Fundamentals on Bionanotechnologies - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 8

Fig. 1.7 ( a ) The gate voltage
dependence of conductance at
zero temperature ( solid line )
and finite temperatures
( dotted line )in( b )a1D
ballistic conductor with
tunable width

a

G / G 0

4

3

2

1

V

- V 1 - V 2 - V 3 - V 4

b

metallic gate

V

W

2DEG

contact contact

ballistic wire with a variable width, as illustrated in Fig. 1.7 a( del Alamo et al. 1998 ).
The conductance rises in steps of G 0 for any increases with one unity of M,
this stair-like shape being “smoothed” as the temperature increases due to thermal
vibrations. A split-gate geometry as that displayed in Fig. 1.7 bmustbeusedto
obtain a 1D ballistic quantum wire from a 2DEG. In this geometry, a narrow slit,
which has a width W on the order of F , is cut in a depleting gate patterned above
the 2DEG. The effective width W of the conductor can be decreased by applying a
gradually increasing negative gate voltage V , so that the number of transverse modes
M is modified in a stepwise manner. The split-gate configuration is termed quantum
point contact if the constriction length is small enough (in fact, is comparable to its
width) and is referred to as electron waveguide if the constriction is much longer
than W .
The hypothesis made in deriving ( 1.12 ), i.e., that all electrons originating in
the left contact reach the right contact, is not always valid. For instance, if the
ballistic conductor is composed of several sections with different potential energies
or widths, the electrons from the left contact are only partially transmitted to the
right contact. If T designates the transmission probability of the ballistic conductor
attached to reflectionless contacts via ballistic leads, as illustrated in Fig. 1.8 ,the
zero-temperature conductance between the contacts is given in this situation by the
Landauer formula ( Datta 1997 )

2e 2
h MT ;

G D (1.13)