Electric Clock for NanoMagnet Logic Circuits - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 79

2.1 Magnetic Material Choice

While there is little room for different choices of piezoelectric material, the selec-
tion of the magnetic material to be used is more complex. The reason behind
this fact lies in the limited amount of mechanical stress that can be applied to
the magnets. In current-based clock systems there is virtually no limit to the
amount of current that can be supplied to the circuit. There is indeed a limit to
the value of current that can be used but it is very high, as shown in [ 11 ] where
a current of 545 mA is used to generate the magnetic field. In this clock system,
instead, the maximum stress that can be applied to the magnets is quite limited.
The reason is simple: If the mechanical stress is to high there is a mechanical
damage on the structure. To evaluate the maximum stress that can be used, two
contributions must be considered, the contribution of the piezoelectric substrate
and the contribution of the magnets.
Since the piezoelectric material is an insulator, there is a maximum value
of electric field that can be applied without breaking it. As a consequence the
maximum strain that it is possible to have is given by Eq. 3 .

ʾ MAX RIG = Ef MAX · d (3)

Ef MAX is the maximum electric field tolerated by the piezoelectric substrate,
while d = d 33 is the longitudinal piezoelectric coecient that relates the strain
induced with the applied voltage. As can be seen from Table 1 , PZT is one of
the material that can tolerate the highest values of electric field, bigger than
50 MV/m. However, structural limitations of the piezoelectric materials must be
considered, because, also if the applied electric field is lower than the maximum
tolerated, the generated strain can be bigger than the maximum strain due to
material structural limitations ( ʾ MAX STRUCT ). As a consequence, the maxi-
mum strain of the piezoelectric material ( ʾ MAX )) is the minimum between these
two contributions, as shown in Eq. 4 .

ʾ MAX = min ( ʾ MAX RIG ,ʾ MAX STRUCT ) (4)

PZT has a very high tolerance to structural deformations, because ʾ MAX STRUCT
is equal to 500

10 − 6 [ 35 ], so the lower bound is due to the maximum electric
field that can be applied. Once the maximum strain tolerated by the piezoelectric
material is evaluated, it can be converted to a stress as shown in Eq. 5 :

·

˃ MAX PIEZO = Y Magnet · ʾ MAX (5)

Multiplying the maximum value of strain ( ʾ MAX ) for the Young modulus
( Y Magnet ) of the magnetic material gives the maximum stress that can be applied
to the magnets ( ˃ MAX PIEZO ). This assumption is valid only if the thickness
of the magnetic material is much smaller than the thickness of the piezoelectric
substrate, because only if this condition is satisfied the mechanical stress gen-
erated by the substrate is completely transferred to the magnets. Table 2 shows
the comparison between some magnetic materials, where the Young modulus is
in the range of 80-209 GPa.