U.S. patent application number 17/321891 was filed with the patent office on 2021-09-02 for thermoelectric device utilizing non-zero berry curvature.
The applicant listed for this patent is Ohio State Innovation Foundation. Invention is credited to Claudia Felser, Joseph P. Heremans, Timothy McCormick, Nandini Trivedi, Sarah Watzman.
Application Number | 20210273150 17/321891 |
Document ID | / |
Family ID | 1000005585330 |
Filed Date | 2021-09-02 |
United States Patent
Application |
20210273150 |
Kind Code |
A1 |
Heremans; Joseph P. ; et
al. |
September 2, 2021 |
THERMOELECTRIC DEVICE UTILIZING NON-ZERO BERRY CURVATURE
Abstract
Thermoelectric devices and methods of using thermoelectric
devices. A thermoelectric device includes a thermoelectric element
comprised of a material having a non-zero Berry curvature. The
device may operate as a Nernst generator that generates electricity
in response to application of a temperature gradient to the
thermoelectric element, or as an Ettingshausen cooler that pumps
heat into or out of an object to be heated or cooled in response to
application of a current to the thermoelectric element. In either
application, the non-zero Berry curvature of the material allows
the device to operate without an externally applied magnetic
field.
Inventors: |
Heremans; Joseph P.; (Upper
Arlington, OH) ; Watzman; Sarah; (Cincinnati, OH)
; Trivedi; Nandini; (Columbus, OH) ; McCormick;
Timothy; (Ashburn, VA) ; Felser; Claudia;
(Halle, DE) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Ohio State Innovation Foundation |
Columbus |
OH |
US |
|
|
Family ID: |
1000005585330 |
Appl. No.: |
17/321891 |
Filed: |
May 17, 2021 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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16157522 |
Oct 11, 2018 |
11011692 |
|
|
17321891 |
|
|
|
|
62570782 |
Oct 11, 2017 |
|
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H01L 37/00 20130101 |
International
Class: |
H01L 37/00 20060101
H01L037/00 |
Claims
1-20. (canceled)
21. A method of generating electricity comprising: providing a
temperature gradient across a first dimension of a thermoelectric
element including a material having a non-zero Berry curvature
along the first dimension; generating a voltage gradient along a
second dimension of the thermoelectric element aligned with a
cross-product of the temperature gradient and the non-zero Berry
curvature; and coupling a voltage provided by the voltage gradient
to an electrical load.
22. The method of claim 21 wherein providing the temperature
gradient across the first dimension of the thermoelectric element
comprises: coupling a first side of the thermoelectric element to a
heat source; and coupling a second side of the thermoelectric
element to a heat sink, the second side located a first distance
from the first side along a third dimension transverse to both the
first dimension and second dimension.
23. The method of claim 22 further comprising: applying a magnetic
field aligned with the non-zero Berry curvature to the
thermoelectric element.
24. The method of claim 21 wherein the material is a Weyl
semimetal.
25. The method of claim 21 wherein the temperature gradient is
orthogonal to the non-zero Berry curvature.
26. A method of pumping heat into or out of a thermal load,
comprising: passing a current through a thermoelectric element
including a material having a non-zero Berry curvature along a
first dimension such that the current flows across the first
dimension; generating a temperature gradient along a second
dimension of the thermoelectric element aligned with a
cross-product of the current and the non-zero Berry curvature; and
coupling the temperature gradient to the thermal load.
27. The method of claim 26 wherein coupling the temperature
gradient to the thermal load comprises: coupling a first side of
the thermoelectric element to a heat sink; and coupling a second
side of the thermoelectric element to an object to be cooled or
warmed, the second side located a first distance from the first
side along the second dimension.
28. The method of claim 27 wherein passing the current through the
thermoelectric element in a first direction cools the object, and
passing the current in a second direction opposite the first
direction warms the object.
29. The method of claim 26 further comprising: applying a magnetic
field aligned with the non-zero Berry curvature to the
thermoelectric element.
30. The method of claim 26 wherein the material is a Weyl
semimetal.
31. The method of claim 26 wherein the non-zero Berry curvature is
orthogonal to both the temperature gradient and the current.
32. A thermoelectric device comprising: a thermoelectric element
including a material having a non-zero Berry curvature along a
first dimension of the thermoelectric element; a first thermal
coupler thermally coupled to a first side of the thermoelectric
element; a second thermal coupler thermally coupled to a second
side of the thermoelectric element, the second side located a first
distance from the first side along a second dimension transverse to
the first dimension; a first terminal electrically coupled to a
third side of the thermoelectric element; and a second terminal
electrically coupled a fourth side of the thermoelectric element,
the fourth side located a second distance from the third side along
a third dimension aligned with a cross-product of the second
dimension and the non-zero Berry curvature.
33. The thermoelectric device of claim 32 wherein the
thermoelectric element generates a voltage across the first and
second terminals in response to an application of a temperature
gradient across the first and second thermal couplers.
34. The thermoelectric device of claim 32 wherein the
thermoelectric element generates a temperature gradient across the
first and second thermal couplers in response to an application of
an electrical current through the first and second terminals.
35. The thermoelectric device of claim 32 wherein the non-zero
Berry curvature is orthogonal to a temperature gradient to which
the thermoelectric element is exposed or the thermoelectric element
generates.
36. The thermoelectric device of claim 32 wherein: the first
thermal coupler is configured to thermally couple the first side to
a heat source; and the second thermal coupler is configured to
thermally couple the second side to a heat sink, wherein a voltage
is generated between the third and fourth sides in response to
application of a temperature gradient between the first thermal
coupler and the second thermal coupler.
37. The thermoelectric device of claim 32 further comprising: a
magnet configured to provide a magnetic field aligned with the
non-zero Berry curvature to the thermoelectric element.
38. The thermoelectric device of claim 32 wherein the material is a
Weyl semimetal.
39. The thermoelectric device of claim 38 wherein the Weyl
semimetal breaks time-reversal symmetry.
Description
[0001] This application claims the benefit of U.S. Application No.
62/570,782 filed on Oct. 11, 2017 entitled "Thermoelectric Device
Using Weyl Semimetal", and U.S. application Ser. No. 16/157,522
filed on Oct. 11, 2018 entitled "Thermoelectric Device Utilizing
Non-Zero Berry Curvature", the disclosures of which are each
incorporated by reference herein in their entireties.
BACKGROUND
[0002] It is estimated that in 2017, the United States consumed
97.7 quads providing for its residential, commercial, industrial,
and transportation energy needs. Approximately 80% of this energy
was produced by fossil fuels such as petroleum (37.1%), natural gas
(28.7%), and coal (14.3%). Nuclear power (8.62%) and biomass
(5.03%) accounted for another 13.7% of the energy produced. The
approximately 6% remaining was generated from sources such as
hydroelectric, wind, geothermal, and solar. Of the energy consumed,
it is further estimated that only 32% produced useful work, with
the remaining 68% being rejected into the environment as waste
heat. Transportation applications are particularly inefficient,
with about 79% of the energy consumed producing waste heat.
Recovery of even a portion of this waste heat could significantly
reduce the amount of energy consumed.
[0003] Attempts to recover energy from waste heat include using the
heat to generate electricity. For example, waste heat may be used
to vaporize liquids or heat gases that are provided to an engine
which powers an electric generator. Another approach to generating
electricity from waste heat is to use the waste heat to produce a
temperature gradient across a thermoelectric device that produces
electricity through a thermoelectric effect.
[0004] Thermoelectric devices include thermoelectric generators,
Peltier devices, and Nernst/Ettingshausen devices. Conventional
thermoelectric devices include thermoelectric generators that
generate electricity from a temperature gradient and Peltier
devices such as thermoelectric heat-pumps (also referred to as
Peltier coolers or thermoelectric coolers) that use an applied
current to generate a temperature gradient. Thermoelectric
generators and Peltier devices have a longitudinal geometry in
which the temperature gradient and induced voltage run parallel to
one another. Conventional longitudinal thermoelectric devices
require both n-type and p-type materials electrically connected in
series and thermally connected in parallel. To increase efficiency,
Peltier devices are often cascaded (e.g., stacked with increasingly
smaller surface areas on top) as shown in FIG. 1. The need for
electrical connections between the n-type and p-type materials, as
well as the need for this cascading in Peltier devices, add to the
cost and complexity of conventional, longitudinal thermoelectric
devices.
[0005] Nernst/Ettingshausen devices are solid-state devices where
an applied temperature gradient and perpendicular magnetic field
generate a mutually orthogonal voltage, or an applied current and
perpendicular magnetic field generate a mutually orthogonal
temperature gradient. The magnetic field generates a skew force
(Lorentz force) that accelerates charge carriers in a direction
perpendicular to the temperature gradient in the device. As with
Peltier devices, Nernst/Ettingshausen devices include
thermoelectric heat-pumps (also referred to as Ettingshausen
coolers) that use an applied current to generate a temperature
gradient, and thermoelectric generators (also referred to as Nernst
generators) that generate electricity from a temperature gradient.
Nernst/Ettingshausen devices utilize a transverse geometry and thus
only require one polarity of material.
[0006] To increase efficiency, Nernst/Ettingshausen devices may be
shaped as shown in FIG. 2. Because the shaping is done on the
thermoelectric material itself, this technology is more simplistic
than that of Peltier devices and eliminates losses due to the
multiple electrical connections of n-type and p-type thermoelectric
materials. However, unlike Peltier devices, conventional
Nernst/Ettingshausen devices require an externally applied magnetic
field that is orthogonal to the electrical current and temperature
gradient. The magnetic fields used in conventional
Nernst/Ettingshausen devices must be relatively intense, which can
make Nernst/Ettingshausen devices impractical for commercial
applications.
[0007] Thus, there is a need for improved thermoelectric devices
and methods of using thermoelectric devices to provide
thermoelectric electricity generation and/or cooling with improved
efficiency that do not require different types of materials or
intense externally applied magnetic fields.
SUMMARY
[0008] In an embodiment of the invention, a thermoelectric device
is provided comprising a thermoelectric element including a
material having a non-zero Berry curvature.
[0009] In an aspect of the invention, the thermoelectric element
may be configured to generate a voltage in response to being
exposed to a temperature gradient.
[0010] In another aspect of the invention, the thermoelectric
element may be configured to generate a temperature gradient in
response to application of an electrical current.
[0011] In another aspect of the invention, the non-zero Berry
curvature may be along an axis of the material orthogonal to a
temperature gradient to which the thermoelectric element is exposed
or the thermoelectric element generates.
[0012] In another aspect of the invention, the thermoelectric
element may have a first side, a second side located a first
distance from the first side along a first dimension, a third side
that intersects the first and second sides, and a fourth side
located a second distance from the third side along a second
dimension orthogonal to the first dimension and that intersects the
first and second sides. The thermoelectric device may further
include a first thermal coupler configured to thermally couple the
first side to a heat source and a second thermal coupler configured
to thermally couple the second side to a heat sink. A voltage may
be generated between the third and fourth sides in response to
application of a temperature gradient between the first thermal
coupler and the second thermal coupler.
[0013] In another aspect of the invention, the thermoelectric
device may include a magnet configured to provide a magnetic field
to the thermoelectric element.
[0014] In another aspect of the invention, the thermoelectric
device may be one of a Ettingshausen cooler or a Nernst
generator.
[0015] In another aspect of the invention, the material may be a
Weyl semimetal.
[0016] In another aspect of the invention, the Weyl semimetal may
break time-reversal symmetry.
[0017] In another embodiment of the invention, a method of
generating electricity is provided. The method includes providing a
temperature gradient across a thermoelectric element including a
material having a non-zero Berry curvature.
[0018] In an aspect of the invention, providing the temperature
gradient across the thermoelectric element may include coupling the
first side of the thermoelectric element to the heat source and
coupling the second side of the thermoelectric element to the heat
sink, wherein the second side may be located the first distance
from the first side along the first dimension.
[0019] In another aspect of the invention, the method may further
include applying the magnetic field to the thermoelectric
element.
[0020] In another aspect of the invention, the method may include
orienting the thermoelectric element so that the axis of the
material having the non-zero Berry curvature is orthogonal to the
temperature gradient.
[0021] In another embodiment of the invention, a method of
generating a temperature gradient is provided. The method includes
passing a current through the thermoelectric element including the
material having the non-zero Berry curvature.
[0022] In another aspect of the invention, generating the
temperature gradient may include coupling the first side of the
thermoelectric element to the heat sink, and coupling the second
side of the thermoelectric element to an object to be cooled or
warmed, wherein the second side is located the first distance from
the first side along the first dimension.
[0023] In another aspect of the invention, the method may include
applying the magnetic field to the thermoelectric element.
[0024] In another aspect of the invention, passing the current
through the thermoelectric element from the third side to the
fourth side may cool the object, and passing the current from the
fourth side to the third side may warm the object.
[0025] In another aspect of the invention, the method may include
orienting the thermoelectric element so that the axis of the
material having the non-zero Berry curvature is orthogonal to the
temperature gradient and the current.
[0026] The above summary presents a simplified overview of some
embodiments of the invention to provide a basic understanding of
certain aspects of the invention discussed herein. The summary is
not intended to provide an extensive overview of the invention, nor
is it intended to identify any key or critical elements, or
delineate the scope of the invention. The sole purpose of the
summary is merely to present some concepts in a simplified form as
an introduction to the detailed description presented below.
BRIEF DESCRIPTION OF THE DRAWINGS
[0027] The accompanying drawings, which are incorporated in and
constitute a part of this specification, illustrate various
embodiments of the invention and, together with the general
description of the invention given above, and the detailed
description of the embodiments given below, serve to explain the
embodiments of the invention.
[0028] FIG. 1 is an isometric view of a Peltier device having a
cascaded configuration.
[0029] FIG. 2 is an isometric view of an Nernst/Ettingshausen
device configured to have a cross-sectional area that varies along
the length of a temperature gradient applied across the device.
[0030] FIG. 3 is a diagrammatic view of a thermoelectric element
depicting movement of charge carriers in response to a temperature
gradient across the element.
[0031] FIG. 4 is an isometric view of a longitudinal thermoelectric
module that utilizes two thermoelectric elements of FIG. 3 to
generate a voltage based on the Seebeck effect.
[0032] FIG. 5A is an isometric view of a thermoelectric generator
including a plurality of the thermoelectric modules of FIG. 4.
[0033] FIG. 5B is an enlarged view of a portion of the
thermoelectric generator of FIG. 5A showing additional details
thereof.
[0034] FIG. 6 is an isometric view of a transverse thermoelectric
element that utilizes the Nernst effect to generate a voltage from
a temperature gradient.
[0035] FIG. 7 is an isometric view of the thermoelectric element of
FIG. 6 showing a spatial relationship between a crystallographic
axis of the thermoelectric element along which a non-zero Berry
curvature exists, the temperature gradient applied to the
thermoelectric element, and the voltage produced by the
thermoelectric element.
[0036] FIG. 8 is a diagrammatic view of an exemplary transverse
thermoelectric generator, or Nernst generator, including the
thermoelectric element of FIG. 7.
[0037] FIG. 9 is an isometric view of a thermoelectric test device
used to collect Nernst effect performance data on the
thermoelectric element of FIG. 7.
[0038] FIG. 10 is graphical view illustrating the Nernst
thermopower verses applied magnetic field at different operating
temperatures.
[0039] FIG. 11 is graphical view illustrating Nernst thermopower as
a function of temperature in the absence of an applied magnetic
field for a thermoelectric element having a transverse
geometry.
[0040] FIG. 12 is a graphical view illustrating thermoelectric
figures of merit verses temperature for different thermoelectric
materials in transverse and longitudinal configurations without an
externally applied magnetic field.
DETAILED DESCRIPTION
[0041] Conventional thermoelectric devices use a longitudinal
geometry and depend on the Seebeck effect to generate electricity
from waste heat. Thermoelectric devices having transverse
geometries have significant advantages in cost and complexity over
those having a longitudinal geometry. However, because conventional
transverse thermoelectric devices depend on the Nernst effect to
generate electricity, they normally need a large externally applied
magnetic field to function. Embodiments of the invention provide
the advantages of transverse geometries in thermoelectric devices
having little or no need for an external magnetic field. This
improvement in thermoelectric devices has been achieved by using
thermoelectric materials that have a non-zero Berry curvature, such
as found in certain Weyl semimetals.
[0042] A Weyl semimetal is a material having inverted conduction
and valence bands where the bands are linear Dirac bands near the
crossing points. The breaking of time-reversal symmetry or
spatial-inversion symmetry may lift the degeneracy of the band
crossing points, giving rise to pairs of Weyl nodes. Separated Weyl
nodes may result when the electron band structure of the material
has singly degenerate bands that include bulk band crossings known
as "Weyl points". Electrons around the Weyl points have a property
called Berry curvature .OMEGA..sub.z that behaves like an internal
magnetic field. The Berry curvature .OMEGA..sub.z may give
electrons an additional velocity that is normal to the direction of
their momentum. One Weyl semimetal that breaks time-reversal
symmetry and has a non-zero Berry curvature is YbMnBi.sub.2. A
thermoelectric device made from YbMnBi.sub.2 in accordance with an
embodiment of the invention has demonstrated previously unknown
thermoelectric efficiency in a transverse geometry without the need
for an externally applied magnetic field. Use of materials having
non-zero Berry curvatures thereby provides transverse
thermoelectric devices with significant advantages in cost and
reliability over conventional devices.
[0043] Embodiments of the invention may utilize the transverse
geometry and cascaded shape of conventional Nernst/Ettingshausen
devices, but do not require an externally applied magnetic field.
Weyl semimetals having a non-zero net Berry curvature may be used
to form these new Nernst/Ettingshausen devices. The non-zero Berry
curvature may act as an intrinsic magnetic field in k-space,
generating a skew force to the applied current and thus inducing a
temperature gradient. Materials with a non-zero Berry curvature may
allow thermoelectric devices to be built with the simplicity of the
Nernst/Ettingshausen geometry without the need for an externally
applied magnetic field. Thermoelectric devices made in accordance
with embodiments of the invention also provide previously unheard
of thermoelectric figures of merit in a transverse geometry.
[0044] FIG. 3 depicts a cross-sectional view of a thermoelectric
element 10 comprising a length of thermoelectric material 12 having
a cold end 14 and a hot end 16. Application of heat to the
thermoelectric element 10 that produces the depicted temperature
difference 4T may cause charge carriers 18 to migrate toward and/or
condense at the cold end 14 of thermoelectric material 12 as
indicated by the single headed arrows 20. This phenomenon is known
as the Seebeck effect.
[0045] For a thermoelectric material 12 in which the majority
carriers are positive charge carriers 18 (e.g., a p-type
semiconductor), the carrier migration may cause a positive voltage
V to build up across the length of the thermoelectric material 12
such that the cold end 14 has a higher potential than the hot end
16. For a thermoelectric material 12 in which the majority carriers
are negative charge carriers 18 (e.g., an n-type semiconductor),
the carrier migration may cause a negative voltage V to build up
across the thermoelectric material 12 such that the cold end 14 has
a lower potential than the hot end 16. The thermopower or Seebeck
coefficient .alpha. of the length of thermoelectric material 12 is
provided by:
.alpha. = - E .gradient. T Eqn . .times. 1 ##EQU00001##
where E is the electric field and .gradient.T is the temperature
gradient. Equation 1 may simplify to .alpha.=V/.DELTA.T when the
voltage V and temperature difference .DELTA.T are measured over the
same length of material. Thus, Equation 1 may be used to determine
an expected voltage that will be generated by the thermoelectric
element 10 given the dimensions of the element. In order to define
a consistent flow of current I that is independent of the type of
charge carrier, current I is defined herein as always moving in the
direction of positive charge flow. Thus, in materials having
negative charge carriers 18, current I flows in the opposite
direction of the charge carriers 18, and in materials having
positive charge carriers 18, the current I flows in the same
direction as the charge carriers 18.
[0046] It is typically desirable to use a thermoelectric material
12 with a relatively large Seebeck coefficient .alpha. in order to
generate a higher voltage V for a given temperature difference
.DELTA.T than would be generated by a thermoelectric material with
a low Seebeck coefficient .alpha.. A typical Seebeck coefficient
.alpha. for a semiconductor may have a magnitude that ranges from
200 to 300 .mu.V/K at room temperature. The thermoelectric
efficiency of a thermoelectric material can be quantified by a
dimensionless figure of merit zT given by:
z .times. T = .alpha. 2 .times. .sigma. .kappa. .times. T Eqn .
.times. 2 ##EQU00002##
where Tis the average absolute temperature of the thermoelectric
element 10 in kelvin, .sigma. is the electrical conductivity of the
thermoelectric material 12, .kappa. is the thermal conductivity of
the thermoelectric material 12, and each of the parameters may vary
with temperature.
[0047] According to Equation 2, the thermoelectric figure of merit
zT is proportional to the electrical conductivity .sigma. and the
square of the Seebeck coefficient .alpha., and inversely
proportional to the thermal conductivity .kappa.. A low thermal
conductivity .kappa. may enable a temperature gradient .gradient.T
to be maintained across the thermoelectric element 10 with a lower
flow of heat through the thermoelectric element 10 as compared to a
high thermal conductivity .kappa.. A high electrical conductivity
.sigma. may lower the impedance of the thermoelectric element 10,
thereby allowing it to source a larger amount of current I as
compared to a thermoelectric element 10 with a low electrical
conductivity .sigma..
[0048] It is normally desirable to use materials with as high of a
thermoelectric figure of merit zT as possible. Useful devices may
be made from thermoelectric materials with a thermoelectric figure
of merit of 0.3. In contrast, a thermoelectric figure of merit of
1.0 is considered good, and a thermoelectric figure of merit of 2.0
or more is considered to be near the limit of what is possible with
conventional technology. As can be seen from Equations 1 and 2, the
voltage V generated by thermoelectric element 10 from a given
temperature difference .DELTA.T due to the Seebeck effect is
limited by the intrinsic properties of the thermoelectric material
12, e.g., the Seebeck coefficient .alpha., electrical conductivity
.sigma., and thermal conductivity .kappa..
[0049] The temperature difference .DELTA.T may be generated by the
thermoelectric element 10 itself in response to a current I being
driven through the thermoelectric element 10. Thus, the
thermoelectric element 10 can be used as a heat pump by passing an
externally sourced current I through the element. To generate the
shown temperature difference .DELTA.T in a thermoelectric material
in which the majority carriers are positive charge carriers (e.g.,
holes), the current I may be driven from the cold end 14 toward the
hot end 16. In contrast, to generate the shown temperature
difference .DELTA.T in a thermoelectric material in which the
majority carriers are negative charge carriers (e.g., electrons),
the current I may be driven from the hot end 16 toward the cold end
14.
[0050] FIG. 4 depicts a thermoelectric module 22 which utilizes the
Seebeck effect and has a longitudinal geometry. Thermoelectric
module 22 may include a thermoelectric element 24 made of a p-type
thermoelectric material having a hot end 26 and a cold end 28, a
thermoelectric element 30 made of an n-type thermoelectric material
having a hot end 32 and a cold end 34, an upper electrode 36
coupling the cold end 28 of thermoelectric element 24 to the cold
end 34 of thermoelectric element 30, and lower electrodes 38
coupling the hot ends 26, 32 of thermoelectric elements 24, 30 to
an electrical load 42. Because the depicted type of thermoelectric
module 22 relies on the Seebeck effect to generate electrical
power, it uses thermoelectric elements 24, 30 having different
types of charge carriers and has an electrical output that scales
intrinsically with the properties of the thermoelectric materials
used in the thermoelectric elements 24, 30.
[0051] Application of a temperature difference .DELTA.T across the
thermoelectric module 22 may cause heat to flow from the hot ends
26, 32 to the cold ends 28, 34 of thermoelectric elements 24, 30,
as indicated by single headed arrows 44, 46. The resulting
temperature gradient .gradient.T may cause a flow of positive
charge carriers from the hot end 26 to the cold end 28 of
thermoelectric element 24 that results in a positive current flow
toward the cold end 28, as indicated by single headed arrow 48. The
temperature gradient .gradient.T may also cause a flow of negative
charge carriers from the hot end 32 to the cold end 34 of
thermoelectric element 30 that results in a positive current flow
toward the hot end 32 as indicated by single headed arrow 50. The
electrodes 36, 38 may be configured to complete the circuit,
thereby allowing current to flow through the thermoelectric module
22 and electrical load 42.
[0052] Because the voltage generated by thermoelectric module 22 is
limited by the intrinsic properties of the thermoelectric materials
from which it is made, thermoelectric generators using a
longitudinal geometry are typically assembled from a large number
of modules in order to produce a useful output voltage. FIGS. 5A
and 5B depict an exemplary thermoelectric generator 52 including a
plurality of thermoelectric modules 22 electrically coupled in a
series configuration. The upper electrodes 36 of thermoelectric
modules 22 are thermally coupled to an upper substrate 54, and the
lower electrodes 38 of thermoelectric modules 22 are thermally
coupled to a lower substrate 56. The thermoelectric modules 22 are
thus thermally coupled to the upper and lower substrates 54, 56 in
parallel. The substrates 54, 56 may be made from a material that
has a low electrical conductivity, or is electrically isolated from
the electrodes 36, 38 by an electrically insulating layer (not
shown), in order to avoid shorting out the thermoelectric generator
52.
[0053] One of the substrates 54, 56 (e.g., the lower substrate 56)
may be thermally coupled to a heat source 58 (e.g., the exhaust
from combustion used to heat a boiler), and the other substrate 54,
56 (e.g., the upper substrate 54) may be thermally coupled to a
heat sink 60 (e.g., a cooling medium such as the atmosphere or a
reservoir of water). Thermally coupling the thermoelectric
generator 52 between a heat source and a heat sink as described
above may cause a temperature difference .gradient.T develop across
each of the thermoelectric modules 22. The resulting temperature
gradient .gradient.T in thermoelectric elements 24, 30 may in turn
cause each thermoelectric module 22 to generate a voltage. The
electrodes 36, 38 of thermoelectric modules 22 may be configured to
electrically couple the thermoelectric modules 22 in a series
configuration so that the voltages generated by the thermoelectric
modules 22 add constructively to generate an output voltage V that
causes a current I to flow through an electrical load 62 coupled to
output terminals 64, 66 of thermoelectric generator 52.
[0054] FIG. 6 depicts a thermoelectric element 70 having a
transverse geometry that utilizes the Nernst effect to generate a
voltage from a temperature difference .DELTA.T. The thermoelectric
element 70 may include a height dimension h that generally
corresponds with an x-axis of a three-dimensional coordinate system
72, a length dimension l that generally corresponds with a y-axis
of coordinate system 72, and a width dimension w that generally
corresponds with a z-axis of coordinate system 72.
[0055] To generate a voltage V across the length l of
thermoelectric element 70, the Nernst effect requires a force that
urges charge carriers in a direction orthogonal (i.e.,
perpendicular) to the temperature gradient .gradient.T produced by
temperature difference .DELTA.T across the element, e.g.,
orthogonal to the height h of thermoelectric element 70. In
conventional devices, this force is a Lorentz force resulting from
the cross-product of the temperature gradient .gradient.T and a
magnetic field H applied in a direction orthogonal to both the
temperature gradient .gradient.T and the voltage gradient
.gradient.V generated by the device. For the thermoelectric element
70 depicted in FIG. 6, this magnetic field H may be generally
parallel to the z-axis of coordinate system 72.
[0056] As carriers move toward the cold side of the thermoelectric
element 70 under the influence of the temperature gradient
.gradient.T (as indicated by single headed arrow 71), the magnetic
field H may generate forces on the carriers that urge positive and
negative charge carriers in opposite directions. For the depicted
temperature difference .DELTA.T and magnetic field H, this force
may urge positive charge carriers in a positive direction along the
y-axis and negative charge carriers in a negative direction along
the y-axis. The movement of the charge carriers in thermoelectric
element 70 under the influence of the temperature gradient
.gradient.T and magnetic field H may thereby produce a voltage V
across the thermoelectric element 70 having the shown polarity.
[0057] In contrast to the output of thermoelectric module 22, which
is limited by the intrinsic properties of the materials from which
it is made, the output of thermoelectric element 70 scales with the
size of the device. Advantageously, this allows the voltage V
generated by thermoelectric element 70 to be scaled by simply
adjusting its dimensions. Thus, thermoelectric generators based on
this type of element may avoid the complexity of assembling a large
number of thermoelectric elements as shown in FIG. 5. However,
because the magnetic field H required to generate useful amounts of
electricity is typically quite large, conventional thermoelectric
elements utilizing a transverse geometry and the Nernst effect are
generally not suitable for power recovery from waste heat or other
practical commercial applications.
[0058] Embodiments of the invention advantageously reduce or
eliminate the need to provide a magnetic field H to thermoelectric
elements utilizing the Nernst effect by using materials having a
non-zero Berry curvature, such as certain Weyl semimetals. A Weyl
semimetal is a solid-state crystal having low energy excitations
that comprise Weyl fermions which carry electrical charge. It has
been determined that Weyl semimetals having a non-zero integral
over the Fermi surface of the projection of the Berry curvature
.OMEGA..sub.z of the dispersion relation of their conduction
electrons along a specific crystallographic axis can be used to
create or increase Nernst thermopower .alpha..sub.xyz.
[0059] This property may enable materials having a non-zero Berry
curvature to generate a thermoelectric voltage along a direction
orthogonal to the direction of an applied temperature gradient
without an externally applied magnetic field. Thermoelectric
devices made using materials having a non-zero Berry curvature may
be used to generate power and/or pump heat, and thus may have
wide-ranging applications in many industries, such as the energy
and electronics industries.
[0060] The origin of this thermoelectric effect is believed to lie
in the presence of a non-zero Berry curvature of the electronic
band structure at each electron energy and momentum value. A Berry
curvature may be produced by an electronic band structure that
exhibits spin-orbit canting, which may cause the material having
the canted spin-orbit to exhibit a non-zero magnetic moment. The
ability of a Weyl semimetal to generate voltages as described above
may depend on the integral of the projection of the Berry curvature
over the Fermi surface being non-zero. One way this may occur is
when electrons in the solid break time-reversal symmetry. The Weyl
nodes act as monopole sources (or sinks) of the Berry curvature.
This Berry curvature acts as an effective magnetic field that
exists in the electrons' momentum-space, introducing an anomalous
velocity to electron motion that is skew to both the Berry
curvature and the electrons' momentum. This skew force is believed
to generate a non-zero thermoelectric power in a direction
orthogonal to both the net Berry curvature integrated over the
whole Fermi surface and the direction of the applied temperature
gradient. This effect has been observed experimentally in the
compound YbMnBi.sub.2, which is a Weyl semimetal that breaks
time-reversal symmetry and is a canted antiferromagnet material
having a net Berry curvature .OMEGA..sub.z along its [110] crystal
axis.
[0061] By aligning the [110] crystal axis of a YbMnBi.sub.2 crystal
with the z-axis as depicted in FIG. 7, the above described effect
may be used to produce transverse thermoelectric devices, namely
Nernst generators and their thermodynamic reciprocal, Ettingshausen
coolers. Unlike classical Nernst generators and Ettingshausen
coolers, thermoelectric devices made with materials having a
non-zero Berry curvature do not require an external magnetic field
H, the role of which is provided by the Berry curvature
.OMEGA..sub.z. An external magnetic field can, however, still be
applied, and its presence can be used to adjust (e.g., reinforce or
counteract) the effect of the Berry curvature in certain
circumstances.
[0062] Transverse thermoelectric devices such as shown in FIG. 7
have several advantages over classical Peltier devices, such as the
thermoelectric modules and generator shown in FIGS. 4 and 5.
Because the electrodes applied to the thermoelectric material can
lie in an isothermal plane of a transverse device, the electrodes
can both be applied at either the hot end or the cold end of the
device. That is, there is no need to return the current from the
hot end to the cold end of the device. Thus, there is no need for a
thermocouple pair, with a p-type material carrying the current from
hot to cold and an n-type material carrying the current back from
cold to hot.
[0063] Transverse thermoelectric devices have several advantages
over conventional, longitudinal thermoelectric devices. For
example, there is no need to simultaneously develop n-type and
p-type thermoelectric materials with similar temperature
dependences in their zT values. One material with one polarity
suffices for the entire device. Another advantage is that there is
no need to connect several thermocouples together electrically in
series and thermally in parallel as must be done in thermoelectric
modules and Peltier devices. Rather, in Nernst generators and
Ettingshausen coolers, the current capacity and the voltage rating
can be increased by simply increasing the physical size of the
thermoelectric material in the device. More advantageously, having
one pair of current contacts and one pair of thermal contacts may
allow the parasitic losses in contact resistances of thermoelectric
modules and Peltier devices to be decreased as compared to Seebeck
effect-based devices using series electrical couplings.
[0064] The temperature difference in classical Peltier devices may
be limited by the following equation:
.DELTA.T.sub.max=1/2.times.(zT.times.T.sub.cold) Eqn. 3
Therefore, when larger temperature drops are required in a Peltier
device, several Peltier elements are typically connected in
cascaded coolers. This increases the complexity of devices aimed at
generating cooling over large temperature gradients, especially in
cryogenic cooling applications. However, these limitations in the
maximum temperature gradient do not hold for Nernst/Ettingshausen
devices. Therefore, Nernst/Ettingshausen devices can operate with
large temperature gradients without cascading series
connections.
[0065] The large transverse Nernst thermopower .alpha..sub.xyz of
Weyl semimetals has been demonstrated experimentally using
YbMnBi.sub.2. The peak in the Nernst thermopower .alpha..sub.xyz of
YbMnBi.sub.2 in the absence of a magnetic field is approximately
1000 .mu.V/K near 50K and 30 .mu.V/K near room temperature. By way
of comparison, commercially available thermoelectric materials have
a Seebeck coefficient .alpha..sub.xxz near 200-300 .mu.V/K at room
temperature. The transverse thermoelectric figure of merit zT may
be calculated using Equation 4 below:
z .times. T x .times. y = ( .alpha. x .times. y .times. z ) 2
.times. .sigma. y .times. y .kappa. xx .times. T Eqn . .times. 4
##EQU00003##
where .alpha..sub.xyz is the Nernst thermopower, .sigma..sub.yy is
the electrical conductivity in the direction parallel to the
measured voltage, and .kappa..sub.xx is the thermal conductivity in
the direction parallel to the applied and measured temperature
gradient.
[0066] For YbMnBi.sub.2, the transverse zT in the absence of a
magnetic field is estimated to be 2.42 at 59.55 K. This value is
greater than that of any other known thermoelectric for this low of
a temperature range, and for a transverse geometry (i.e. Nernst or
Ettingshausen geometry) at any temperature. The performance of this
new thermoelectric material, which is based on new physical
principles, enables the novel approach to solid-state cryogenic
cooling provided by embodiments of the invention, and may be useful
in numerous cooling applications. For example, a number of
detectors including infra-red detectors, focal plane arrays, and
x-ray and gamma-ray detectors, could benefit from Ettingshausen
coolers using thermoelectric elements having a non-zero Berry
curvature.
[0067] FIG. 8 depicts an exemplary thermoelectric device 80 in
accordance with an embodiment of the invention. The thermoelectric
device 80 may include a thermoelectric element 82 comprising a
material having a non-zero Berry curvature, a thermal coupler 84
configured to couple a hot side 86 of the thermoelectric element 82
to a heat source 88, and a thermal coupler 90 configured to couple
a cold side 92 of the thermal element to a heat sink 94. The
thermoelectric element 82 may be configured so that an axis of the
material having the non-zero Berry curvature is generally
orthogonal to the temperature and voltage gradients. Voltage output
sides 96, 98 of thermoelectric element 82 may be electrically
coupled to respective terminals 100, 102 to facilitate connection
of the thermoelectric device 80 to an electrical load 104. The
thermoelectric device 80 may also include one or more magnets 106,
108 configured to provide a magnetic flux 110 to the thermoelectric
element 82. The magnetic flux 110 may enter and exit the
thermoelectric element 82 through the remaining sides 112, 114, and
may be generally aligned with the axis having the non-zero Berry
curvature. The magnetic flux 110 may be used to adjust (e.g.,
reinforce or counteract) the effect of the Berry curvature, thereby
providing a mechanism for controlling the output and/or efficiency
of the thermoelectric device 80.
EXPERIMENTAL RESULTS
[0068] FIG. 9 depicts a test device 120 including a thermoelectric
element 122 comprising YbMnBi.sub.2. The thermoelectric element 122
is affixed to a silicon substrate 124. The thermoelectric element
122 includes an outward facing surface 126 having a rectangular
shape that faces away from the substrate 124, and a downward facing
surface (not shown) generally parallel to and spaced about 0.44 mm
from the outward facing surface 126. The thermoelectric element 122
is oriented so that the [110] crystal axis of the YbMnBi.sub.2 (and
thus the non-zero Berry curvature) is orthogonal (i.e., normal) to
the outward and downward facing surfaces, e.g., projecting outward
from the outward facing surface 126. The rectangular shape of
outward facing surface 126 is defined by a left facing surface 127,
a right facing surface 128 generally parallel to and about 2.58 mm
from the left facing surface 127, a top facing surface 129 that
intersects the left and right facing surfaces 127, 128, and a
bottom facing surface 130 generally parallel to and 1.85 mm from
the top facing surface 129. Each of the surfaces 127-130 is
generally orthogonal to the outward facing and downward facing
surfaces so that the thermoelectric element 122 generally forms a
polyhedron having six sides and dimensions of 0.44 by 1.85 by 2.58
mm.
[0069] The left facing surface 127 of thermoelectric element 122 is
thermally coupled to a resistive heater 136 by a copper foil heat
spreader 138. The heat spreader 138 is configured to provide heat
generated by the resistive heater 136 evenly to the left facing
surface 127 of thermoelectric element 122. The right facing surface
128 of thermoelectric element 122 is coupled to a copper foil heat
sink 140. When the resistive heater 136 is energized, a temperature
gradient forms having a decreasing temperature across the
thermoelectric element 122 from the left facing surface 127 to the
right facing surface 128. A gold-plated copper bracket 142 attached
to (e.g., epoxied to) the heat sink 140 and substrate 124 holds the
test device 120 in place with respect to the substrate 124. A clamp
146 holds the bracket 142 in place relative to a base 144 so that
the substrate 124 is suspended above the base 144. The bracket 142
is in thermal contact with the heat sink 140, and thermally and
electrically isolated from the base 144. Insulated copper leads
148, 150 electrically couple the top and bottom surfaces 129, 130
to respective terminals 152, 154 that facilitate measuring voltages
V and/or currents I generated by or provided to the thermoelectric
element 122.
[0070] FIG. 10 depicts a graph 160 including plots 162-168 of the
Nernst thermopower .alpha..sub.xyz in .mu.V/K verses magnetic field
strength H in Oersteds (Oe). The data used to define plots 162-168
was measured using the test device 120 at sample temperatures of
15.86 K (plot 162), 23.17 K (plot 163), 41.48 K (plot 164), 59.44 K
(plot 165), 75.15 K (plot 166), 118.4 K (plot 167), and 323.1 K
(plot 168). The plots 162-168 illustrate the Nernst Effect in
YbMnBi.sub.2. The magnetic field was applied along an axis
orthogonal to the outward facing surface 126 of thermoelectric
element 122, which is aligned with the [110] crystallographic axis
and is thus the direction of the expected non-zero Berry curvature.
Positive values of H indicate the field is oriented in an outward
facing direction with respect to the outward facing surface 126 as
depicted in FIG. 8. As can be seen from plot 128, the Nernst
thermopower .alpha..sub.xyz has a non-zero value in the absence of
an externally applied magnetic field that is significantly larger
than that produced by conventional thermoelectric materials.
[0071] FIG. 11 depicts a scatter plot 180 including data points 182
illustrating the Nernst thermopower .alpha..sub.xyz in .mu.V/K
verses the temperature of the thermoelectric element 122 in kelvin
for a transverse geometry (i.e., produced by the Nernst effect),
and data points 184 illustrating the Seebeck coefficient
.alpha..sub.xxz .mu.V/K verses the temperature of the
thermoelectric element 122 in kelvin for a longitudinal geometry
(i.e., produced by the Seebeck effect) in the absence of an
externally applied magnetic field. The data points 182, 184 were
extracted from data taken without an externally applied magnetic
field. In the absence of a Berry curvature, the Nernst thermopower
.alpha..sub.xyz indicated by data points 182 would be expected to
be 0 .mu.V/K at all temperatures. Thus, the non-zero values shown
for the Nernst thermopower .alpha..sub.xyz indicate the presence of
a Berry curvature and confirm the effect of the Berry curvature on
the Nernst thermopower .alpha..sub.xyz, which is significantly
larger than would be expected for conventional thermoelectric
materials configured in a transverse geometry. The disparity
between the coefficients .alpha..sub.xyz and .alpha..sub.xxy
produced by the Nernst and Seebeck effects support the conclusion
that a non-zero Berry curvature produces the Nernst effect even in
the absence of an externally applied magnetic field.
[0072] The conventional thermoelectric figure of merit, zT, may be
calculated using Equation 5 below:
z .times. T = .alpha. xx 2 .times. .sigma. xx .kappa. xx .times. T
= .alpha. xx 2 .kappa. xx .times. .rho. xx Eqn . .times. 5
##EQU00004##
where .rho..sub.xx is the resistivity of the thermoelectric
material. The maximum value of zT known by the Applicant to have
been measured in a laboratory is 2.2 at 915 K. The transverse
figure of merit zT may be calculated using Equation 6:
z .times. T x .times. y = .alpha. xy 2 .times. .sigma. y .times. y
.kappa. xx .times. T = .alpha. xy 2 .kappa. xx .times. .rho. y
.times. y = .alpha. xy 2 .kappa. xx .times. .rho. xx Eqn . .times.
6 ##EQU00005##
[0073] FIG. 12 depicts a scatter plot 190 including data points
192-194 showing figures of merit zT for different thermoelectric
materials in the absence of an external magnetic field. Data points
192 illustrate the transverse figure of merit zT verses temperature
in kelvin for YbMnBi.sub.2 in a Nernst/Ettingshausen configuration.
Data points 193 illustrate the longitudinal figure of merit zT
verses temperature in kelvin for PbTe doped with 2 mol % Na and
nanostructured with 4 mol % SrTe. Data points 194 illustrate the
longitudinal figure of merit zT verses temperature in kelvin for
commercially available Bi.sub.2Te.sub.3.
[0074] The depicted properties of YbMnBi.sub.2 provide experimental
support for the improved performance of thermoelectric devices in
accordance with embodiments of the invention. Use of materials
having a non-zero Berry curvature, such as YbMnBi.sub.2, in
fabricating thermoelectric devices allows a simpler transverse
geometry that operates without an externally applied magnetic
field. Moreover, the peak zT of YbMnBi.sub.2 occurs in a
temperature range appropriate for cooling (e.g., zT=2.42 at
59.55K). Thus, thermoelectric devices using materials such as
YbMnBi.sub.2 may be suitable for use in both power recovery
applications and for heat pumps that cryogenically cool electronic
devices.
[0075] The terminology used herein is for the purpose of describing
particular embodiments only and is not intended to be limiting of
the embodiments of the invention. As used herein, the singular
forms "a", "an" and "the" are intended to include the plural forms
as well, unless the context clearly indicates otherwise. It will be
further understood that the terms "comprises" and/or "comprising,"
when used in this specification, specify the presence of stated
features, integers, actions, steps, operations, elements, and/or
components, but do not preclude the presence or addition of one or
more other features, integers, actions, steps, operations,
elements, components, and/or groups thereof. Furthermore, to the
extent that the terms "includes", "having", "has", "with",
"comprised of", or variants thereof are used in either the detailed
description or the claims, such terms are intended to be inclusive
in a manner similar to the term "comprising".
[0076] While all the invention has been illustrated by a
description of various embodiments, and while these embodiments
have been described in considerable detail, it is not the intention
of the Applicant to restrict or in any way limit the scope of the
appended claims to such detail. Additional advantages and
modifications will readily appear to those skilled in the art. The
invention in its broader aspects is therefore not limited to the
specific details, representative apparatus and method, and
illustrative examples shown and described. Accordingly, departures
may be made from such details without departing from the spirit or
scope of the Applicant's general inventive concept.
* * * * *