Fundamentals on Bionanotechnologies - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 7

Fig. 1.6 The DOS of QWR

r QD

z

x y

E

E S,111 E S,112 E S,113

When a one-dimensional (1D) ballistic conductor is situated between two
contacts with the role of electron reservoirs, an external bias V induces the electron
transfer and imposes a nonequilibrium regime, with no common Fermi energy level
across the structure. However, it is possible to define a spatially varying local quasi-
Fermi level, with values E FL and E FR , respectively, in the left and right contacts.
Then, in a ballistic quantum wire conductor, supposing that E FL >E FR and that the
contacts are reflectionless, we have eV D E FL E FR if the bias is not very large.
At zero temperature, the electrons participating at current flow have energies only in
the E FR <E<E FL interval. Moreover, for a ballistic conductor with unchanging
cross section, in which no electron scattering between different subbands occurs,
each occupied subband adds a term of I D ev ın to the total net current, where
ın D .dn=dE/ eV denotes the additional electron density in the left contact and
v D„ 1 .dE=dk/ is the velocity of electrons along the direction of current flow.
The total current is then I D .2e 2 =h/ MV if the number of subbands M.E/ does
not change across the energy range E FR <E<E FL . In this case, the conductance
is given by

G D I=V D 2e 2 M=h (1.12)
and is an integer multiple of G 0 D 2e 2 =h, called quantum conductance. In the
ballistic regime, the resistance R D 1=G D 1=.MG 0 / Š 12:9 k=M originates
in the difference at the conductor/contact interface between the infinite number of
subbands in the contacts and the finite number of transverse modes in the conductor.
So R is termed contact resistance, and its value becomes increasingly smaller than
the quantum value R 0 D 12:9 k as the number of occupied energy subbands in
the conductor raises.
In bulk materials, Ohm's law states that the conductance G is inversely pro-
portional to the length of the sample. In deep contrast, in ballistic structures, the
conductance does not depend on the conductor length but only on its width W since
the number of subbands that are occupied by electrons with the Fermi wavenumber
k F is given by M Š IntŒk F W=, where Int[x] symbolizes the integer value of the
argument x.
The step-like conductance dependence on the number of occupied subbands in
( 1.12 ) was demonstrated experimentally by low-temperature measurements on a