Strong piezoelectricity in single-layer graphene deposited on SiO2 grating substrates

Electromechanical response of materials is a key property for various applications ranging from actuators to sophisticated nanoelectromechanical systems. Here electromechanical properties of the single-layer graphene transferred onto SiO2 calibration grating substrates is studied via piezoresponse force microscopy and confocal Raman spectroscopy. The correlation of mechanical strains in graphene layer with the substrate morphology is established via Raman mapping. Apparent vertical piezoresponse from the single-layer graphene supported by underlying SiO2 structure is observed by piezoresponse force microscopy. The calculated vertical piezocoefficient is about 1.4 nm V−1, that is, much higher than that of the conventional piezoelectric materials such as lead zirconate titanate and comparable to that of relaxor single crystals. The observed piezoresponse and achieved strain in graphene are associated with the chemical interaction of graphene's carbon atoms with the oxygen from underlying SiO2. The results provide a basis for future applications of graphene layers for sensing, actuating and energy harvesting.


Supplementary Note 1 Raman spectroscopy measurements Typical Raman spectrum of single-layer graphene
The typical Raman spectrum of the single-layer graphene (SLG) consists of 3 main lines: D, G and 2D bands 1 (Supplementary Figure 1). The D-band (at about 1350 cm -1 ) is due to the breathing vibrations of sp 2 carbon rings and requires defects for its activation in the spectrum.
The doubly degenerated G-band (at about 1580 cm -1 ) corresponds to the in-plane vibrations of sp 2 carbon atoms and is ideal to study in-plane stresses and strains. The 2D-band (at about 2672 cm -1 ) is the second order of the D-band. This peak, being a single in SLG, splits into several peaks in bilayer graphene.

Estimation of graphene quality
High confocality of the microscope makes the Raman lines intensities dependent on the surface relief. Therefore, for accurate analysis of the G and 2D-band variations of graphene, all the spectra were normalized by the maximum value of the Si first order Raman line Shape of the 2D-band outside the spot represents a single peak, whereas inside the spot it splits into several peaks, which is characteristic for bilayer graphene. 1 Thus, the largest part of the surface is covered by the single layer graphene.

Estimation of mechanical stresses on the graphene by Raman spectroscopy
Previous works show that the G-band in SLG shifts with applied uniaxial stress. 1,3-5 The rate of change of the G-band position with the applied strain (1) Integration of this expression allows calculating the shift of the G-band position under the external stress: ( Strain dependence of the G-band position depends on a way of graphene creation. Tensile strain in exfoliated graphene leads to  substrate the position of the G-band was defined as 1580 cm -1 , but for CVD graphene this value can be different. Therefore, Raman spectra were measured in 10 points out of the grating region, where the strain is assumed to be zero. Fitting of these spectra allowed us to obtain the average position of the G-band ω 0 equal to 1585.6 cm -1 (dashed line in Supplementary Figure 4(b)) and estimate the value of the strains (right axis in Supplementary Figure 4(b)). Since the lowest position of the G-band nowhere reaches the initial value, we concluded that graphene sheet is stressed in greater or lesser degree at each point of the grating.
Spatial distribution of the strains (strain map) is shown in Supplementary Figure 4 Figure 4(b)). This effect can be attributed to strains appeared in the grating modulated graphene sheet.

Supplementary Note 2 Electrostatic equation for tip potential
To calculate the piezoelectric coefficient, we need to know electric field E in the carbon oxide layer (Supplementary Figure 5). Consider electric field below the tip in the thin carbon- For N particles of charge q i located at points i r : In the model where tip is considered as a sphere of radius R 0 we can use a relation of potential for one particle with the charge located at the center of the sphere (Supplementary The electric field below the tip in the layer is: Substituting it into Supplementary Equation 8 gives: The average field within the GO layer below the tip is integral over the GO layer thickness h divided by h:  (9) Typical distance between graphene layers in graphite is 2.5 -3 Å. Assuming