Page 149 - Science at the nanoscale

8:11
June 9, 2009
6.3. Quantum Dots, Quantum Wires
6.3 Show that density of states functions in 3D, 2D and 1D is
given by the expressions:
√
8π 2
∗3/2
p
m
E − E min , E ≥ E min
g 3D =
=
3
h
dE
4πm
∗
dn 2D
, E ≥ E min
=
g 2D =
2
h
dE
r
2m
1
∗
dn 1D
√
g 1D =
, E ≥ E min
=
2
h
dE
E − E min
6.4 The conductance of a ballistic conductor between two
reflectionless contacts at 0 K is given by:
2
2e
MT
G =
h
Define the symbols in the equation, and account for
the contributions to the total resistance of this system
comprising two contacts and a ballistic conductor with
transmission of 50% between the contacts.
6.5 For a room temperature Coulomb blockade device to be
constructed using a spherical quantum dot, estimate how
small the quantum dot should be.
Hint: For a sphere (QD):
Q
Q
= 4πε 0 R
=
Q
V
4πε 0 R
where ε 0 is the permittivity of free space (8.854 × 10
F/m). dn 3D C = RPS: PSP0007 - Science-at-Nanoscale −12 139 ch06