2.3 MRAM Devices
2.3.2 Figures of Merit
When characterizing and engineering material systems to design optimal MRAM devices,
there are several figures of merit. The measurement and data analysis programs in this
work are designed to extract values as quickly and accurately as possible. The physical
background and use of each of these values is explained in detail.
Critical Field
The value at which an external field causes switching in a device. In the measurements
presented in this work, this value varies with applied current and applied in-plane field,
as heating and alignment of magnetic moments both influence the energy necessary to
change the magnetization of a layer from one orientation to another [18, 58].
Thermal Stability
For all MRAM devices, the energy of a two state system (parallel and anti-parallel) can be
thought of as two equilibrium states separated by an energy barrier (Fig. 2.9). The height
of this energy barrier Ebis the value that must be overcome for a switching event to occur.
The thermal stability of a device is the ratio of this energy barrier and the operational
temperature as shown in Equation 2.6 [59].
∆ = Eb
kbT (2.6)
Figure 2.9: Energy barrier between parallel and anti-parallel states [7]
The thermal stability of a device determines the memory retention failure in standby
mode [6]. As the number of devices increase, the thermal stability factor must also
in-crease to ensure that the number of failures over 10 years stays below the acceptable
toler-ance. One of the main reasons devices with PMA are preferable to devices with in-plane
anisotropy is the origins of anisotropy, which directly corresponds to the height of the
energy barrier [6]. The stability factor of circular PMA devices where switching is
gov-erned by the macrospin model (typically dimensions of less than 30 nm) is given by the
following equation:
∆ = Eb
kbT = [(Kv− (1/4)µ0(3Nz− 1)Ms2)t + Ks]π4w2
kbT (2.7)
where the Kvand Ksare the bulk and interfacial anisotropy energy terms. For CoFeB/
MgO interfaces, PMA generally comes from interfacial effects. The height of this energy
barrier, it is possible to calculate the mean time between flipping events over this energy
barrier is given by the Néel-Brown theory of relaxation [6] given by the equation:
τN = τ0exp KV
kBT (2.8)
where τ0 is the attempt time, (generally 1 ns), and KV is the height of the energy
barrier, which is determined by the magnetic anisotropy energy density and the volume as
seen in Equation 2.7.
For large devices, switching is no longer coherent but instead driven by domain wall
nucleation and subsequent motion. The energy barrier for domain wall nucleation can be
significantly lower than that given by the macrospin model. In the case where domain
wall nucleation and motion dominates, the energy barrier can be estimated by using the
energy of a domain wall which is given by the following formula [59, 60]:
∆ = 4wt√
AexHk(MS/2)
kbT (2.9)
where Hkis the anisotropy field, MS is the saturation magnetization, wt is the width
and thickness and Aexis the exchange length.
Critical Current
Critical current, also known as the switching current Icis the minimum necessary current
required for switching the magnetization of device. This value is of key importance in
MRAM devices as it will determine the power consumption of the device. It is standard
to refer to the corresponding current density Jcwhich is area independent, allowing more
convenient comparison between different devices regardless of size. The most general
case for the zero-thermal-fluctuation critical current is given by [60]:
Jc0 = 2e
¯
hµ0MStα(Hc+ Mef f/2)
Js/Je (2.10)
where Hc is the coercive field of the FM layer, Mef f is the effective demagnetizing
field and α is the damping constant. For devices with PMA, generally the effective
de-magnetizing field is much smaller than that of the coercive field and can be ignored.
Fur-thermore, in the case of SOT switching, the torque direction does not compete with the
damping and so is independent of the damping constant [38]. Upon extracting the critical
current, it is possible to calculate the thermal stability based upon the Néel-Brown
equa-tion (2.8) where the thermally-activated critical current Jcis less than the critical current
at zero temperature, also known as the zero-thermal-fluctuation critical current, Jc0[61]
as shown in the following equation:
JC = JC0[1− 1
∆0 lntp
τ0] (2.11)
In order to extract both the thermal stability and the zero-thermal-fluctuation critical
current from this equation, measurements can be run over a range of varying pulse widths.
For different pulse widths there are two regimes, a thermally activated regime, where
ther-mal fluctuations aid switching and a regime where therther-mal effects are minither-mal, requiring
large current to generate strong enough torques to induce switching. The details of this
process are explained in further detail in Chapters 4 and 5.
Spin Hall Angle and Torque Efficiencies
The Spin Hall Angle ΘSH is a material dependent term that shows how much charge
current is converted into spin current in a given system. Materials that have large spin
hall angles are of particular interest to MRAM applications, as a larger angle means lower
power consumption. The origins of the spin Hall angle in material systems can come
from the SHE (large spin-orbit interactions) or from the intrinsic band structure of the
material, such as the Rashba effect from dissimilar interfaces or spin-momentum locking
in topological insulators and some 2D material systems. For SOT-MRAM devices, heavy
metals (HM), such as W, Ta, Pt, with stronger spin orbit coupling, leading to larger spin
Hall angles. The spin Hall angle is commonly defined as:
ΘSH = 2e
¯ h
|Js|
|Je| (2.12)
However, when measuring the spin Hall angle of a material system it is important to
also consider interfacial effects, which tend to reduce the interfacial spin transparency and
thereby reduces the effective spin Hall angle [37]. This transparency is determined by
primarily by the spin-mixing conductance and yields:
ΘSH = ξDL
(2G↑↓ef f/GN M) = ξDL
Tint (2.13)
where ξDLis the damping-like SOT efficiency, G↑↓ef f is the effective spin mixing
con-ductance, GN Mis the spin conductance of the normal metal and Tintis the interfacial spin
transparency [37]. Measurements of the spin Hall angle for a system are quite sensitive to
the transparency term which is based not on a single material but on the interface of the
two materials. Due to this and the choice of measurement technique, comparison of SHA
of a material across multiple systems can result in a wide range of values (shown in Fig.
2.10) [62]).
Figure 2.10: Spin Hall ratio measurements. Measurements of spin Hall angles values should be constant for a given material [8, 9, 10, 11, 12, 13, 14, 15, 16, 17]
An easier and more clear approach to classifying SOTs that allows for comparison
across different material systems is through measuring the damping-like SOT efficiency
ξDL from Equation 2.13. This efficiency in multidomain systems with PMA is given by
the equation:
ξDL = 2e
¯ h(2
π)µ0Mstef fF M(Hzef f
Je ) (2.14)
where Hzef f is the effective field generated by the applied current Je [18, 63]. For
devices with in-plane anisotropy, the damping-like SOT efficiency can be written as:
ξDL = 2e
¯
hµ0Mstef fF Mα(Hc+Mef f
2 )/Jc0 (2.15)
where Mef f is the effective demagnetization field and Jc0is the threshold critical
cur-rent density [19, 63].
Chapter 3
Measurement Systems
Measurements in our lab can be broken into two groups, electrical and optical. Each probe
station is capable of doing real-time optical (MOKE) measurements and also real-time
electrical measurements. As probe stations are added for increasingly specific purposes,
a universal system of calibrating instruments, running measurements and data collection
is important for maintaining consistency in measurements and speed and flexibility in the
measurement process. This section outlines the framework from which the measurement
programs are built.
3.1 Machine Configuration
Currently our lab has two probe stations, with several additional stations still being set up.
The first probe station consists of an in-pane and out-of-plane electromagnet, both with
their own power supply, a DSP 7265 Signal Recovery Lockin-amplifier and a Keithley
2400 sourcemeter and Keithley 2000 multimeter and a Lakeshore 475 Gaussmeter. The
second probe station has the same machines but the in-plane and out-of-plane
electromag-nets are separated. Both stations have a optical microscope for MOKE measurements and
to ensure proper contact is made between the probes and the electrodes. Diagrams of a
probe station setup are provided in the figure below. The Gaussmeter probe and optical
microscope are stationed above the location marked (a) where the sample is placed upon
a stage. The arrows from (b) mark the locations of the electromagnets.
Figure 3.1: Example Probe Station