Sensing of Biomolecules - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 69

including LEDs, inverters, and transistors, but more complex electronic devices,
such as NW transistor logic, crossbar memory elements, or addressable arrays,
require bottom-up methods ( Lu and Lieber 2007 ).
The NW FET biosensors are based on the changes in I D V D characteristics, as
in the cases of other FETs. The concentration of charge carriers can be expressed as

n D V th C=e.d=2/ 2 L; (2.20)

where V th is the threshold voltage, d denotes the NW diameter, L is the active length
of the NW channel, and the capacitance is given by

C D 2" 0 " d L= lnŒ.2h C d/=d; (2.21)

where " d and h are, respectively, the permittivity and thickness of the gate dielectric.
The dc characteristics of ballistic Si NW FETs with coaxial gates are found using
the Natori theory which, for a nondegenerate carrier statistics, predicts that

I D D C v T .V G V th /Œ1 exp.eV D =k B T/=Œ1 C exp.eV D =k B T/; (2.22)

where v T D .2k B T=m eff /, whereas in the case of a degenerate carrier statistics, for
very small charges in the channel, we have

I D D .2e 2 =h/V D : (2.23)

Unlike in a standard MOSFET, in which the channel conductance is controlled by
V G , in NW FETs, this conductance is independent of V G if the gate voltage has
sufficiently large values to induce carrier degeneracy.
NW FETs can be fabricated also from different nanowires, in particular the
core/shell Ge/Si nanowire depicted in Fig. 2.13 a( Xiang et al. 2006 ). Figure 2.13 b
shows that a 1D hole gas develops in the inner Ge NW, which becomes a quantum
well with high mobility and low carrier scattering rates. The transport of charge
carriers is ballistic for devices shorter than the mean-free path of 500 nm. Because
the Fermi level is located below the Ge valence band and in the bandgap of Si,
the contacts are not Schottky-like, but ohmic. These better contacts and the efficient
carrier confinement in these radial NWs with a length of 1m and an outer diameter
of 20 nm encouraged the production of FETs with high-k dielectrics gate isolator
layers and high performances. Typical high-k dielectric materials are HfO 2 and
ZrO 2 . The transconductance of the radial NW FETs is of 3:3 mS.m/ 1 and its
on-current takes a value of 2.1 mA, both parameters exceeding several times the
corresponding values in state-of-the-art MOSFETs.
Another common way to produce high-quality NW FETs focuses on decreasing
the contact resistance of the transistor. To achieve this, multiple NWs are arranged
in parallel by dielectrophoresis, performed by a low-frequency alternative current
flowing between drain and source. The multi-NW transistor is presented in Fig. 2.14 .