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such calculations (Fig.2c) quantitatively explains the experimental observations. V th g , the value at which the crossover from negative to positive dispersion occurs is a function of the dimensions of the NW and the capacitive geometry of the device. The effect of the device dimension is clearly seen in a larger value of V th g in device-2 shown in Fig.2b where the doubly clamped beam is 120 nm thick, as against 100 nm for device-1 in Fig.2a (the lengths differ by 200 nm). 

Next, we consider another complementary aspect of the data – the amplitude of the mixing current. Fig.2d shows I$_{mix}$ (Δ ω ) (log-scale) as a function of V DC g . We see that the amplitude of the mixing current for the negative values of V DC g are significantly larger than those for positive V DC g for the same mechanical mode; this is also seen in Fig.1b. We now try to understand this asymmetry as our InAs NW are n-type semiconductors [26] as seen in Fig.1c. To understand this asymmetry we have carried out detailed fits of the experimental data for the amplitude of mixing current as a function of frequency using Eqn.1. The amplitude z ( ω ) of oscillation at frequency ω is given by 

<img src='content_image/352422.jpg'>

where z reso amp is the amplitude at resonant frequency ω$_{0}$ , Q is the quality factor and Δ φ is the relative phase difference between the ω and ω + Δ ω signals that depends on the device parameters like the contact resistance. Fitting from Eqns.1 and 2 allow us to extract the variation of Q as a function of V DC g as shown in Fig.2e ([35]). We have also estimated the amplitude of oscillation using Eqns.1 and 2 by examining the ratio I$_{oscn}$ (Δ ω ) I$_{back}$ (Δ ω ) = dC g dz z ( ω ) V DC g C$_{g}$V$_{g}$ ( ω ) . A plot of the calculated amplitude ( z reso $_{amp}$) is seen in Fig.2f. We see that as the | V DC g | is increased Q and z reso amp are observed to decrease. We also observe that there are noticeable differences in Q and z reso amp for positive and negative values of V DC g . The values of Q and z reso amp are larger for positive V DC g . One of the possible mechanisms that can explain this behavior in the amplitude is that with increasing V DC g one increases the density of electrons in the NW leading to reduction in the screening length. This implies that the simple geometrical capacitance is inaccurate particularly since the screening length can be comparable to NW diameter at low densities (at negative V DC g in our case). In our device geometry, using Thomas-Fermi approximation [22], screening length is around 20-40 nm (diameter of our devices are 100 nm) and the distance between the nanowires and gate oxide 200nm. So, 

