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采用基于密度泛函理论的第一性原理方法,在广义梯度近似下,计算了Ⅳ族元素晶体的面心立方结构和电子性质.结果表明:Ⅳ族元素晶体的面心立方结构均可存在,面心立方结构Ge晶体的结合能最大,结构最稳定;面心立方结构C、Si、Ge和Sn的晶格常数分别为0.3509nm、0.4322nm、0.4225nm、0.4903nm,不随原子序数的增加而单调增加,是由面心立方锗晶体比面心立方硅晶体中电子云交叠小,产生的排斥较弱所导致的;面心立方结构C晶体是间接能隙为6.5e V的宽禁带半导体,面心立方结构Si晶体的导带和价带存在较小的交叠而呈现出半金属性,面心立方结构Ge和Sn的电子结构相似均表现为金属性,Ⅳ族元素面心立方结构晶体的电学性质由宽禁带半导体向金属转变.
The first-principle method based on density functional theory (DFT) is used to calculate the face-centered cubic structure and electronic properties of the Group IV elements under the generalized gradient approximation. The results show that the face-centered cubic structure of Group IV elements can exist, The lattice energy of face-centered cubic Ge crystal is the largest and its structure is the most stable. The lattice constants of face-centered cubic C, Si, Ge and Sn are 0.3509nm, 0.4322nm, 0.4225nm and 0.4903nm, respectively. The monotonous increase is caused by the small overlap of the electron cloud in the face-centered cubic germanium crystal and the weak exclusion generated in the face-centered cubic silicon crystal. The face-centered cubic crystal structure C is a wide band gap with an indirect energy gap of 6.5eV The conduction band and valence band of the semiconductor, face-centered cubic Si crystal exhibit a little overlap with half-metallicity. The electronic structures of Ge and Sn in the face-centered cubic structure are similar to each other in metallic structure. The IV group face centered cubic The electrical properties of the crystalline structure of the transition from a wide band gap semiconductor to the metal.