I had read the many papers, in-which they had proved the modification of materials thin-films due to the transient temerature spike arises because of ion beam irradiation. Can anyone explain, how exactly one could do that calculations...
There are many (older papers - 1976 trough 1985) on pulse heating (annealing ion implants) in semiconductors using lasers and/or electron beams. Major modeling programs may now be able to do the calculations but simple 1-D calculations follow basic principles and were done with simple code. Results are discussed in one of my old papers:
"Pulsed Electron Beam Annealing of Ion Implantation Damage," A.C. Greenwald, A.R. Kirkpatrick, R.G. Little, and J.A. Minnucci, J. Appl. Phys. 50, 783 (1979). Heating with pulsed or rapidly scanning ion beams is similar.
Basically, a beam that is absorbed in a thickness of about one micron could melt silicon in a few tens of microseconds at a flux of about one joule per square centimeter. The surface will cool very rapidly (one microsecond) and regrow the crystalline structure but dopants are redistributed.
Yoiu can revise some articles about (attached). Urbassek calculated the temperature.
We tried calculate the temperature in linear cascade (NIMB Cascade T) by using a simple estimation that an average kinetic energy of all atoms in the cascade is the cascade temperature.
In the case of thermal spike the energy distribution of recoils and atoms in the spike should be Maxwell - type. So you can try calculate yourself.