Transient structure of thin films based on one-dimensional chain model

Functional materials have received much attention in the development of scientific technology. Macroscopic function of material is usually linked to the microscopic properties. In order to understand the relationship between structure and function, it is necessary to observe transient structural change of material in real time. In the earlier experimental work femtosecond optical probes were used to measure associated modulation in optical properties like transmissivity or reflectivity and extract the information about structural dynamics through sophisticated theoretical modeling. Since the development of laser-based ultrafast X-ray sources, there has been extensive work on femtosecond X-ray diffraction measurements. The coupling of sensitive X-ray with time-resolved pump-probe technique provides a way to directly monitor the time-dependent lattice structural changes in condensed matter. Recent researches are devoted to the study of non-thermal melting and coherent acoustic photons. The classical continuous elastic equation can only provide a limited view of structural dynamics. So, simulation of structural dynamics at an atomic level and comparison of such simulation with time-resolved X-ray diffraction data are necessary. In this paper, we use the one-dimensional chain model to study the effect of thermal stress on the lattice due to the inhomogeneity of temperature distribution after ultrafast laser heating. It is developed from the classic continuous elastic equation by considering a nanometer film as a chain of point mass connected by springs. The simulation can directly reveal the positon of each point mass (atom) as a function of time for a given temperature (stress) profile. The simulation results accord very well with experimental data obtained with femtosecond X-ray diffraction. Compared with simulation results, the ultrafast X-ray diffraction experimental results are not enough to distinguish the compression near the zero time, but the characteristic time (similar to 123 ps) and broadening of the diffraction peak are clearly observed. The simulation and experimental study of the lattice structural response are of great help for understanding the direct relationship between the lattice responses caused by ultrafast laser excitation, the generation and propagation of strain, one-dimensional chain model has important applications in studying the recoverable ultrafast lattice dynamics of metals, semiconductors and other materials.