Electric-Field-Controlled MRAM: Physics and Applications
159
becomes necessary to estimate the VCMA effect within the actual perpendicular MTJ
stack where both the reference and the free layer show PMA. This estimation can
be done by measuring the distribution of the switching fields in the MTJ using the
following equation,
P = 1 − exp
−H k f 0
√
π
2R
√ Δ
erfc
√ Δ
1 −
H − H 0
H k
(8)
where f 0 is the attempt frequency (assumed to be 1 GHz), R, the sweep rate. H o is
the median offset field and, is the thermal stability. The change in anisotropy can
then be extracted when H k is determined at various applied voltages. The determination of H k is illustrated in Fig. 7c,d taken for a single applied voltage. Figure 7c shows
the hysteresis that is obtained by sweeping an external field multiple times. This gives
us a distribution of the switching fields (left and right P → AP and AP → P). As
shown by Fig. 7d, this distribution is then fitted into the cumulative distribution, P,
given by Eq. 8, which gives us values for H k and [58].
We have discussed in Sect. 2.2, the determination of ξ from the absorption spectrum using the field-sweep FMR in a resonant cavity. However, other forms of FMR
can also be used, such as the homodyne detection method where the device employed
is not a single ferromagnetic stack but rather an MTJ [27, 59]. For this method, the
DC resistance of the MTJ is measured while the AC voltage is applied to the MTJ.
The FMR signal is then read out via the rectified DC voltage across the device.
2.4 Summary of Materials Dependence
Table 1 shows a list of heterostructure stacks (not exhaustive) and the corresponding
VCMA efficiencies.
The large efficiencies of certain materials, e.g. the V/Fe/MgO stack, have been
attributed to the electromigration of defects in the MgO barrier. For VCMA originating from electromigration, the mechanical motion of chemical migration limits
the switching speed and may be susceptible to reliability issues similar to resistive random access memory (RRAM) [60]. Note that for the typical Ta/CoFeB/MgO
heterostructure, a range of values, 30–100 fJV
−1 m
−1 , have been reported. It is generally believed that the typical value is around 30 fJV
−1 m
−1 and values at the high or
low end correspond to a difference in the level of oxidation of the Co/Fe oxide at the
CoFeB/MgO interface [61].
As indicated by Table 1 and eluded in Sect. 2.1, the underlayer plays an integral
part in the magnitude of VCMA. It has been reported by Barnes et al. [62] that
there is an efficiency inversion between 4d and 5d metals. However, apart from a
single study with Ru [63], most studies have not been able to replicate this successfully [59], indicating perhaps stringent preparation conditions. It is also noteworthy
that VCMA generally decreases with increasing annealing temperature [59]. On
the other hand, W and Mo underlayer structures do not show a strong dependence
159
becomes necessary to estimate the VCMA effect within the actual perpendicular MTJ
stack where both the reference and the free layer show PMA. This estimation can
be done by measuring the distribution of the switching fields in the MTJ using the
following equation,
P = 1 − exp
−H k f 0
√
π
2R
√ Δ
erfc
√ Δ
1 −
H − H 0
H k
(8)
where f 0 is the attempt frequency (assumed to be 1 GHz), R, the sweep rate. H o is
the median offset field and, is the thermal stability. The change in anisotropy can
then be extracted when H k is determined at various applied voltages. The determination of H k is illustrated in Fig. 7c,d taken for a single applied voltage. Figure 7c shows
the hysteresis that is obtained by sweeping an external field multiple times. This gives
us a distribution of the switching fields (left and right P → AP and AP → P). As
shown by Fig. 7d, this distribution is then fitted into the cumulative distribution, P,
given by Eq. 8, which gives us values for H k and [58].
We have discussed in Sect. 2.2, the determination of ξ from the absorption spectrum using the field-sweep FMR in a resonant cavity. However, other forms of FMR
can also be used, such as the homodyne detection method where the device employed
is not a single ferromagnetic stack but rather an MTJ [27, 59]. For this method, the
DC resistance of the MTJ is measured while the AC voltage is applied to the MTJ.
The FMR signal is then read out via the rectified DC voltage across the device.
2.4 Summary of Materials Dependence
Table 1 shows a list of heterostructure stacks (not exhaustive) and the corresponding
VCMA efficiencies.
The large efficiencies of certain materials, e.g. the V/Fe/MgO stack, have been
attributed to the electromigration of defects in the MgO barrier. For VCMA originating from electromigration, the mechanical motion of chemical migration limits
the switching speed and may be susceptible to reliability issues similar to resistive random access memory (RRAM) [60]. Note that for the typical Ta/CoFeB/MgO
heterostructure, a range of values, 30–100 fJV
−1 m
−1 , have been reported. It is generally believed that the typical value is around 30 fJV
−1 m
−1 and values at the high or
low end correspond to a difference in the level of oxidation of the Co/Fe oxide at the
CoFeB/MgO interface [61].
As indicated by Table 1 and eluded in Sect. 2.1, the underlayer plays an integral
part in the magnitude of VCMA. It has been reported by Barnes et al. [62] that
there is an efficiency inversion between 4d and 5d metals. However, apart from a
single study with Ru [63], most studies have not been able to replicate this successfully [59], indicating perhaps stringent preparation conditions. It is also noteworthy
that VCMA generally decreases with increasing annealing temperature [59]. On
the other hand, W and Mo underlayer structures do not show a strong dependence