，我們仍然奮力向前去建立一個模型對於跨越異質接面的k.p波函數的連結，並且進一步研究在金屬薄膜及半導體之間的能帶混合效應。

Recent experiments of angle resolve photoemission (ARPE) for system of metal thin film on the surface of a semiconductor showed complicated electron band structure along the parallel direction. These complexities were ascribed to the effect of band mixing between metal and semiconductor. Motivated by these experiments, we studied the confine levels of metallic thin film on semiconductor surface.

First, this system was modeled by an asymmetric quantum well—the metallic film was sandwiched between vacuum (with metal work function as the energy barrier) and the semiconductor (valence band offset as the barrier). We numerically computed the energy of each confined level, and compared with the ARPE experiment at the points. The results didn’t agree with the experimental observation. It indicated that the band mixing effect cannot be neglected in the confinement of metal thin film.

In order to take the band mixing into consideration, we have to go beyond the parabolic band and effective mass approximation. We employed the k.p method to model the semiconductor bulk band structure. Two k.p Hamiltoninans were examined: the 8x8 Kane Hamiltonian and 4x4 Luttinger Hamitonian. We redefined the k.p Hamiltonian with a set of dimensionless parameters, and reproduced the bulk band structure of semiconductor GaAs. But there remained some difficulties in connecting the k.p wave function across the interface between metal and semiconductor.

In the future study, we will press forward to build a model for the connection of k.p wave function across the hetro-junction, and further study the effect of band mixing between metal film and semiconductor.

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