The author reports on idea of momentum effect of gaseous beam particles as to thin film epitaxial crystal growth such as molecular beam epitaxial growth or metal organic chemical vapor deposition epitaxial growth on stiffness of epitaxial growth thin film. The author presented that liquid glass encapsulation squeeze compression effect of liquid-glass-encapsulation Czochralski technique (LEC) crystal growth [Y.Saito, presented at the 10th Int. Conf. on Crystal Growth, 1992], third element different from crystal matrix elements [Y.Saito, presented at the 9th Int. Conf. on Ternary and Multinary Compounds, 1993], light momentum pressure of substance cooling thermal cycle [Y.Saito, presented at the 1st Int.Symposium on Laser and Optoelectronics Technology & Applications, 1993] can yield firmly binded bonds of substance elements. On the other hand, collisions of particles sputtered from solid target slabs [Y.Saito, presented at the 2nd Int.Symposium on Sputtering & Plasma Processes, 1993] or accelerated ions or particles evaporated from molten metals with themselves on the thin films can yield binded bonds. It was shown that internal compression in a crystal by ion implantation in crystal cell lattices can make the refractory state to gas phase chemical attack.[Y.Saito, in the Materials Research Society Symposium Proc. Vol. 279, pp. 135–140.] From these results, we can consider momentum effect at collision on binding state. After collision binding, internal compression by thermal transition variation in a multilayer structure during cooling thermal cycle influences binding stiffness.