The low-energy phonon spectrum of ultrathin germanium film with a free surface. The method of molecular dynamics

The vibrational density of states of ultrathin germanium films with a thickness of 1 and 2 u.c. has been studied using the molecular dynamics method. The calculations were carried out on Ge crystallites of 50×100×1 and 50×100×2 u.c. The periodic boundary conditions were set along the X and Y axes, and the free ones along the Z axis. The vibrational density of states was calculated as a Fourier transform of the autocorrelation velocity functions for all the atoms of the surface and inner atomic layers of the film. It is shown that the behavior of the low-energy part of the spectrum is mainly determined by the vibrations of the atoms of the surface layers, and the spectrum of the inner layers of the film morphologically coincides with that calculated for a bulk crystallite. It is shown that in the low-energy (up to 5 meV) region of the vibrational spectrum of a Ge film with a thickness of 2 u.c. (~12 Å), a frequency dependence close to cubic is observed for both a "clamped" crystallite and that with a free surface. When the thickness of the Ge film is reduced to one cell (~6 Å), a qualitative restructuring of the low-energy region of the spectrum is observed. In this case, the law of functional dependence on frequency has a variable exponent, which varies from 0.6 to 2.14. In other words, a transition is observed from a quasi-two-dimensional case with cubic dependence to a two-dimensional case with linear power-law low-frequency dependence.