Optical second-harmonic generation induced by electric current in graphene on Si and SiC substrates

We find that the flow of direct electric current (dc) through graphene on substrate enhances surface optical second-harmonic generation (SHG) from the graphene/substrate system. The current can enhance surface SHG by about 300% for a chemical-vapor-deposition (CVD) graphene monolayer on a SiO${}_2/\mathrm{Si}\left(001\right)$ substrate, and by about 25% for an epitaxial four-layer-graphene film on a 3.5°-miscut vicinal SiC(0001) substrate. The enhancement in both the CVD and epitaxial graphene samples is due to electric field-induced SHG, which is produced by the current-associated vertical electric field at the SiO${}_2/$Si interface or at the graphene/SiC interface. Measurements of rotational-anisotropy SHG (RA-SH) from both samples revealed that the current-induced SHG varies strongly with the measurement location along the current flow direction. By measuring RA-SH from the vicinal SiC(0001) substrate, we determined all three second-order susceptibility tensor elements ($d_{33}$ = −52.0 pm/V, $d_{15}$ = 20.0 pm/V, and $d_{31}$ = 18.7 pm/V) that characterize the SHG response of hexagonal SiC at the fundamental wavelength of 740 nm. We further determined the three effective susceptibility tensor elements ($d_{33}$ = −135.8 pm/V, $d_{15}$ = 18.5 pm/V, and $d_{31}$ = 14.6 pm/V) that characterize the surface SHG from the graphene/vicinal-SiC(0001) sample and finally showed that the current-dependent tensor element $d_{33}$ can be enhanced to a large value of $d_{33}$ = −199.0 pm/V by electric current in epitaxial graphene.

Figure 1

(a), (left panel): Measured rotational-anisotropy SHG (RA-SH) scans from the graphene/SiO${}_2/\mathrm{Si}\left(001\right)$ sample at a fixed graphene location for 0 and different negative currents (−0.5, −1.1, and −2.4 A/m). (b), (left panel): The above scans for different positive currents. The S and D electrodes, measurement location, and definition of the negative/positive current direction are illustrated by the inset in each panel. Right panel: RA-SH scans at a fixed current $I$ = ±2.4 A/m measured at three different graphene locations: (a) nearby the S electrode, (b) halfway between S and D, and (c) nearby the D electrode. Measurement locations are illustrated in each panel as an inset.

Figure 2

(a) Schematic illustration of the graphene/SiO${}_2/\mathrm{Si}\left(001\right)$ sample with patterned electrodes, showing two mirror planes of symmetry of the system when $I$ = 0. (b) Polar plot of RA-SH scans measured at the central graphene location for a fixed current of ±2.4 A/m, showing kitelike RA-SH patterns. Electric current is in (perpendicular to) the plane of incidence when ϕ = 90° (0°), as illustrated by the insets. (c) Schematic illustration of the lateral distribution of local electric field across the SiO${}_2/$Si interface, laser sampling ring, definition of the positive ($I$ > 0) current direction.

Figure 3

(a) Fit coefficients $a_0$ and 4 × $a_4$ of RA-SH patterns in Fig. 1 (left panel) measured at a fixed graphene location $x$ = 1.00 mm for different current amplitudes and both positive and negative current directions. The measurement location with respect to the S and D electrodes and the positive current direction are illustrated by the inset. (b) Fit coefficients $a_0$ and 4 × $a_4$ at different graphene locations $x$, at a fixed current amplitude $I$ = 2.4 A/m, and for both positive and negative current directions. Note that a sign flip of $a_0$ develops through a 0.3-mm-wide transition region in the central graphene area.

Figure 4

(a) Measured rotational-anisotropy SHG (RA-SH) scans from the graphene/SiO${}_2/\mathrm{Si}\left(001\right)$ sample for zero and different positive bias voltages (+6, +12, +18, and +25 V). (b) The above RA-SH scans for zero and different negative bias voltages. Thin lines in (a) and (b) are experimental data, and thick smooth curves are Eq. (6) fits. (c) Fit coefficients $a_0$ and 4 × $a_4$ for different bias voltages and polarities. Linear fits of the bias-dependence of $a_0$ are shown for bias amplitudes above 6 V. The positive bias situation for the measurement of electric field-induced SHG (FI-SH) is illustrated by the inset.

Figure 5

Measured rotational-anisotropy SHG (RA-SH) scans for four different polarization configurations ($pp$, $sp$, $ss$, and $ps$) from (a) the vicinal SiC(0001) substrate and (b) the graphene/vicinal-SiC(0001) sample. The dotted lines are experimental data, and the smooth curves are Eqs. (9) and (10) fits.

Figure 6

Measured $pp$-polarized rotational-anisotropy SHG (RA-SH) scans from the graphene/vicinal-SiC(0001) sample when current $I$ = 0 and ±23 A/m ($I$ > 0 and $I$ < 0) in graphene for three different measurement locations (as illustrated by an inset in each panel): (a) nearby the S electrode, (b) halfway between S and D, and (c) nearby the D electrode. The S and D electrodes, measurement location, and definition of the negative current ($I$ < 0) are illustrated as an inset in panel (a). The dotted lines are experimental data, and the smooth curves are Eq. (9) fits.