磷化物三元混晶中电子-声子相互作用的维度和体积效应

考虑电子-声子耦合强度因维度而异,导出了描述三维、二维和一维混晶中电子-声子相互作用的哈密顿量。考虑构成三元混晶的两种二元晶体的晶格失配会使混晶体积随元素组分比改变,在推导三维、二维和一维三元混晶中极化子自陷能量和重整化有效质量时计入了离子相对位移与二元晶体原胞体积的关系。结果表明:磷化物三元混晶中极化子自陷能量和重整化有效质量随元素组分的变化关系呈明显的非线性特征,对晶格适配明显、电子-声子耦合较强的材料,体积效应不可忽略。维度越低,非线性特征和体积效应越明显。     

二维声学极化子的基态能量和有效质量

自陷电子对了解光电材料的光学性质非常重要.近些年来,形变晶格中电子自陷的问题受到研究人员的广泛关注.电子既与声学模耦合,也与光学模相互作用,但电子由自由态向自陷态的转变缘于近程的电子-声学声子耦合.研究表明:声学极化子在大多数半导体以及Ⅲ-Ⅴ族化合物,甚至碱卤化物中都不可能自陷.另一方面,电子-声子耦合在束缚结构,如二维、一维系统中,会有所增强.换言之,电子在低维结构中更容易自陷.Farias等人指出:声学极化子在二维系统中自陷的临界电子-声子耦合常数为定值,不随声子截止波矢的变化而改变.这种结论在物理上不尽合理.通过计算二维系统中的声学极化子基态能量和有效质量,讨论了二维声学极化子自陷问题.研究发现,二维声学极化子自陷转变的临界耦合常数随声子截止波矢的增加朝电子-声子耦合较弱的方向变化.这一特征与前人关于体和表面极化子研究获得的结论定性一致.所得二维声学极化子基态能量的表达式与Farias等人一致,但自陷的结果与Farias等人的结果在定性和定量上均有不同,我们认为Farias等人关于二维声学极化子自陷转变点的确定方式有不妥之处.通过改进自陷转变点的确定方式,得到了在物理上更合理的结果.     

On the possibility of self-trapping transition of acoustic polarons in two dimensions

A 2D electron-longitudinal-acoustic-phonon interaction Hamiltonian is derived and used to calculate the ground-state energy of the acoustic polarons in two dimensions. The numerical results for the ground-state energy of the acoustic polarons in two and three dimensions are obtained. The 3D results agree with those obtained by using the Feynman path-integral approach. It is found that the critical coupling constant of the transition from the quasifree state to the self-trapped state in the 2D case is much smaller than in the 3D case for a given cutoff wave-vector. The theory has been used to judge the possibility of the self-trapping for several real materials. The results indicate that the self-trappings of the electrons in AlN and the holes in AlN and GaN are expected to be observed in 2D systems.     

Self-Trapping of Acoustic Polaron in One Dimension

The ground-state energy and effective mass of an acoustic polaron in one dimension are calculated by using an electron-longitudinal-acoustic-phonon interaction Hamiltonian derived here. The self-trapping of the acoustic polaron is discussed. It is found that the critical coupling constant shifts toward weaker electron-phonon interaction with the increasing cutoff wave vector and the products of the critical coupling constant by the cutoff wave vector tend to a certain value. The self-trapping of acoustic polarons in one dimension is easier to be realized than that in three- and two-dimensional systems. The self-trapping transition of acoustic polarons is expected to be observed in the one dimensional systems of alkali halides and wide-band-gap semiconductors.