Fundamentals on Bionanotechnologies - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 6

Fig. 1.5 The DOS of QWR

r QW R

z

y

x

E

E S,11 E S,12 E S,13

so that the DOS becomes

X

.2m/ 1=2
„ L y L z

.E E s;pq / 1=2 : QWR .E/ D (1.9)

p;q

The DOS of QWR is represented in Fig. 1.5 .
Similar to the optical waveguides, the QWRs with L y ;L z <L x L fp ;L ph
and L y ;L z Š F are called electron waveguides if the energy difference between
adjacent subbands is higher than the thermal energy k B T and the possible poten-
tial drop along the waveguide, eV ,whereV is the applied bias ( Dragoman
and Dragoman 2004 ). At temperatures around 4 K, this condition is satisfied in
modulation-doped AlGaAs/GaAs heterostructures for L y ;L z Š 0:1-0:5 mand
V<1mV.
In a quantum dot (QD), the motion of charge carriers is spatially constrained
along all three directions in regions much smaller than the mean-free path and the
phase relaxation length. In this case, the discrete energy dispersion is given by

p
L x

2 q

L y

2 r

L z

2

2 2 2

E.k x ;k y ;k z / D E c C „ C „ C „ D E s; pqr ; (1.10)

2m 2m 2m

and the DOS is proportional to the Dirac function

QD / ı.E E s; pqr /: (1.11)

The DOS of QD is shown in Fig. 1.6 . The discrete energy spectrum of quantum dots
is similar to that of atoms or molecules, and therefore, sometimes, QDs are referred
to as artificial atoms.
In the ballistic regime, only electrons with energies around E F take part at
transport, whereas in the diffusive regime, electrons with a wide energy spectrum
contribute to electrical transport.