Raman spectroscopy of electrochemically gated graphene transistors: Geometrical capacitance, electron-phonon, electron-electron, and electron-defect scattering

We report a comprehensive micro-Raman scattering study of electrochemically gated graphene field-effect transistors. The geometrical capacitance of the electrochemical top-gates is accurately determined from dual-gated Raman measurements, allowing a quantitative analysis of the frequency, linewidth, and integrated intensity of the main Raman features of graphene. The anomalous behavior observed for the G-mode phonon is in very good agreement with theoretical predictions and provides a measurement of the electron-phonon coupling constant for zone-center (Gamma point) optical phonons. In addition, the decrease of the integrated intensity of the 2D-mode feature with increasing doping, makes it possible to determine the electron-phonon coupling constant for near zone-edge (K and K' points) optical phonons. We find that the electron-phonon coupling strength at Gamma is five times weaker than at K (K'), in very good agreement with a direct measurement of the ratio of the integrated intensities of the resonant intra- (2D' mode) and intervalley (2D mode) Raman features. We also show that electrochemical reactions, occurring at large gate biases, can be harnessed to efficiently create defects in graphene, with concentrations up to approximately 1.4 x 10(12) cm(-2). At such defect concentrations, we estimate that the electron-defect scattering rate remains much smaller than the electron-phonon scattering rate. The evolution of the G- and 2D-mode features upon doping remain unaffected by the presence of defects and the doping dependence of the D mode closely follows that of its two-phonon (2D mode) overtone. Finally, the linewidth and frequency of the G-mode phonon as well as the frequencies of the G- and 2D-mode phonons in doped graphene follow sample-independent correlations that can be utilized for accurate estimations of the charge carrier density.