which technique you follow for deposition?

What do you understand under critical thickness? Is it the thickness for which the isolated islands forming from condensating vapours start to be connected?

Dear Prof. Walid Tawfik,

I am using "sputtering" technique.

Dear Prof. Lech Pawlowski,

You are asking an interesting question in trying to answer my question. I am not sure how to determine the critical thickness when it comes to various coating techniques. However, are you implying that the isolated islands form below critical thickness and then upon connecting the grow thicker than the critical thickness?

I would deeply appreciate some answers on this topic. This issue has occupied my mind for a long time.

Best regards

My question concerns rather the word "critical" which you are using. One characteristic thickness for each technique which bases onto vapours condensation is the one related to connection of isolated islands. It must be added that, firstly the thickness defined in such way depends on the temperature of deposition, and, secondly, on chemical affinity between substrate and film. The factors determine, to my understanding, the size of islands (see diagrams of Movchan and Demchishin and of Thornton)

Misfit dislocations only form once the overlayer has reached and surpassed a critical thickness. This is the thickness beyond which the fully strained layer is no longer stable, a concept first defined by Frank and van der Merwe. Sufficiently thin strained layers are thermodynamically stable because the strain energy is linearly proportional to the film thickness and vanishes at zero thickness. The energy of the defects, in contrast, has a nonvanishing lower limit and depends more weakly on thickness.

(1) Kolasinski, K. W. Surface Science: Foundations of Catalysis and Nanoscience; 3rd ed.; Wiley: Chichester, 2012.