show the result of such a calculation for varying V DC g for space charge density in the center of the NW. For positive voltages the Fermi energy is very close to the conduction band of the InAs and as a result the charge density is very uniform while behaving as a metal like system. This simple modeling supports our arguments that a gradient of electron density can modify the capacitive coupling and the resulting amplitude. Further analysis is needed to solve self consistent solutions to the Poisson’s equation where the dielectric constant is itself a function of the density and the quantitative variation of Q and amplitude with sign of V DC g . Our measurements suggest a way to tune the efficiency of actuation by tuning the density of carriers. We next consider three other features of our data – first, the presence of other mechanical modes near the fundamental mode; second, the mixing of modes as a function of the V DC g , and third, the non-linear properties of NW oscillators driven to large amplitudes. Fig.4a and 4b show the plot of I$_{mix}$ (Δ ω ) as a function of V DC g and ω for device-3 and device-2. It is well known that for a doubly clamped beam with no tension, f$_{n}$ = C$_{n}$ r l 2 √ E ρ with C$_{0}$ = 1 . 78, C$_{1}$ = 4 . 90 and C$_{2}$ = 9 . 63 for the transverse modes. It is clear that if the fundamental mode ( f$_{0}$ ) is described by a mode with zero nodes and moving in a plane perpendicular to the substrate, the other observed modes, in the frequency range near f$_{0}$ (Fig.4a, 4b), cannot be defined by f$_{1}$ and f$_{2}$ . We have observed the anticipated f$_{1}$ and f$_{2}$ modes at higher frequencies. The other modes beside the fundamental in Fig.4a, 4b, are explained due to geometrical asymmetry along the diameter in the NW (Fig.4c, details of this calculation provided in Supporting Information). These are the modes involving motion in a plane that is not perpendicular to the substrate. This would explain the less steep slope of the dispersion as a function of V DC g . Fig.4a and 4b also show the mixing of the modes as a function of V DC g . The mode mixing can be seen clearly in Fig.4d which shows a close-up of the data in Fig.4b. Displacement along the transverse direction y (perpendicular to z ) will weakly affect the capacitance because of any slight asymmetry in the physical structure of the NW. The coupling coefficient 1 2 ∂ $^{2}$C $_{∂z∂y}$( V DC g ) 2 appearing in the potential energy gives rise to mode-mixing (see Supporting Information). For the device shown in Fig.4b the minimum frequency gap in the region of level repulsion is 0 . 25 ± 0 . 02 MHz. The asymmetry in the amplitude of the modes away from the region of mixing can also be understood within this model. We next consider the non-linear response of these NEMS oscillators. Due to electrostatic 7