To understand the band bending caused by metal contacts, we study the potential and charge density induced in graphene in response to contact with a metal strip. We find that the screening is weak by comparison with a normal metal as a consequence of the ultrarelativistic nature of the electron spectrum near the Fermi energy. The induced potential decays with the distance from the metal contact as x−1/2 and x−1 for undoped and doped graphene, respectively, breaking its spatial homogeneity. In the contact region, the metal contact can give rise to the formation of a p-p′, n-n′, and p-n junction (or with additional gating or impurity doping, even a p-n-p′ junction) that contributes to the overall resistance of the graphene sample, destroying its electron-hole symmetry. Using the work functions of metal-covered graphene recently calculated by Khomyakov et al. [Phys. Rev. B 79, 195425 (2009)], we predict the boundary potential and junction type for different metal contacts.
|Journal||Physical review B: Condensed matter and materials physics|
|Publication status||Published - 2010|