Sensing of Biomolecules - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 84

Fig. 2.25 Nanoscale metallic
CNT cantilever and the forces
actingonit

y

F el

CNT

D

V

F e-s

F vdW

h

x

Fig. 2.26 Double-clamped
CNT working as a switch

y

CNT

V

h

x

The van der Waals force influences dramatically the deflection of nanocantilevers.
It can attract the cantilever toward the substrate electrode even in the absence of
an applied voltage; because it is an attractive force, this phenomenon occurring
especially when the distance between the cantilever and the substrate is of only few
nanometers. Moreover, the van der Waals force reduces the threshold voltage of the
cantilever illustrated in Fig. 2.25 , but has no significant effect for double-clamped
CNT. A double-clamped CNT cantilever, as that represented in Fig. 2.26 ,whether
of microscale or of nanoscale dimensions, can act as a switch in the presence of
a substrate electrode or as a mechanical resonator in the absence of this electrode.
In the last case, the double-clamped CNT resonator has a mechanical oscillation
frequency given by f osc Š 1:03.E=/ 1=2 .2R=L 2 /,where is the density of the
cantilever material.
When a bias V is applied between the contacts of the double-clamped CNT
cantilever, its deflection is not a continuous function of the actuation voltage but
a discrete function if the carriers are injecting from the contacts in the cantilever via
tunneling ( Sapmaz et al. 2003 ). Each step of the cantilever deflection corresponds to
an electron injected inside the CNT. In addition to the deflection induced by the gate
voltage V G , the CNT bends due to an electrostatic contribution of the bias V ,which
generates a maximum discrete deflection of the double-clamped CNT resonator
given by

y max D 0:013. ne / 2 L 2 = ER 4 h; (2.54)

when the total stress T is much larger than EI =L 2 ,and