Electric Clock for NanoMagnet Logic Circuits - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 83

Fig. 9. Process variation evaluation. The analysis is extended considering process vari-
ations on the shorter magnets side, for nickel of ± 5 % (A), ± 10 % (B), ± 20 % (C), then
for terfenol of ± 5 % (D), ± 10 % (E) and ± 20 % (F).

To comply to these rules the NML circuit design chosen for this particular clock
system is based on NAND/NOR gates, since they are universal gates that can
implement any kind of logic function. Figure 10 shows the layout of NAND
gate. A NOR gate can be simply obtained changing the shape of the central
magnet [ 17 ].
Every clock zone is made by a mechanical isolated island of piezoelectric
material. Magnets are deposited directly on top of the piezoelectric layer to
maximize the mechanical coupling. A NAND gate can be built coupling a AND
gate [ 17 ] with an inverter, which is simply built by an horizontal wire with an odd
number of magnets. Helper blocks [ 36 ] are used to help the signal propagation
in presence of vertical NML wires. Every gate has two inputs and can have up
to two outputs as outlined in Fig. 10 .
Theoretically, the electrodes should be placed at both sides of the piezoelec-
tric island, as shown in Fig. 6 (B). However, this makes the fabrication process
more complex. A first possible solution is to use electrodes placed at both sides of
the piezoelectric island but buried under it (Fig. 11 (A)). The fabrication of elec-
trodes under the piezoelectric layer, however, is complex. The processes involved
in the fabrication of piezoelectric materials works at very high temperature and
they can therefore damage the electrodes, since the PZT is created on top of
them. Moreover, if Copper is used to fabricate the electrodes, an interface layer
is required to stick together electrodes and PZT. Figure 11 (B) shows a simu-
lation of the electric field distribution, obtained through Comsol Multiphysics
[ 37 ], of the structure with buried electrodes. The structure is 350 nm width, the
PZT is 100 nm thick and electrodes are 50

50 nm 2 . As can be seen the electric
field is quite uniform between the two electrodes (3-4 MV/m with an applied
voltage of 1 V) but it is lower near the area correspondent to the electrodes and

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