Temperature Dependence of Debye-Waller Factors of Sphalerite III-V Semiconductors Calculated From Ab Initio Force Constants

Abstract

Recently the interest in scanning transmission electron microscopy (STEM) has increased a lot due to the development of microscopes that combine conventional TEM and STEM by incorporating a high angle annular dark field (HAADF) detector. Such detectors sum up all the electrons scattered into high angles of about 40-150 mrad. The signal recorded using a HAADF detector is highly depending on the atomic number Z and therefore is very useful for the quantification of compositions in e.g. semiconductor quantum well structures. The electrons scattered into such high angles are mainly due to the displacements of atoms caused by the finite temperature. This scattering process is called thermal diffuse scattering. However, since the signal of the HAADF detector stems from electrons scattered into high angles the signal is strongly influenced by the Debye-Waller factor (DWF), which is proportional to the mean square displacement of the atoms. For many materials the DWFs are not accurately known or are not known over a large range of temperatures. In this contribution we calculate the DWFs from force constant matrices using a supercell approach for temperatures between 0 and 1000 K and fit them using only one fit parameter.For the calculation of the DWFs 2x2x2 supercells for the group III and the group V elements were generated, respectively. In each supercell a group III or a group V atom was displaced by about 3 pm. Using the WIEN2k code the Hellmann-Feynman forces due to the displaced atom on all the other atoms were calculated. From the Hellmann-Feynman forces dynamical matrices were derived and phonon eigenfrequencies were calculated by diagonalization of the dynamical matrices

Debye-Waller Factor in an Isotopically Disordered Semiconductor Crystal

“…The progress of research in semiconductor physics is achieved due to its (DWF) use to find the magnetic form factor of Eu 2+ in EuS [18], local structural properties in the terahertz semiconductor Zn 1−x Cd x Te [19], to describe observed band gap dependence [20], thermodynamic properties of semiconductor compounds [21], and vibrational dynamics and band structure of methylterminated Ge(111) [22]. The temperature dependence of DWF is governed by the molecular dynamics study * e-mail: dgsureshc@yahoo.co.in; scgairola@rediffmail.com in InSb [23], calculated from ab initio force constants in sphalerite III-V semiconductors [24], and also obtained from statistical moment method in compound semiconductors [25]. In addition to these works, effect of anharmonicity has been applied to calculate different cumulants.…”