Electron-hole puddles in graphene form near the electroneutrality point . They represent a local change in the concentration of negatively charged carriers (electrons) and positively charged (holes) of quasiparticles and arise due to an inhomogeneous distribution of charged impurities in the substrate, as well as a local change in the density of states , for example, due to defects or deformation of the lattice, etc. reasons. In general, the charge of graphene at the point of electroneutrality is zero, that is, the number of electrons and holes coincides, but their concentration depends on the coordinates. At the boundary between the electron and hole regions, pn junctions are formed. Since the forbidden zone of graphene is equal to zero, the current through such a transition is not equal to zero, and the material remains conductive at any temperature [1] .
Substrate Effect
The quality of the substrate and the amount of impurities in it strongly affect the level of disorder in graphene: the concentration of carriers in electron-hole pools and their sizes. The first graphene samples were made on a substrate of oxidized silicon, not differing in purity, due to which the concentration fluctuations reached 10 12 cm -2 . The size of the puddles and the local position of the Dirac point were measured using a single-electron transistor sensitive to local charge [2] .
In later implementations, graphene samples were transferred onto clean smooth substrates from hexagonal boron nitride, which partially avoided the fluctuating potential, and the depth of the pools significantly decreased. This led to significantly higher carrier mobilities.
Notes
- ↑ Castro Neto et. al., 2009 .
- ↑ Martin J., Akerman N., Ulbricht G., Lohmann T., Smet JH, von Klitzing K., Yacoby A. Observation of electron – hole puddles in graphene using a scanning single-electron transistor (Eng.) // Nature Physics. - 2008 .-- Vol. 4 . - P. 144—148 . - DOI : 10.1038 / nphys781 . - arXiv : 0705.2180 .
Literature
- Katsnelson MI Graphene: Carbon in Two Dimensions . - New York: Cambridge University Press, 2012 .-- 366 p. - ISBN 978-0-521-19540-9 .
- Castro Neto AH, Guinea F., Peres NMR, Novoselov KS, Geim AK Electronic properties of graphene (English) = The electronic properties of graphene // Rev. Mod. Phys. - 2009. - Vol. 81 . - P. 109—162 . - DOI : 10.1103 / RevModPhys.81.109 . - arXiv : 0709.1163 .