Dear Ayca Coskun , what we usually do for cleaving mica is using a razor blade, or adhesive tape if we want something thinner. In both cases the splited surfaces should be clean enough and they should need further cleaning. It is true that the surfaces can be formed by terraces or steps, but each one should be clean and equally oriented if the mica crystal is a single one.
In principle, when you split apart two crystalline plates, you are breaking the bonds between the planes and therefore you end up with pristine clean surfaces.
It is possible that some splinters or small fragments from the edge of the plates will be produced in the process. A clean flow of dry N2 gas can remove these tiny flackes.
The best idea to keep the surfaces clean is to produce them just before their use.
You don´t need cleaning what is already clean. Piranha is used both for cleaning and also for surface modification.
According the review by Christenson and Thomson, when mica is cleaved in air and the fresh mica surface and CO2 and water from the air reacts immediately, forming K2CO3 (a molecule per nm2) and properties of mica in air or water vapour cannot be properly understood without the presence of these K2CO3 at the surface.
Epitaxial crystal growth has been achieved by vapor deposition and solution, and according the cited work, the presence or absence of potassium ions appears to have a major effect on crystal growth and epitaxy on the mica surface. Chirstenson et al found for example that epitaxial growth of CaCO3 did not happen on solution on freshly cleaved mica, while it grew up epitaxially on mica after 30min exposed to low humidity air.
In other cases, such as vapour deposition of pentacene, it grows differently if the surface is fresh than if the potasium ions are removed by water or ethanol.
Please have a look to this review, which I think will be useful to you:
Article The nature of the air-cleaved mica surface
I looked at the article you sent with the necessary information for me, it contains answers to many questions I will ask from now on. Thank you both for the article and for sincerely answering my questions.