# Synopsis: Imaging puddles

A gold nanoparticle at the end of an STM tip is used to image the local charge fluctuations on a sheet of graphene.

Graphene, a two-dimensional form of carbon where charged carriers behave like massless Dirac particles, has some remarkable properties that hold much promise for device applications, but there remain several challenges. One of them is to control the effect of randomly charged impurities located on graphene, as well as between graphene and the substrate, typically, ${\text{SiO}}_{2}$. These impurities lead to the formation of electron and hole puddles that reduce the high mobility of charge carriers in graphene. Charge puddles, whose characteristic size is unknown, can also be caused by strain from ripples in a graphene sheet.

In a paper to appear in Physical Review B, A. Deshpande and colleagues from the University of Arizona in Tucson and the University of California, Riverside, use scanning tunneling microscopy with a gold particle attached to the STM tip to image the local potential over graphene on a ${\text{SiO}}_{2}$ substrate. They achieve unprecedented resolution and show that the characteristic puddle size is about $20\phantom{\rule{0.333em}{0ex}}\text{nm}$. Previous measurements using a single electron transistor (SET) and relying on a shift of the local density of states were able to measure charge density variations on a scale of approximately $150\phantom{\rule{0.333em}{0ex}}\text{nm}$. In the setup of Deshpande et al., the availability of two tunnel barriers, tip-to-nanoparticle and nanoparticle-to-graphene, permits the use of the Coulomb blockade phenomenon. Coulomb blockade is essentially the suppression of electron tunneling when the charging energy ${e}^{2}/2C$, $C$ being the capacitance of the nanoparticle, is too high for electrons at low temperature and voltage. As the Coulomb blockade phenomenon is sensitive to both the capacitance and the electrostatic environment of the nanoparticle, peaks in the differential conductance permit a significantly higher energy resolution. This technique will enable the detection of impurities on graphene flakes for quality control during device fabrication. – Sarma Kancharla

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