mixing to work as it controls the overall amplitude I$_{mix}$ (Δ ω ). The hysteresis observed in the measurement of conductance is typical for our suspended devices and is associated with charge trap states with dipolar nature on surface of the nanowire [30, 31]. 

We can connect the resonant frequency of the fundamental mode, f$_{0}$ , of a doubly clamped beam at zero V DC g , to the material properties of the beam as f$_{0}$ = C$_{0}$ r l 2 V$_{s}$ where V$_{s}$ = √ E ρ is the velocity of sound; r is the radius of the beam, l is the length of the beam, E is the Young’s modulus, ρ is the density of the material and C$_{0}$ = 1 . 78. Fig.1d shows a plot for V$_{s}$ that does not vary much from the bulk value [32] (dashed line) for eight different devices. The scatter around the V$_{s}$ calculated using bulk values could be due to the relative volume fraction contribution of the amorphous layer around the NWs; this needs further detailed study. 

Fig.2a and 2b show the colorscale plot of I$_{mix}$ (Δ ω ) as a function of V DC g and ω on a logscale spanning more than 3 decades. Data is taken by sweeping V DC g for each value of frequency. In the data from both the devices we see a symmetric evolution of the resonant frequency as a function of V DC g . The parabolic behavior is expected as the attractive force exerted by the gate on the wire is given by F$_{DC}$ = 1 $_{2}$( V DC g ) $^{2}$∇ C$_{g}$ . An increase in V DC g enhances the tension in the NW[33]. We now discuss the particular W-shaped dispersion of modes as a function of V DC g . As | V DC g | is increased, initially the mode disperses negatively and after a certain threshold voltage V th g it disperses with a positive slope. Although purely negatively and positively dispersing modes have been studied in detail before by Kozinsky et al. [34], we observe the crossover regime where these interactions compete. This particular dispersion can be understood using a toy-model in which a wire is suspended from a spring of force constant K$_{i}$ above the substrate. The wire and the substrate make up the two electrodes of a capacitor. There are two consequences of increasing | V DC g | : first, it changes the equilibrium position by moving the NW closer to the substrate and second, it makes the local potential asymmetric and less steep. The effective force constant, K$_{eff}$, is reduced, resulting in negative dispersion of the mode for | V DC g | < | V th g | . If the intrinsic force constant K$_{i}$ had been independent of V DC g , the modes would always disperse negatively when motion occurs perpendicular to the gate plane. However, in general K$_{i}$ can be written as k + α ( V DC g ) 2 + β ( V DC g ) 4 + H.O. ( V DC g )); where k , α , and β are constants. With V DC g ̸ = 0 then, to a first approximation, K$_{eff}$ = K$_{i}$ − 1 $_{2}$( V DC g ) 2 d $^{2}$C$_{g}$ dz 2 . We find that the W-shape of the dispersion curve can be explained only if one considers the case where β > 0. The result of 

