本文使用緊束縛模型以及自洽理論計算單層有參雜矽，鍺，石墨烯的能帶結構和能帶激發。

激發能譜的特性由能帶中的費米能，結構，轉移動量所影響。藉由參雜可以感應出自由載子，而自由載子在激發譜會導致帶內躍遷的產生。

而本文使用的材料單層矽和鍺就跟石墨烯之於石墨類似，是單層的矽原子晶體結
構並且有些許的彎曲,晶體結構是蜂巢狀，但和石墨稀最大的不同在於,單層矽和
鍺彎曲結構會產生自旋軌道耦合效應,而此效應會產生約微小的能隙，而石墨烯
依然維持著平坦對應結構，能隙依然為零。

We calculate the energy dispersions and the electronic excitations of doped monolayer silicene , germanium and graphene by using the generlized tight-binding model and self-consistent theorem.
Monolayer silicene and germanium , with the slightly buckled honeycomb geometric structures , have a small band gap which are opened by spin-orbital effect.
On the other hand , monolayer graphene possesses the flat honeycomb structure
with zero-gap energy bands.
The features of excitation spectra are dominated by the Fermi energy , the band structure and the transferred momentum, doping would induce free carriers, which further cause the intraband single-particle and collective excitations. Moreover , the
plasmons (collective excitations) are strongly dependent in the free carriers.

1. Behnaz Gharekhanlou and Sina Khorasani , Nova Science Publishers, Inc(2011)

2 . P.R.Wallcae. phys . Rev. 71. 622 (1947)

3 . Rafael Roldan , Instituto de Ciencia de Materiales de Madrid CSIC (2012)
4 . A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim .Rev. Mod. Phys. 81, 109 – Published 14 January (2009)
5 . C. W. Chiu, S. H. Lee, S. C. Chen, and M. F. Lin .Journal of Applied Physics 106, 113711 (2009)

6 . Ming-Fa Lin and Feng-Lin Shyu , Journal of the Physical Society of Japan
Vol. 69, No. 2 (2000)

7 . Cheng-Cheng Liu, Hua Jiang, and Yugui Yao , PHYSICAL REVIEW B 84, 195430 (2011)