10 6 0 Space Charge (C/m$^{3}$) b) c)c a) d) e) f) FIG. 3: (color online) a) and b) Shows the result of a FEM based self-consistent solution of Poisson’s equation giving the potential around a doubly clamped suspended nanowire device 100 nm in diameter and 1.5 µ m long. The separation of the NW and 300 nm thick SiO$_{2}$ is 100 nm. The back plane of the nanowire is the gate held at -5V and the two terminals of the wire are grounded. The maximum of the colorscale bar (red)is 0V and the minimum (blue) is -5 V. c) The space distribution in the cross section of the nanowire for V DC g = -25V shows the gradient. The log- colorscale below varies from 10 C/m 3 (blue) to 10 6 C/m 3 (red). d) Plot of space charge density in the vertical direction at V DC g = -25V through the middle of the wire. The asymmetry along the vertical direction due the gate below the wire is clearly seen. e) The space distribution in the cross section of the nanowire for V DC g = -5V shows the gradient. The log-colorscale below varies from 10 3 C/m 3 (blue) to 10 5 C/m 3 (red). f) The space distribution in the cross section of the nanowire for V$_{g}$ = 5V shows uniform space charge distribution as the electron density in the nanowire is increased when the nanowire field effect transistor is turned on. The log-colorscale below varies from 10 3 C/m 3 (blue) to 10 5 C/m 3 (red). 14