Geometric progress in the thickness of exfoliated van der Waals crystals on the example of MoS2

Abstract

To obtain molecularly thin flakes via mechanical exfoliation from a bulk layered crystal, the process should be repeated multiple times, but the mathematical principle behind this phenomenon remains unknown. In this paper, we show how the thickness of the MoS2 flake changes with subsequent cleavages of the adhesive tape, with the tests carried out on two widely used dicing tapes and Scotch removable tape. In the beginning, we assumed that with each subsequent tear of the tape, the thickness of the material decreases by half. We discovered that the exfoliated crystal thickness decreases with geometric progress and proposed a formula depicting that phenomenon. In addition, the exfoliated flakes are observed to crumble during the process and the fragmentation factor is discussed as well. Our observations will allow for more efficient estimation of the number of steps required to produce a sample of the desired thickness, relevant for tuning electronic transport properties and optical activity of two-dimensional materials.