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The InAs NWs used for this work were grown using metal organic vapor phase epitaxy (MOVPE) [25, 26]. The NWs are oriented in the < 111 > direction and are 80 to 120 nm in diameter with a length of several micrometers. The substrate used for making the devices is a degenerately doped silicon wafer with 300 nm thick SiO$_{2}$. We have fabricated suspended InAs NW devices by sandwiching the NWs between two layers of electron-beam resist and then using electron beam lithography to define the electrodes and suspend them by depositing ∼ 150 nm Cr and ∼ 250 nm Au after development followed by in situ plasma cleaning [26]. The ohmic contacts also serve as mechanical supports for the NW suspended ∼ 200 nm above the surface of SiO$_{2}$. Fig.1a shows the SEM image of a resonator device and scheme for actuating and detecting the motion of the resonator. All the measurements were done at 300 K and pressure less than 1 mBar. 

To actuate and detect the resonance we use the device as a heterodyne mixer [6, 12, 18, 27– 29]. We use electrostatic interaction between the wire and gate to actuate the motion in a plane perpendicular to the substrate. We apply a radio frequency (RF) signal V$_{g}$ ( ω ) and a DC voltage V DC g at the gate terminal using bias-tee. Another RF signal V$_{SD}$ ( ω + Δ ω ) is applied to the source electrode (Fig.1a). The RF signal applied at the gate V$_{g}$ ( ω ) modulates the gap between NW and substrate at angular frequency ω , and V DC g alters the overall tension in the NW. The amplitude of the current through the NW at the difference frequency (Δ ω ), also called the mixing current I$_{mix}$ (Δ ω ), can be written as [12] 

<img src='content_image/352956.jpg'>

where G is the conductance of the NW, q is the charge induced by the gate, C$_{g}$ is the gate capacitance, z ( ω ) is the amplitude of oscillation at the driving frequency ω and z axis is perpendicular to the substrate. The term I$_{back}$ (Δ ω ) = 1 2 dG dq C$_{g}$V$_{g}$ ( ω ) V$_{SD}$ is the background mixing current which is independent of the oscillation of the NW and I$_{oscn}$ (Δ ω ) = 1 2 dG dq dC$_{g}$ dz z ( ω ) V DC g V$_{SD}$ depends on the amplitude of oscillation. Measuring I$_{mix}$ (Δ ω ) using a lock-in allows us to monitor the resonance of the NW as the frequency is swept. Fig.1b shows I$_{mix}$ (Δ ω ) as a function of ω for V DC g = ± 36.4 V. The sharp fea- ture corresponds to the mechanical resonance of the NW. We address the asymmetry of the mixing current signal for ± V DC g later. Fig.1c shows the plot of conductance ( G ) as a function of V DC g . The variation of G with V DC g is very critical for this scheme of heterodyne 

