size (a ), operation energy (E
bit
), device density (n) and the total number of devices in system (N)is
given in Table 3.7. The transition to 3D circuits will require a new device geometry, e.g. cylindrical
nanowire, and new interconnect strategies.
Devices beyond FET also need to be analyzed for their potential to offer more functionality at less
device count and/or smaller energy of operation. In the nanomorphic cell, volume utilization and
energy minimization are the two main criteria for device evaluation.
The volumetric constraints imposed by the nanomorphic cell suggest device scaling beyond the
limits of the electron-charge-based FET needs to be explored. Device scaling below 5 nm might utilize
information-bearing particles whose mass exceeds that of the electron. It has been shown theoretically
that ‘atomic switches’ based on moving atoms as information carriers can offer superb switching
characteristics relative to electron-based devices in deep nanometer domain [22]. ‘Nanoionic’ devices
have already attracted the attention of several research groups and several promising experimental
devices have been recently demonstrated [5,6,8,23–25].
APPENDIX 1: QUANTUM CONFINEMENT
Consider a particle (e.g. an electron) confined in a one-dimensional potential well of width w with
abrupt (vertical) walls (Fig. A1.1). The Heisenberg coordinate-momentum relation (3.5b) for a ¼ 1
and
D
x ¼ w results in
Dp,w h (A1.1)
Let the electron possess a certain kinetic energy E and therefore, a momentum p ¼
ffiffiffiffiffiffiffiffiffi
2mE
p
(the
reflects the fact that the direction of the momentum is undefined (i.e. right or left). Thus
Dp ¼ p
p
¼ 2p ¼ 2
ffiffiffiffiffiffiffiffiffi
2mE
p
(A1.2)
Substituting (A1.2) in (A1.1) results in
2w
ffiffiffiffiffiffiffiffiffi
2mE
p
h (A1.3)
or
w
ffiffiffiffiffiffiffiffiffi
2mE
p
h
2
(A1.4)
Table 3.7 Projected device characteristics for binary switches for different system size
and topology
System
size
System
Topology E
bit
a, nm n N
Lower bound 2D, 3D w3 k
B
T ¼ 10
20
J1nmw10
13
cm
2
w10
19
cm
3
–
2022 planar FET w cm 2D 600 k
B
Tw2$10
18
J 5 nm 10
10
cm
2
10
10
2022 planar FET w10
m
m 2D 260 k
B
Tw 10
18
J 5 nm 10
10
cm
2
10
4
2022 NW FET w10
m
m3D 56k
B
Tw2$10
19
J 5 nm 10
17
cm
3
10
7
Appendix 1: Quantum confinement 85
Thus the minimum kinetic energy (also called the ground-state energy) of a particle in a well is
E
min
¼
h
2
8mw
2
(A1.5)
Equation (A1.5) coincides with a standard solution of a quantum mechanical problem for a particle in
a rectangular box with infinite walls [11].
Note that the ground state energy E
min
is always above the bottom of the well and it moves higher
when the width of the well decreases, an effect called quantum confinement. Quantum confinement
sets a limit on the minimum width of the well for the binary switch shown in Figure 3.4. If the well is
formed by barriers of finite height E
b
, the effective barr ier height for a particle confined in the well is
less than E
b
:
E
b
eff
¼ E
b
E
min
(A1.6)
If the effective barrier becomes very small, the particle can jump over due to, e.g., thermal excitations.
Thus an estimate for the minimum size of the well is suggested by E
b
¼ E
min
. From (A1.5):
E
b
E
min
E
beff
=E
b
-E
min
FIGURE A1.1
Electron confined in a rectangular well
FIGURE A1.2
Effective barrier height for an electron confined in a potential well
86 CHAPTER 3 Nanomorphic electronics
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