Open AccessThe numerical-aperture-dependent optical contrast and thickness determination of ultrathin flakes of two-dimensional atomic crystals: A case of graphene multilayers
Author(s) -
Wenjuan Han,
Yanmeng Shi,
Xiaoli Li,
Shiqiang Luo,
Yan Lü,
PingHeng Tan
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.110702
Subject(s) - materials science , graphene , numerical aperture , optics , transfer matrix method (optics) , diffraction , wavelength , substrate (aquarium) , aperture (computer memory) , dielectric , transfer matrix , matrix (chemical analysis) , optoelectronics , nanotechnology , composite material , physics , oceanography , geology , computer science , acoustics , computer vision
The optical and electronic properties of two-dimensional atomic crystals including graphene are closely dependent on their layer numbers (or thickness). It is a fundamental issue to fast and accurately identify the layer number of multilayer flakes of two-dimensional atomic crystals before further research and application in optoelectronics. In this paper, we discuss in detail the application of transfer matrix method to simulate the optical contrast of ultrathin flakes of two-dimensional atomic crystals and further to identify their thickness, where numerical aperture of microscope objective is considered. The importance of numerical aperture in the thickness determination is confirmed by the experiments on the graphene flakes. Furthermore, two lasers with different wavelengths can be serviced as light sources for the thickness identification of flakes of two-dimensional atomic crystals with a size close to the diffraction limit of the microscope objective. The transfer matrix method is found to be very useful for the optical-contrast calculation and thickness determination of flakes of two-dimensional atomic crystals on multilayer dielectric substrate.