Electron-ion coupling in semiconductors beyond Fermi's golden rule

Abstract

In the present work, a theoretical study of electron-phonon (electron-ion) coupling rates in semiconductors driven out of equilibrium is performed. Transient change of optical coefficients reflects the band gap shrinkage in covalently bonded materials, and thus, the heating of atomic lattice. Utilizing this dependence, we test various models of electron-ion coupling. The simulation technique is based on tight-binding molecular dynamics. Our simulations with the dedicated hybrid approach (XTANT) indicate that the widely used Fermi's golden rule can break down describing material excitation on femtosecond time scales. In contrast, dynamical coupling proposed in this work yields a reasonably good agreement of simulation results with available experimental data.

Influence of model parameters on a simulation of x-ray irradiated materials: example of XTANT code

“…where f e (E i ) is the transient electron distribution (a fractional occupation number on the energy level E i ); I e-e is the electron-electron collision integral, and I e-i is the electron-ion scattering integral which reduces to electron-phonon scattering in the case of long timescales, a harmonic potential and an ideal crystal structure 19 . We assume an instantaneous electron thermalizaion (infinitely fast electron-electron scattering), which leads to Fermi-Dirac distribution.…”

“…We use Verlet algorithm in its velocity form with the timestep of 0.01 fs for propagation of the atomic coordinates and velocities in time, as well as for the super-cell coordinates and velocities (in a case of NPH ensemble) 28,29 . This time-step is chosen as to achieve convergence in calculations of both, Molecular Dynamics, as well as the Boltzmann collision integral 19 . Additionally, a velocity scaling is used for transferring energy to atoms which was calculated from the Boltzmann integral, Eq.…”

“…[19,22,23], was based on sp 3 parameterization. It takes into account only the 3s, 3p x , 3p y and 3p z valence orbitals of silicon.…”

“…The coupling of electrons to ions, I e-i , is calculated via the Boltzmann collision integral beyond the Fermi's Golden Rule as described in detail in Ref. [19].…”

“…(c) The transferable tight binding (TB) method is used to calculate the transient Hamiltonian, electron band structure, collective potential energy surface for atoms, and matrix elements used in the electron-ion coupling entering Bolztmann collision integral 14,19 . This method allows to include influence of the electron distribution, f e , on the interatomic potential, Ф:…”