Fundamentals on Bionanotechnologies - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 2

CMOS technology NEMS carbon nanotube

/graphene

nanowires

1 mm 100 nm 1 nm

10 nm

bacteria

viruses DNA

proteins

Fig. 1.1 Dimension scale of biological systems and electron devices, where NEMS stands for
nanoelectromechanical systems

Fig. 1.2 The Fermi-Dirac
distribution function

f

T 1

1

0.5

T 2 > T 1

E

E F

In the case of nanoscale devices, the confinement of carrier wavefunctions
produces a discretization of the energy spectrum of charge carriers as well as
discontinuities in the density of states. These effects cause further important changes
in the transport properties of charge carriers depending on the number of dimensions
along which the motion of carriers is restricted.
In bulk materials with dimensions of few millimeters, the transported carriers
move randomly due to repeated scatterings with impurities and phonons. The carrier
transport is thus of a diffusive type, which is modeled in general by a stochastic
Boltzmann equation. The Boltzmann equation loses its validity as soon as the
dimensions of the material shrink to nanoscale. The nanoscale is often termed as
mesoscale since it is intermediate between the macroscopic scale and the atomic
scale, where the atoms and molecules with sizes of the order of 1 A D 10 10 mare
described by quantum mechanical laws.
At the nanoscale, the electron transport is dictated by the relation between the
dimensions of the sample and three parameters ( Datta 1997 ):

1. The mean-free path L fp , which is the average distance between two electron
collisions with phonons or impurities that cancel the initial momentum of a
charge carrier.
2. The phase relaxation length L ph , which represents the propagation distance
after which the electron coherence, i.e., the phase memory of electrons, van-
ishes as a result of time-reversal breaking. Examples of such processes are