U.S. patent application number 15/195248 was filed with the patent office on 2017-12-28 for magnetization alignment in a thin-film device.
This patent application is currently assigned to Alcatel-Lucent USA Inc.. The applicant listed for this patent is Alcatel-Lucent USA Inc.. Invention is credited to Gavin D. Scott.
Application Number | 20170372826 15/195248 |
Document ID | / |
Family ID | 60674849 |
Filed Date | 2017-12-28 |
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United States Patent
Application |
20170372826 |
Kind Code |
A1 |
Scott; Gavin D. |
December 28, 2017 |
MAGNETIZATION ALIGNMENT IN A THIN-FILM DEVICE
Abstract
We disclose a magnetic device having a pair of coplanar
thin-film magnetic electrodes arranged on a substrate with a
relatively small edge-to-edge separation. In an example embodiment,
the magnetic electrodes have a substantially identical footprint
that can be approximated by an ellipse, with the short axes of the
ellipses being collinear and the edge-to-edge separation between
the ellipses being smaller than the size of the short axis. In some
embodiments, the magnetic electrodes may have relatively small
tapers that extend toward each other from the ellipse edges in the
constriction area between the electrodes. Some embodiments may also
include an active element inserted into the gap between the tapers
and electrical leads connected to the magnetic electrodes for
passing electrical current through the active element. When
subjected to an appropriate external magnetic field, the magnetic
electrodes can advantageously be magnetized to controllably enter
parallel and antiparallel magnetization states.
Inventors: |
Scott; Gavin D.; (Hoboken,
NJ) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Alcatel-Lucent USA Inc. |
Murray Hill |
NJ |
US |
|
|
Assignee: |
Alcatel-Lucent USA Inc.
Murray Hill
NJ
|
Family ID: |
60674849 |
Appl. No.: |
15/195248 |
Filed: |
June 28, 2016 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H01F 10/3254 20130101;
B82Y 10/00 20130101; G11C 13/0016 20130101; B82Y 25/00 20130101;
G11C 13/025 20130101; H01L 29/66984 20130101; G11C 13/0014
20130101; H01L 29/0665 20130101; G11C 11/14 20130101; H01L 29/7613
20130101 |
International
Class: |
H01F 7/06 20060101
H01F007/06 |
Claims
1. An apparatus comprising: a substrate; and a first set of
electrodes supported on the substrate, the first set including a
first thin-film magnetic electrode and a second thin-film magnetic
electrode, each of the first and second thin-film magnetic
electrodes having a substantially oval shape; wherein the
substantially oval shape is characterized by a first axis having a
first size and a second axis having a second size, the first and
second axes being orthogonal to one another, and the second size
being larger than the first size; wherein the first axis of the
first thin-film magnetic electrode and the first axis of the second
thin-film magnetic electrode are collinear; wherein a distance
between the second axis of the first thin-film magnetic electrode
and the second axis of the second thin-film magnetic electrode is
greater than the first size; and wherein an edge-to-edge separation
between the first thin-film magnetic electrode and the second
thin-film magnetic electrode is smaller than the first size.
2. The apparatus of claim 1, wherein each of the first and second
thin-film magnetic electrodes includes a respective taper that
extends from a respective electrode edge in a constriction area
between the first and second thin-film magnetic electrodes.
3. The apparatus of claim 2, wherein a gap between the respective
tapers has a width that is smaller than the edge-to-edge
separation.
4. The apparatus of claim 3, wherein the width of the gap varies
along a length of the gap.
5. The apparatus of claim 3, wherein the width of the gap varies as
a function of a distance from the substrate.
6. The apparatus of claim 3, further comprising an active element
at least a portion of which is located in the gap between the
respective tapers.
7. The apparatus of claim 6, wherein the active element is one or
more of a quantum dot, a nanocrystal, a single molecule, a polymer,
and a metal-organic complex.
8. The apparatus of claim 6, wherein the active element comprises a
fullerene molecule.
9. The apparatus of claim 6, wherein the active element comprises
one or more linkers, each of which is chemically bonded to a
respective metal atom of the respective taper.
10. The apparatus of claim 2, wherein the respective tapers are
connected to one another to form a magnetic bridge between the
first and second thin-film magnetic electrodes.
11. The apparatus of claim 1, further comprising a plurality of
additional sets of electrodes, each of the additional sets of
electrodes being a nominal copy of the first set of electrodes,
wherein the first set of electrodes and the plurality of additional
sets of electrodes are arranged in an array on the substrate.
12-16. (canceled)
17. The apparatus of claim 1, wherein the first set of electrodes
further includes: a first non-magnetic metal electrode attached to
the first thin-film magnetic electrode; and a second non-magnetic
metal electrode attached to the second thin-film magnetic
electrode.
18-19. (canceled)
20. The apparatus of claim 1, wherein each of the first thin-film
magnetic electrode and the second thin-film magnetic electrode has
a thickness that is smaller than the first size.
21. An apparatus comprising: a substrate; and a first set of
electrodes supported on the substrate, the first set including a
first thin-film magnetic electrode and a second thin-film magnetic
electrode, each of the first and second thin-film magnetic
electrodes having a substantially oval shape; wherein the
substantially oval shape is characterized by a first axis having a
first size and a second axis having a second size, the first and
second axes being orthogonal to one another, and the second size
being larger than the first size; wherein the first axis of the
first thin-film magnetic electrode and the first axis of the second
thin-film magnetic electrode are collinear; wherein an edge-to-edge
separation between the first thin-film magnetic electrode and the
second thin-film magnetic electrode is smaller than the first size;
and wherein each of the first and second thin-film magnetic
electrodes includes a respective taper that extends from a
respective electrode edge in a constriction area between the first
and second thin-film magnetic electrodes.
22. The apparatus of claim 21, wherein a gap between the respective
tapers has a width that is smaller than the edge-to-edge
separation.
23. The apparatus of claim 22, wherein the width of the gap varies
along a length of the gap.
24. The apparatus of claim 22, further comprising an active element
at least a portion of which is located in the gap between the
respective tapers.
25. The apparatus of claim 24, wherein the active element is one or
more of a quantum dot, a nanocrystal, a single molecule, a polymer,
and a metal-organic complex.
26. The apparatus of claim 24, wherein the active element comprises
a fullerene molecule.
27. The apparatus of claim 24, wherein the active element comprises
one or more linkers, each of which is chemically bonded to a
respective metal atom of the respective taper.
28. An apparatus comprising: a substrate; and a first set of
electrodes supported on the substrate, the first set including a
first thin-film magnetic electrode and a second thin-film magnetic
electrode, each of the first and second thin-film magnetic
electrodes having a substantially oval shape; wherein the
substantially oval shape is characterized by a first axis having a
first size and a second axis having a second size, the first and
second axes being orthogonal to one another, and the second size
being larger than the first size; wherein the first axis of the
first thin-film magnetic electrode and the first axis of the second
thin-film magnetic electrode are collinear; wherein an edge-to-edge
separation between the first thin-film magnetic electrode and the
second thin-film magnetic electrode is smaller than the first size;
and wherein the first set of electrodes further includes: a first
non-magnetic metal electrode attached to the first thin-film
magnetic electrode; and a second non-magnetic metal electrode
attached to the second thin-film magnetic electrode.
Description
BACKGROUND
Field
[0001] The present disclosure relates generally to spintronics and,
more specifically but not exclusively, to methods and apparatus for
controllably manipulating magnetization distribution(s) in
thin-film devices.
Description of the Related Art
[0002] This section introduces aspects that may help facilitate a
better understanding of the disclosure. Accordingly, the statements
of this section are to be read in this light and are not to be
understood as admissions about what is in the prior art or what is
not in the prior art.
[0003] Some applications of thin-film magnetic devices rely on the
ability to controllably generate the parallel and antiparallel
magnetization alignment of two adjacent magnetic electrodes. More
specifically, the parallel alignment corresponds to a situation in
which the magnetization vectors of two adjacent magnetic electrodes
are parallel to one another, i.e., pointing in the same direction
or having the relative orientation angle of zero degrees. In
contrast, the antiparallel alignment corresponds to a situation in
which the magnetization vectors of two adjacent magnetic electrodes
are antiparallel, i.e., pointing in the opposite directions or
having the relative orientation angle of 180 degrees. While the
parallel alignment can be generated in a relatively straightforward
manner, the antiparallel alignment is significantly more difficult
to generate, e.g., when the two magnetic electrodes have a
nanometer-scale separation and/or are laterally adjacent to one
another, rather than being stacked vertically.
SUMMARY OF SOME SPECIFIC EMBODIMENTS
[0004] Disclosed herein are various embodiments of a magnetic
device having a pair of coplanar thin-film magnetic electrodes
arranged on a substrate with a relatively small edge-to-edge
separation. In an example embodiment, the magnetic electrodes have
a substantially identical footprint that can be approximated by an
ellipse, with the short axes of the ellipses being collinear and
the edge-to-edge separation between the ellipses being smaller than
the size of the short axis. In some embodiments, the magnetic
electrodes may have relatively small tapers that extend toward each
other from the ellipse edges in the constriction area between the
electrodes. Some embodiments may also include an active element
inserted into the gap between the tapers and electrical leads
connected to the magnetic electrodes for passing electrical current
through the active element. When subjected to an appropriate
external magnetic field, the magnetic electrodes can advantageously
be magnetized to controllably enter parallel and antiparallel
magnetization states.
[0005] According to one embodiment, provided is an apparatus
comprising, a substrate; and a first set of electrodes supported on
the substrate, the set including a first thin-film magnetic
electrode and a second thin-film magnetic electrode, each of the
first and second thin-film magnetic electrodes having a
substantially oval shape; wherein the substantially oval shape is
characterized by a first axis having a first size and a second axis
having a second size, the first and second axes being orthogonal to
one another, and the second size being larger than the first size;
wherein the first axis of the first thin-film magnetic electrode
and the first axis of the second thin-film magnetic electrode are
collinear; and wherein an edge-to-edge separation between the first
thin-film magnetic electrode and the second thin-film magnetic
electrode is smaller than the first size.
BRIEF DESCRIPTION OF THE DRAWINGS
[0006] The patent or application file contains at least one drawing
executed in color. Copies of this patent or patent application
publication with color drawing(s) will be provided by the Office
upon request and payment of the necessary fee.
[0007] Other aspects, features, and benefits of various disclosed
embodiments will become more fully apparent, by way of example,
from the following detailed description and the accompanying
drawings, in which:
[0008] FIGS. 1A-1B illustrate top and cross-sectional side views of
a magnetic device according to an embodiment;
[0009] FIGS. 2A-2E show enlarged schematic top views of a
constriction between two magnetic electrodes in the magnetic device
of FIG. 1 according to example embodiments;
[0010] FIGS. 3A-3C show enlarged schematic side views of a
constriction between two magnetic electrodes in the magnetic device
of FIG. 1 according to example embodiments;
[0011] FIGS. 4A-4B illustrate alternative embodiments of the
magnetic device of FIG. 1, each having a respective active element
therein;
[0012] FIGS. 5A-5D show schematic top views of an array of the
magnetic devices of FIG. 1 according to example embodiments;
[0013] FIG. 6 shows a schematic top view of an array of magnetic
devices of FIG. 1 according to an alternative embodiment;
[0014] FIG. 7 pictorially illustrates a system in which an array of
FIG. 5 can be used according to an embodiment;
[0015] FIG. 8 shows a schematic diagram of a system in which the
array of FIG. 6 can be used according to an embodiment;
[0016] FIGS. 9A-9B graphically illustrate certain magnetic
properties of the magnetic device of FIG. 1 according to an
embodiment;
[0017] FIGS. 10A-10C illustrate magnetization distributions in the
magnetic device of FIG. 1 according to an embodiment;
[0018] FIGS. 11A-11E illustrate magnetization distributions in the
magnetic device of FIG. 1 according to an alternative embodiment;
and
[0019] FIGS. 12A-12G illustrate a fabrication method that can be
used to make the magnetic device of FIG. 1 according to an
embodiment.
DETAILED DESCRIPTION
[0020] FIGS. 1A-1B illustrate top and cross-sectional side views,
respectively, of a magnetic device 100 according to an embodiment.
The dashed line in FIG. 1A indicates the position of the
cross-section plane BB corresponding to FIG. 1B. An example
fabrication process that can be used to make magnetic device 100 is
described in more detail below in reference to FIG. 12. An example
method of generating parallel and antiparallel alignment of
magnetization vectors in magnetic device 100 is described in more
detail below in reference to FIGS. 9-11.
[0021] Device 100 comprises a substrate 102 that supports a pair of
thin-film magnetic electrodes 110.sub.1 and 110.sub.2. In some
embodiments, device 100 further comprises a pair of (optional)
non-magnetic, electrically conducting electrodes 120.sub.1 and
120.sub.2 that are configured to provide electrical leads to
magnetic electrodes 110.sub.1 and 110.sub.2, respectively.
Depending on the polarity of the voltage/current applied to
electrically conducting electrodes 120.sub.1 and 120.sub.2, one of
magnetic electrodes 110.sub.1-110.sub.2 may be referred to as a
"source" electrode, and the other electrode may be referred to as a
"drain" electrode. Magnetic electrodes 110.sub.1 and 110.sub.2 are
referred to herein as "thin-film" electrodes because the
electrodes' lateral dimensions indicated in FIG. 1A are
significantly larger than the electrodes' thickness or height
indicated in FIG. 1B. In an example embodiment, the lateral
dimensions of magnetic electrodes 110.sub.1 and 110.sub.2 can be in
the range between about 100 nm and about 500 nm, whereas the
electrodes' thickness can be smaller than about 10 nm.
[0022] The following materials can be used in some embodiments of
device 100. Substrate 102 may comprise silicon and/or silicon
oxide. Magnetic electrodes 110.sub.1 and 110.sub.2 may comprise a
ferromagnetic or ferrimagnetic material. One example ferromagnetic
material that can be used to make magnetic electrodes 110.sub.1 and
110.sub.2 is supermalloy, whose chemical composition can be
described by the following chemical formula:
Ni.sub.80Fe.sub.14Mo.sub.5X, where X is another metal. Another
example ferromagnetic material that can be used to make magnetic
electrodes 110.sub.1 and 110.sub.2 is permalloy. Some ferromagnetic
materials suitable for magnetic electrodes 110.sub.1 and 110.sub.2
may have a tendency to form native oxide layers, such as layers 112
shown in FIG. 1B, over electrode portions exposed to ambient air
for a sufficiently long period of time. Non-magnetic electrically
conducting electrodes 120.sub.1 and 120.sub.2 may comprise gold,
titanium, and/or other electrically conducting materials suitable
for creating ohmic contacts. Various adhesion layers (not
explicitly shown in FIGS. 1A-1B) can be used as known in the
pertinent art to ensure good structural adhesion between the shown
parts of device 100.
[0023] A person of ordinary skill in the art will understand that
other suitable materials can similarly be used in alternative
embodiments of device 100.
[0024] In an example embodiment, each of magnetic electrodes
110.sub.1 and 110.sub.2 has a substantially oval shape. As used
herein, the term "substantially" refers to possible relatively
small deviations (if any) of the shape of a magnetic electrode 110
from a Cartesian oval shape, e.g., in the general area of a
constriction 114 between magnetic electrodes 110.sub.1 and
110.sub.2. For example, the mass of an electrode 110 located
outside of the footprint of the corresponding Cartesian oval shape
near constriction 114 can be less than about 10% (or 5%, or 1%) of
the total mass of that electrode.
[0025] In some embodiments, each of magnetic electrodes 110.sub.1
and 110.sub.2 can be approximately shaped as an ellipse, which is a
special case of an oval. As known in the mathematical arts, an
ellipse is a planar shape that has two orthogonal axes about which
the ellipse is symmetric. These axes intersect at the center of the
ellipse. The larger of the two axes is referred to as the major
axis. The smaller of the two axes is referred to as the minor axis.
The ratio of the sizes of the major and minor axes is referred to
as the eccentricity of the ellipse.
[0026] In an example embodiment, each of the ellipses that can be
used to approximate the shape of magnetic electrodes 110.sub.1 and
110.sub.2 can have the major and minor axes that are 200 nm and 100
nm, respectively. Alternative embodiments of magnetic electrodes
110.sub.1 and 110.sub.2 can be generated from this example
embodiment using one or more of the following geometric
modifications: (i) changing the eccentricity of the ellipses while
having the size of one of the major/minor axes unchanged; (ii)
uniformly scaling the ellipses by applying the same scaling factor
to the major and minor axes; and (iii) changing the edge-to-edge
separation, d, between the ellipses (also see FIG. 2A). The
eccentricity can, for example, be in the range between about 1.5
and about 5. The scaling factor can, for example, be in the range
between about 0.2 and about 5. The edge-to-edge separation d can,
for example, be in the range between about 2 nm and about 100
nm.
[0027] FIGS. 2A-2E show enlarged schematic views of constriction
114 between magnetic electrodes 110.sub.1 and 110.sub.2 in device
100 according to example embodiments. More specifically, the views
shown in FIGS. 2A-2E are the top views of constriction 114
corresponding to FIG. 1A. FIG. 2A also pictorially illustrates the
definition of the above-mentioned edge-to-edge separation d.
[0028] Referring to FIG. 2A, each of magnetic electrodes 110.sub.1
and 110.sub.2 comprises a respective one of trapezoid tapers 2101
and 2102, each of which extends from the edge of the corresponding
oval or ellipse. In the shown embodiment, trapezoid tapers 2101 and
2102 are separated by a gap 214. In some alternative embodiments,
gap 214 is not present, which causes tapers 210.sub.1 and 210.sub.2
to be connected to one another, thereby forming a physical bridge
(not explicitly shown in FIG. 2A) between magnetic electrodes
110.sub.1 and 110.sub.2.
[0029] In various embodiments, the bases of the trapezoids
corresponding to tapers 210.sub.1 and 210.sub.2 can have different
respective sizes, e.g., each selected from a range between about 30
nm and 0 nm. Gap 214 can have a width that is smaller than about 5
nm or smaller than about 1 nm. Although FIG. 2A shows tapers
210.sub.1 and 210.sub.2 as having a shape of an isosceles
trapezoid, other trapezoid shapes are also possible, including a
rectangular shape.
[0030] Referring to FIG. 2B, each of magnetic electrodes 110.sub.1
and 110.sub.2 comprises a respective one of convex tapers 220.sub.1
and 220.sub.2, each of which extends from the edge of the
corresponding oval or ellipse. In some embodiments, the geometric
shape of an outer edge of taper 220 can be approximated by a
parabola or a semicircle.
[0031] Referring to FIG. 2C, each of magnetic electrodes 110.sub.1
and 110.sub.2 comprises a respective one of concave or non-convex
tapers 230.sub.1 and 230.sub.2, each of which extends from the edge
of the corresponding oval or ellipse. In some embodiments, the
geometric shape of some of the outer edges of taper 230 can be
approximated by a hyperbola or an exponent.
[0032] FIGS. 2D-2E illustrate a variation of the embodiment shown
in FIG. 2A, in which an outer edge of each of trapezoid tapers
210.sub.1 and 210.sub.2 is not atomically smooth, straight, or
linear. Such edges can be produced, e.g., by an electro-migration
process as further explained below in reference to FIG. 12G. As
indicated in FIG. 2D, gap 214 can have a fairly complex, irregular
overall shape that causes the distance between tapers 210.sub.1 and
210.sub.2 (e.g., the width of gap 214) to vary along the length of
the gap.
[0033] FIG. 2E shows a further enlarged view of a portion 216 (also
see FIG. 2D) of gap 214 in which the distance between tapers
210.sub.1 and 210.sub.2 reaches its minimum. Example arrangement of
the electrode parts in portion 216 can be analogous to that of two
STM (scanning tunneling microscope) tips nearly touching each
other. For some applications of device 100, it is expected that one
or more pertinent device characteristics may be dominated by the
atomic details of portion 216, such as the smallest distance g
between tapers 210.sub.1 and 210.sub.2 and the chemical identity of
the atoms X and Y located at the distance g.
[0034] A person of ordinary skill in the art will understand that
FIGS. 2A-2E show only several example shapes of the tapers that can
be used in constriction 114 and that various alternative geometric
shapes can similarly be used therein.
[0035] FIGS. 3A-3C show additional enlarged schematic views of
constriction 114 between magnetic electrodes 110.sub.1 and
110.sub.2 in device 100 according to example embodiments. More
specifically, the views shown in FIGS. 3A-3C are the side views of
constriction 114 corresponding to FIG. 1B. FIG. 3A illustrates an
embodiment in which the separation between magnetic electrodes
110.sub.1 and 110.sub.2 is uniform and does not depend on the
distance from substrate 102. FIG. 3B illustrates an embodiment in
which the separation between magnetic electrodes 110.sub.1 and
110.sub.2 linearly increases with an increase of the distance from
substrate 102. FIG. 3C illustrates an example vertical profile of
gap 214 in portion 216 illustrated in FIGS. 2D-2E.
[0036] FIGS. 4A-4B illustrate alternative embodiments of device 100
in which an active element 402 is located within constriction 114.
As used herein, the term "active element" refers to a
nanometer-scale object intentionally placed in proximity to or
inserted between the tapers of magnetic electrodes 110.sub.1 and
110.sub.2 (e.g., illustrated in FIGS. 2A-2E). In various
embodiments, active element 402 may or may not be in direct
physical contact with either or both of the tapers. In some
embodiments, active element 402 may form one or more chemical bonds
with either or both of the tapers of magnetic electrodes 110.sub.1
and 110.sub.2. In some embodiments, a voltage applied between
electrodes 120.sub.1 and 120.sub.2 (see FIGS. 1A-1B) causes an
electrical charge to flow through active element 402.
[0037] In the embodiment illustrated by FIG. 4A, active element 402
comprises a bucky-ball molecule, C.sub.60. In the configuration
shown in FIG. 4A, the bucky-ball molecule of active element 402 is
in direct physical contact with magnetic electrode 110.sub.1, but
not with magnetic electrode 110.sub.2. Other positions of the
bucky-ball molecule with respect to magnetic electrodes 110.sub.1
and 110.sub.2 are also possible. In alternative embodiments, other
fullerene molecules can be used to make active element 402.
[0038] In the embodiment illustrated by FIG. 4B, active element 402
comprises an organic molecule--a derivative of the thiol end-capped
oligophenylenevinylene molecule (OPV-5) in which five benzene rings
are connected through four double bonds. In addition to a
delocalized .pi.-electron system, this derivative of OPV-5 has (i)
n-C.sub.12H.sub.25 side arms that make it soluble and (ii) acetyl
protected thiol end groups that enable covalent bonding to metal
electrodes, such as magnetic electrodes 110.sub.1 and 110.sub.2. In
this particular embodiment, after the covalent bonding is achieved,
the organic molecule of active element 402 is bonded to metal atoms
by means of two --S(CO)-- linkers, in each of which the sulfur is
covalently bonded to an aromatic ring of OPV-5, and the carbon is
covalently bonded to a metal atom of the corresponding magnetic
electrode 110. In alternative embodiments, other organic molecules
and/or chemical linkers can similarly be used. The linking chemical
bonds can be covalent bonds, hydrogen bonds, or coordination
bonds.
[0039] A person of ordinary skill in the art will understand that
FIGS. 4A-4B show only two possible examples of active element 402
for device 100 and that other active elements can similarly be used
therein. For example, alternative embodiments of active element 402
may include quantum dots, nanocrystals, biological and bioorganic
molecules, polymers, metal-organic complexes, etc.
[0040] FIGS. 5A-5D show schematic top views of an array 500 of
magnetic devices 100 (FIGS. 1A-1B) according to example
embodiments. In each of the shown embodiments of array 500,
magnetic devices 100 are fabricated on and share a common substrate
102 (also see FIGS. 1A-1B). The embodiment of array 500 shown in
FIG. 5A includes fifteen arrayed magnetic devices 100. Each of the
embodiments of array 500 shown in FIGS. 5B-5D includes sixteen
arrayed magnetic devices 100. A person of ordinary skill in the art
will understand that alternative embodiments of array 500 may
include a different (from 15 or 16) number of arrayed magnetic
devices 100.
[0041] The embodiment of array 500 shown in FIG. 5A includes a
plurality of electrically conducting tracks 502 arranged in a
manner that makes each source electrode and each drain electrode of
arrayed magnetic devices 100 individually addressable from the
periphery of substrate 102.
[0042] In the embodiment of array 500 shown in FIG. 5B, magnetic
devices 100 are arranged in a rectangular array having four rows
and four columns. Electrically conducting tracks 502 are arranged
in a manner that causes each column of magnetic devices 100 to
share a respective common drain contact. However, each source
electrode of arrayed magnetic devices 100 is still individually
addressable from the periphery of substrate 102.
[0043] In the embodiment of array 500 shown in FIG. 5C, magnetic
devices 100 are also arranged in a rectangular array having four
rows and four columns. Electrically conducting tracks 502 are now
arranged in a manner that causes each pair of columns of magnetic
devices 100 to share a respective common drain contact. Each source
electrode of arrayed magnetic devices 100 is still individually
addressable from the periphery of substrate 102.
[0044] In the embodiment of array 500 shown in FIG. 5D, magnetic
devices 100 are similarly arranged in a rectangular array having
four rows and four columns. Electrically conducting tracks 502 are
now arranged in a manner that causes all four columns of magnetic
devices 100 to share a common drain contact. Each source electrode
of arrayed magnetic devices 100 is still individually addressable
from the periphery of substrate 102.
[0045] FIG. 6 shows a schematic top view of an array 600 of
magnetic devices 100 (FIGS. 1A-1B) according to an alternative
embodiment. Similar to magnetic devices 100 of array 500, magnetic
devices 100 of array 600 are fabricated on and share a common
substrate 102. However, substrate 102 is now a part of a disk 610.
Magnetic devices 100 are arranged on a surface of disk 610 along
three circular tracks 612.sub.i (i=1, 2, 3), each having a
different respective radius R.sub.i, e.g., as indicated in FIG. 6.
In alternative embodiments, the number of circular tracks 612 may
be different from three. Note that magnetic devices 100 used in
array 600 do not have electrodes 120. Hence, conducting tracks
similar to conducting tracks 502 (FIG. 5) are not necessary and not
present in array 600. In some embodiments of array 600, magnetic
electrodes 110.sub.1 and 110.sub.2 of individual magnetic devices
100 may not even have tapers analogous to those described above in
reference to FIGS. 2A-2E.
[0046] FIG. 7 pictorially illustrates a system 700 in which array
500 (FIG. 5) can be used according to an embodiment. System 700
comprises a split-coil electromagnet having a cylindrical magnetic
core 710. Array 500 is positioned within a relatively narrow gap
712 between two portions of magnetic core 710, which are labeled in
FIG. 7 as 7101 and 7102, respectively. A magnetic field, B, can be
generated within gap 712 by passing an electrical current through
one or more coils (not explicitly shown in FIG. 7) wrapped around
magnetic core 710. The resulting magnetic field B is directed
generally parallel to the center axis of magnetic core 710, e.g.,
as indicated by the double-headed arrow B in FIG. 7. The direction
of the magnetic field depends on the direction of the flow of the
electrical current through the coil(s) and, as such, can be
reversed by changing the electrical-current direction. The
magnitude of the magnetic field depends on the magnitude of the
electrical current and, as such, can be controllably changed by
changing the latter. In an example embodiment, system 700 can be
used to generate parallel and antiparallel alignment of remanent
magnetization vectors in individual magnetic devices 100 of array
500, e.g., as described in more detail below in reference to FIG.
11.
[0047] FIG. 8 shows a schematic diagram of a system 800 in which
array 600 (FIG. 6) can be used according to an embodiment. System
800 comprises an electromagnetic head 802 that is moveable along
the radius of disk 610 in a manner that enables electromagnetic
head to be positioned over any selected one of circular tracks 612
(also see FIG. 6). Disk 610 is rotatably mounted in system 800 such
that it can be rotated about a rotation axis 804. This rotation
enables electromagnetic head 802 to pass over any one of magnetic
devices 100 of the selected circular track 612. In some
embodiments, electromagnetic head 802 can operate as a read-write
head. In alternative embodiments, electromagnetic head 802 can
operate as a write head only, with a separate read head (not
explicitly shown in FIG. 8) being used to read data written into
array 600 using the shown write head. Each of magnetic devices 100
can be used to store one bit of information, e.g., such that
parallel and antiparallel alignment of magnetization vectors in the
magnetic device correspond to a binary "one" and a binary "zero,"
respectively.
[0048] In an example embodiment, electromagnetic head 802 comprises
a C-shaped magnetic core 810 and a coil 814 of electrical wire
wound about that core as indicated in FIG. 8. A gap 812 of core 810
is positioned to face disk 610 as further indicated in FIG. 8. A
magnetic field, B, generated within and in proximity to gap 812
when an electrical current is passed through coil 814 can be used
to alter the alignment of magnetization vectors in the magnetic
device 100 located under the gap, e.g., as described in more detail
below in reference to FIG. 11. In the disk/head configuration shown
in FIG. 8, the magnetic device located under gap 812 is magnetic
device 100.sub.N. As already indicated above, other magnetic
devices 100 of array 600 can be brought to gap 812 by appropriately
moving electromagnetic head 802 along the radius of disk 610 and
rotating the disk about axis 804.
[0049] FIGS. 9A-9B graphically illustrate certain magnetic
properties of magnetic device 100 (FIG. 1) according to an
embodiment. More specifically, the data shown in FIG. 9 illustrate
a hysteresis loop of normalized total transverse magnetization,
M.sub.y, that is produced in magnetic device 100 by exposure to an
external magnetic field. The data of FIGS. 9A and 9B correspond to
the external magnetic field being parallel to the y-axis and the
x-axis, respectively. The data points in FIG. 9A were obtained
using numerical simulations of the behavior of an embodiment of
magnetic device 100 in which each of magnetic electrodes 110.sub.1
and 110.sub.2 is an ideal ellipse having the following
characteristics: (i) the sizes of the major and minor axes are 400
nm and 200 nm, respectively; (ii) the electrode thickness is 15 nm;
and (iii) the ferromagnetic material is permalloy. No tapers are
present in constriction 114. The edge-to-edge separation d between
magnetic electrodes 110.sub.1 and 110.sub.2 is 20 nm. The data
points in FIG. 9B were obtained using numerical simulations of the
behavior of an embodiment of magnetic device 100 that is the same
as that used for FIG. 9A, except that constriction 114 had
trapezoid tapers 210.sub.1 and 210.sub.2 therein, with the gap 214
between the trapezoid tapers being 3-nm wide (also see FIG.
2A).
[0050] The coordinate frame (xy) used in the numerical simulations
is defined as follows. The x-axis is parallel to the line that
connects the centers of the ellipses. The y-axis is parallel to the
major axes of the ellipses. This coordinate frame is also shown for
reference in FIGS. 10A, 11A, and 11E.
[0051] Referring to FIG. 9A, the external magnetic field is
parallel to the y-axis. The arrows in FIG. 9A indicate the
magnetic-field sweep direction. The positive saturation state
(M.sub.y=+1) is achieved by applying a relatively large (e.g.,
.about.60000 A/m) positive magnetic field. As the magnetic field is
swept in the negative direction, M.sub.y undergoes a step-like
transition 902 at the negative critical field -H.sub.c. Further
increase of the (negative) magnitude of the external magnetic
field, e.g., to -60000 A/m, causes M.sub.y to reach the negative
saturation state (M.sub.y=-1). Reversal of the sweep direction
causes M.sub.y to undergo a step-like transition 904 at the
positive critical field +H.sub.c.
[0052] Referring to FIG. 9B, the external magnetic field is
parallel to the x-axis. The arrows in FIG. 9B indicate the
magnetic-field sweep direction. The positive saturation state
(M.sub.y=+1) is achieved by applying a relatively large (e.g.,
.about.50000 A/m) positive magnetic field. As the magnetic field is
swept in the negative direction, M.sub.y first exits the positive
saturation state and decreases gradually and then undergoes a
step-like transition 912 at the negative critical field -H.sub.c.
Further increase of the (negative) magnitude of the external
magnetic field, e.g., to -50000 A/m, causes M.sub.y to more or less
gradually reach the negative saturation state (M.sub.y=-1).
Reversal of the sweep direction causes M.sub.y to go through
similar changes, but with a corresponding step-like transition 914
now occurring at the positive critical field +H.sub.c.
[0053] FIGS. 10A-10C illustrate magnetization distributions in
magnetic device 100 according to an embodiment. More specifically,
the shown magnetization distributions are obtained using the
numerical simulations described above in reference to FIG. 9A. FIG.
10A schematically shows a parallel magnetization state P.sub.y of
magnetic device 100. FIGS. 10B-10C show maps of two example
magnetization distributions in magnetic device 100 at different
respective strengths of the external magnetic field.
[0054] FIG. 10A shows individual total magnetization vectors
M.sub.1 and M.sub.2 of magnetic electrodes 110.sub.1 and 110.sub.2
in the parallel magnetization state P.sub.y. Also shown is the
above-mentioned xy coordinate frame. Because each of magnetization
vectors M.sub.1 and M.sub.2 is parallel to the y-axis, and both
vectors are pointing in the same positive y direction, the
corresponding magnetization state of magnetic device 100 is denoted
as a parallel magnetization state.
[0055] FIG. 10B shows the map of the magnetization distribution
corresponding to the parallel magnetization state P.sub.y of FIG.
10A at remanence. The map is color-coded using the color bar shown
in FIG. 10C. The small black cones indicate the local magnetization
directions. The magnetization distribution of FIG. 10B can be
generated, e.g., by (i) applying the external magnetic field
(H.sub.ext) of about +60000 A/m and (ii) ramping down the external
magnetic field to H.sub.ext=0 (also see FIG. 9). In an example
embodiment, the external magnetic field can be generated and
changed as appropriate or necessary using system 700 (FIG. 7).
[0056] FIG. 10C shows the map of the magnetization distribution
that can be obtained in magnetic device 100 by further sweeping the
external magnetic field from H.sub.ext=0 (FIG. 10B) to a negative
value that is just past the negative critical field -H.sub.c (also
see FIG. 9). In this state, M.sub.y has just undergone the
transition 902, and each of magnetic electrodes 110.sub.1 and
110.sub.2 exhibits a respective single-vortex magnetization
distribution, as is evident from inspection of the shown
color-coded map. An anti-parallel magnetization state is not
achieved here because very similar magnetization distributions are
produced in both magnetic electrodes 110.sub.1 and 110.sub.2.
[0057] FIGS. 11A-11E illustrate magnetization distributions in
magnetic device 100 according to an alternative embodiment. More
specifically, the shown magnetization distributions are obtained
using the numerical simulations that are analogous to those
described above in reference to FIG. 9B, with the difference being
that constriction 114 did not have trapezoid tapers 210.sub.1 and
210.sub.2 therein. FIG. 11A schematically shows a parallel
magnetization state P.sub.x of magnetic device 100. FIG. 11E
similarly shows an antiparallel magnetization state AP.sub.y of
magnetic device 100. FIGS. 11B-11D show maps of three example
magnetization distributions in magnetic device 100 at different
respective strengths of the external magnetic field. The maps shown
in FIGS. 11B-11D are color-coded using the same color bar as the
color bar shown in FIG. 10C. The small black cones in FIGS. 11B-11D
indicate the local magnetization directions.
[0058] FIG. 11A shows individual total magnetization vectors
M.sub.1 and M.sub.2 of magnetic electrodes 110.sub.1 and 110.sub.2
in the parallel magnetization state P.sub.x. Also shown is the
corresponding xy coordinate frame. Because each of magnetization
vectors M.sub.1 and M.sub.2 is parallel to the x-axis, and both
vectors are pointing in the same positive x direction, the
corresponding magnetization state of magnetic device 100 is denoted
as a parallel magnetization state. The parallel magnetization state
P.sub.x of FIG. 11A can be generated, e.g., by applying a positive
saturating external magnetic field, H.sub.sat, that is parallel to
the x-axis.
[0059] FIGS. 11B and 11C show the maps of the magnetization
distributions that can be obtained in magnetic device 100 by
sweeping the external magnetic field from H.sub.ext=H.sub.sat (FIG.
11A) to a positive value that is slightly smaller than H.sub.sat
(FIG. 11B) and then further to a positive value that is slightly
higher than H.sub.ext=0. Comparison of the maps shown in FIGS. 11B
and 11C reveals that the changing external magnetic field causes
the local magnetization vectors in magnetic electrodes 110.sub.1
and 110.sub.2 to rotate in mostly opposite directions. More
specifically, the local magnetization vectors in magnetic electrode
110.sub.1 mostly rotate counterclockwise, while the local
magnetization vectors in magnetic electrode 110.sub.2 mostly rotate
clockwise.
[0060] FIG. 11D shows the map of the magnetization distribution
that can be obtained in magnetic device 100 by further sweeping the
external magnetic field from that of FIG. 11C to a negative value
that is just past the negative critical field -H.sub.c. In this
state, M.sub.y has just undergone the transition that is analogous
to transition 912 (see FIG. 9B). The resulting magnetization state
is an anti-parallel magnetization state AP.sub.y because the local
magnetization vectors in magnetic electrode 110.sub.1 mostly point
in the positive y direction while the local magnetization vectors
in magnetic electrode 110.sub.2 mostly point in the negative y
direction.
[0061] FIG. 11E shows individual total magnetization vectors
M.sub.1 and M.sub.2 of magnetic electrodes 110.sub.1 and 110.sub.2
in the antiparallel magnetization state AP.sub.y. Also shown is the
corresponding xy coordinate frame. Each of magnetization vectors
M.sub.1 and M.sub.2 is parallel to the y-axis, and the two vectors
are pointing in opposite directions, which causes the corresponding
magnetization state of magnetic device 100 to be an antiparallel
magnetization state.
[0062] In an example embodiment, the external magnetic field needed
to implement the magnetization changes indicated in FIGS. 11A-11E
can be generated using system 700 (FIG. 7) or system 800 (FIG. 8).
In the latter case, the parallel magnetization state P.sub.x of
FIG. 11A can be used to store a binary "one" in the corresponding
magnetic device 100. The antiparallel magnetization state AP.sub.y
of FIG. 11E can similarly be used to store a binary "zero" in the
corresponding magnetic device 100. The stored bit value can be
changed by subjecting the corresponding magnetic device 100 to an
appropriate external magnetic field, e.g., as explained above in
reference to FIGS. 11A-11E.
[0063] FIGS. 12A-12G illustrate a fabrication method that can be
used to make magnetic device 100 according to an embodiment. More
specifically, each of FIGS. 12A-12G shows a side view of the
nascent magnetic device 100 during a respective fabrication step.
The views of FIGS. 12A-12G are generally analogous to the view
shown in FIG. 1B.
[0064] Referring to FIG. 12A, substrate 102 is coated with a layer
1202 of an e-beam resist. Electron-beam lithography (EBL) is then
used to expose and develop layer 1202 to create an opening 1204
therein in the general shape intended for magnetic electrodes
110.sub.1 and 110.sub.2. A layer 1206 of a suitable ferromagnetic
material (e.g., permalloy) is then deposited over the developed
layer 1202 and into opening 1204.
[0065] Referring to FIG. 12B, layer 1202 and the portions of layer
1206 that are not in direct contact with substrate 102 are removed
using a conventional solvent lift-off process involving immersion
into a solvent (e.g., acetone) bath. The surface of a remaining
portion 1206.sub.r of layer 1206 may get oxidized over time to
produce thereon a relatively thin layer 1212 of the corresponding
native metal oxide.
[0066] Referring to FIG. 12C, the structure produced after the
fabrication steps of FIG. 12B is coated with a layer 1214 of an
e-beam resist.
[0067] Referring to FIG. 12D, EBL is used to expose and develop
layer 1214 to create openings 1216.sub.1 and 1216.sub.2 therein in
the general shape intended for non-magnetic electrodes 120.sub.1
and 120.sub.2, respectively. Portions of metal-oxide layer 1212
exposed by openings 1216.sub.1 and 1216.sub.2 are etched off. The
latter can be done using wet or dry methods, e.g., a dry plasma
etch or a wet chemical etch.
[0068] Referring to FIG. 12E, a layer 1218 of a suitable
non-magnetic metal (e.g., Au, Ti) is deposited over the developed
layer 1214 and into openings 1216.sub.1 and 1216.sub.2.
[0069] Referring to FIG. 12F, layer 1214 is removed by immersion
into the solvent bath mentioned above. The removal of layer 1214
also causes a removal of the portions of layer 1218 that are not in
direct contact with substrate 102 and/or portion 1206r. The
remaining portions of layer 1218 form electrodes 120.sub.1 and
120.sub.2.
[0070] Referring to FIG. 12G, a suitable bias voltage, V.sub.b, is
applied to electrodes 120.sub.1 and 120.sub.2 to induce an
electro-migration process in portion 1206.sub.r. The
electro-migration process creates gap 214 (also see FIG. 2D),
thereby splitting portion 1206.sub.r and the remaining portion of
metal-oxide layer 1212 to produce magnetic electrodes 110.sub.1 and
110.sub.2 and separated layers 112 (also see FIG. 1B). The bias
voltage V.sub.b is removed to arrive at the final structure of
magnetic device 100 (also see FIGS. 1A-1B).
[0071] In alternative embodiments, a nanometer-sized gap 214
between magnetic electrodes 110.sub.1 and 110.sub.2 can be created,
e.g., as described in the following publications: (i) J. Tang, E.
P. De Poortere, J. E. Klare, C. Nuckolls, and S. J. Wind,
"Single-molecule transistor fabrication by self-aligned lithography
and in situ molecular assembly" Microelectronic Engineering, 83,
1706-1709 (2006); (ii) A. Fursina, S. Lee, R. G. S. Sofin, I. V.
Shvets, and D. Natelson "Nanogaps with very large aspect ratios for
electrical measurements" Applied Physics Letters, 92, 113102
(2008); (iii) D. Ward, "Electrical and optical characterization of
molecular nanojunctions" Thesis, Rice University (2010). Each of
these publications is incorporated herein by reference in its
entirety.
[0072] According to an example embodiment disclosed above in
reference to FIGS. 1-12, provided is an apparatus comprising: a
substrate (e.g., 102, FIG. 1); and a first set of electrodes
supported on the substrate, the set including a first thin-film
magnetic electrode (e.g., 110.sub.1, FIG. 1) and a second thin-film
magnetic electrode (e.g., 110.sub.2, FIG. 1), each of the first and
second thin-film magnetic electrodes having a substantially oval
shape. The substantially oval shape is characterized by a first
axis having a first size and a second axis having a second size,
the first and second axes being orthogonal to one another, and the
second size being larger than the first size. The first axis of the
first thin-film magnetic electrode and the first axis of the second
thin-film magnetic electrode are collinear, and an edge-to-edge
separation between the first thin-film magnetic electrode and the
second thin-film magnetic electrode is smaller than the first
size.
[0073] In some embodiments of the above apparatus, each of the
first and second thin-film magnetic electrodes comprises a
ferromagnetic material.
[0074] In some embodiments of any of the above apparatus, the
substrate comprises one or more of silicon and silicon oxide.
[0075] In some embodiments of any of the above apparatus, each of
the first and second thin-film magnetic electrodes includes a
respective taper (e.g., 210.sub.i/220.sub.i/230.sub.i, FIG. 2) that
extends from a respective electrode edge in a constriction area
(e.g., 114, FIG. 1) between the first and second thin-film magnetic
electrodes.
[0076] In some embodiments of any of the above apparatus, a gap
(e.g., 214, FIG. 2) between the respective tapers has a width that
is smaller than the edge-to-edge separation.
[0077] In some embodiments of any of the above apparatus, the width
of the gap varies along a length of the gap (e.g., as shown in FIG.
2B or 2D).
[0078] In some embodiments of any of the above apparatus, the width
of the gap varies as a function of a distance from the substrate
(e.g., as shown in FIG. 3B or 3C).
[0079] In some embodiments of any of the above apparatus, the
apparatus further comprises an active element (e.g., 402, FIG. 4)
at least a portion of which is located in the gap between the
respective tapers.
[0080] In some embodiments of any of the above apparatus, the
active element is one or more of a quantum dot, a nanocrystal, a
single molecule, a polymer, and a metal-organic complex.
[0081] In some embodiments of any of the above apparatus, the
active element comprises a fullerene molecule (e.g., C.sub.60, FIG.
4A).
[0082] In some embodiments of any of the above apparatus, the
active element comprises one or more linkers, each of which is
chemically bonded to a respective metal atom of the respective
taper (e.g., as shown in FIG. 4B).
[0083] In some embodiments of any of the above apparatus, the
respective tapers are connected to one another to form a magnetic
bridge between the first and second thin-film magnetic electrodes
(e.g., as indicated in FIG. 12F).
[0084] In some embodiments of any of the above apparatus, the
apparatus further comprises a plurality of additional sets of
electrodes, each of the additional sets of electrodes being a
nominal copy of the first set of electrodes, wherein the first set
of electrodes and the plurality of additional sets of electrodes
are arranged in an array (e.g., 500, FIG. 5; 600, FIG. 6) on the
substrate.
[0085] In some embodiments of any of the above apparatus, the
apparatus further comprises a disk (e.g., 610, FIG. 6), wherein the
substrate is a part of the disk; and wherein the first set of
electrodes and the plurality of additional sets of electrodes are
arranged along one or more circular tracks (e.g., 612, FIG. 6 or 8)
on the disk.
[0086] In some embodiments of any of the above apparatus, the first
set of electrodes further includes: a first non-magnetic metal
electrode (e.g., 120.sub.1, FIG. 1) attached to the first thin-film
magnetic electrode; and a second non-magnetic metal electrode
(e.g., 120.sub.2, FIG. 1) attached to the second thin-film magnetic
electrode; and the apparatus further comprises a plurality of
electrically conducting tracks (e.g., 502, FIG. 5) connected to the
first and second non-magnetic metal electrodes of the first set of
electrodes and of the plurality of additional sets of
electrodes.
[0087] In some embodiments of any of the above apparatus, the array
comprises two or more rows and two or more columns of the sets of
electrodes (e.g., as shown in FIG. 5); and the plurality of
electrically conducting tracks are arranged in a manner that makes
each of the first thin-film magnetic electrodes individually
addressable from the periphery of the substrate (e.g., as shown in
FIG. 5).
[0088] In some embodiments of any of the above apparatus, the
plurality of electrically conducting tracks are further arranged in
a manner that makes each of the second thin-film magnetic
electrodes individually addressable from the periphery of the
substrate (e.g., as shown in FIG. 5A).
[0089] In some embodiments of any of the above apparatus, the
plurality of electrically conducting tracks are further arranged in
a manner that makes the second thin-film magnetic electrodes in a
column to be connected to a corresponding one of the electrically
conducting tracks (e.g., as shown in FIG. 5B or FIG. 5C or FIG.
5D).
[0090] In some embodiments of any of the above apparatus, the first
set of electrodes further includes: a first non-magnetic metal
electrode (e.g., 120.sub.1, FIG. 1) attached to the first thin-film
magnetic electrode; and a second non-magnetic metal electrode
(e.g., 120.sub.2, FIG. 1) attached to the second thin-film magnetic
electrode.
[0091] In some embodiments of any of the above apparatus, each of
the first and second non-magnetic metal electrodes includes one or
both of gold and titanium.
[0092] In some embodiments of any of the above apparatus, the
apparatus further comprises means (e.g., 710, FIG. 7; 802, FIG. 8)
for subjecting the first set of electrodes to an external magnetic
field.
[0093] In some embodiments of any of the above apparatus, the means
for subjecting causes the external magnetic field to have a
component that is parallel to the first axes (e.g., B, FIG. 7).
[0094] In some embodiments of any of the above apparatus, the
substantially oval shape is a substantially ellipse shape.
[0095] In some embodiments of any of the above apparatus, each of
the first thin-film magnetic electrode and the second thin-film
magnetic electrode has a thickness that is smaller than the first
size.
[0096] In some embodiments of any of the above apparatus, the
thickness is smaller than the edge-to-edge separation.
[0097] While this disclosure includes references to illustrative
embodiments, this specification is not intended to be construed in
a limiting sense. Various modifications of the described
embodiments, as well as other embodiments within the scope of the
disclosure, which are apparent to persons skilled in the art to
which the disclosure pertains are deemed to lie within the
principle and scope of the disclosure, e.g., as expressed in the
following claims.
[0098] Unless explicitly stated otherwise, each numerical value and
range should be interpreted as being approximate as if the word
"about" or "approximately" preceded the value or range.
[0099] It will be further understood that various changes in the
details, materials, and arrangements of the parts which have been
described and illustrated in order to explain the nature of this
disclosure may be made by those skilled in the art without
departing from the scope of the disclosure, e.g., as expressed in
the following claims.
[0100] Although the elements in the following method claims, if
any, are recited in a particular sequence with corresponding
labeling, unless the claim recitations otherwise imply a particular
sequence for implementing some or all of those elements, those
elements are not necessarily intended to be limited to being
implemented in that particular sequence.
[0101] Reference herein to "one embodiment" or "an embodiment"
means that a particular feature, structure, or characteristic
described in connection with the embodiment can be included in at
least one embodiment of the disclosure. The appearances of the
phrase "in one embodiment" in various places in the specification
are not necessarily all referring to the same embodiment, nor are
separate or alternative embodiments necessarily mutually exclusive
of other embodiments. The same applies to the term
"implementation."
[0102] Throughout the detailed description, the drawings, which are
not to scale, are illustrative only and are used in order to
explain, rather than limit the disclosure. The use of terms such as
height, length, width, top, bottom, is strictly to facilitate the
description of the embodiments and is not intended to limit the
embodiments to a specific orientation. For example, height does not
imply only a vertical rise limitation, but is used to identify one
of the three dimensions of a three dimensional structure as shown
in the figures. Such "height" would be vertical where the
electrodes are horizontal but would be horizontal where the
electrodes are vertical, and so on. Similarly, while all figures
show the different layers as horizontal layers such orientation is
for descriptive purpose only and not to be construed as a
limitation.
[0103] Also for purposes of this description, the terms "couple,"
"coupling," "coupled," "connect," "connecting," or "connected"
refer to any manner known in the art or later developed in which
energy is allowed to be transferred between two or more elements,
and the interposition of one or more additional elements is
contemplated, although not required. Conversely, the terms
"directly coupled," "directly connected," etc., imply the absence
of such additional elements.
[0104] The description and drawings merely illustrate the
principles of the disclosure. It will thus be appreciated that
those of ordinary skill in the art will be able to devise various
arrangements that, although not explicitly described or shown
herein, embody the principles of the disclosure and are included
within its spirit and scope. Furthermore, all examples recited
herein are principally intended expressly to be only for
pedagogical purposes to aid the reader in understanding the
principles of the disclosure and the concepts contributed by the
inventor(s) to furthering the art, and are to be construed as being
without limitation to such specifically recited examples and
conditions. Moreover, all statements herein reciting principles,
aspects, and embodiments of the disclosure, as well as specific
examples thereof, are intended to encompass equivalents
thereof.
* * * * *