中文摘要：

利用抛物型电子能谱模型,求出了半导体基底的态密度和半导体基底上形成的外延石墨烯的态密度,并与理想单层石墨烯的态密度相比较,分析外延石墨烯态密度特点和能隙产生的条件.以Si基底上形成的外延石墨烯为例,论述了外延石墨烯态密度按能量分布的特点和吸附对外延石墨烯态密度和能隙的影响.结果表明：（1）外延石墨烯的局域态密度曲线与理想单层石墨烯和基底的态密度曲线不同,它不具有对零能量的左右对称性;（2）吸附不仅使理想单层石墨烯和半导体基底的态密度曲线对零能量的左右对称性受到破坏,而且改变了石墨烯的能隙宽度;（3）外延石墨烯的能隙宽度随着半导体基底与石墨烯相互作用能的增大而增大,但变化较小.

英文摘要：

This paper is to utilize the model of parabolic type electron spectrum to figure out the state density of semi-conductor substrate and the state density of epitaxial graphene formed on the semi-conductor substrate.The comparison between these state densities with the state density of ideal single-layer grapheme will be made to analyze the features of the state density in epitaxial graphene and the condition of generating energy gap.Furthermore,the paper will take the epitaxial graphene formed on Si substrate for example to discuss the features of state density of epitaxial graphene by energy distribution,and the effect of absorption on the state density and energy gap of epitaxial graphene.The result indicates that,1）the local density curve of the epitaxial grapheme is different from those of the ideal single-layer graphene and substrate,and it does not have the bilateral symmetry;2）,not only does the adsorption destroy the bilateral symmetry of the state density curve of the ideal single layer graphene and semi-conductor substrate,but it changes the energy gap width of graphene,and,in addition,the energy gap width of epitaxial graphene will increase along with the increase of the interaction between semi-conductor substrate and graphene,but with the less change.