JP2022041249A - Thermoelectric element and thermoelectric device - Google Patents

Abstract

To provide a thermoelectric element and a thermoelectric device which utilize the Ettingshausen effect and have high energy efficiency.SOLUTION: A thermoelectric element 104 comprises a metalloid or a semiconductor having a bandgap of less than or equal to 0.5 eV. In the thermoelectric element, when a current I flows in one direction and a magnetic field H is applied in a direction orthogonal to the current I, temperature gradient (Tc→Th) is generated in a direction orthogonal to both the current I and the magnetic field H. A thermoelectric device includes a plurality of thermoelectric elements 104 each having a shape extending in one direction, the plurality of thermoelectric elements 104 being disposed on a substrate 102 so that the longitudinal directions of the plurality of thermoelectric elements are parallel to each other.SELECTED DRAWING: Figure 4B

Description

The present invention relates to a thermoelectric element and a thermoelectric device including the thermoelectric element.

A heat pump is a device that transports heat from low temperature to high temperature. Until now, heat pumps that use a heat medium have been predominant, and exchange heat and transfer heat by heat of vaporization and heat of condensation. In recent years, CFC substitutes that do not destroy the ozone layer have been used as heat media. However, since CFC substitutes have a much higher greenhouse effect than CO ₂ , the Kigali Amendment enacted in 2016 requires a significant reduction in the amount of CFC substitutes used. Therefore, there is an urgent need to develop a heat pump with a new mechanism that replaces the current mechanism that uses CFC substitutes as a heat medium.

Research on the use of the thermoelectric effect in heat pumps has been ongoing since the 1950s. For example, Non-Patent Document 1 proposes a cooling device using the Peltier effect, which is the reverse process of the Seebeck effect, as the thermoelectric effect. Further, as another thermoelectric effect, a cooling device using the Ettingshausen Effect, which is the reverse process of the Nernst effect, has also been proposed (see, for example, Non-Patent Document 2 and Non-Patent Document 3). ).

T. Metzger, R.P. Huebener, “Modeling and cooling behavior of Peltier cascades,” Cryogenics, Volume 39, 1999, Pages 235-239. B. J. O'Brien and C. S. Wallace, “Ettingshausen Effect and Thermomagnetic Cooling,” Journal of Applied Physics 29, 1958, Pages 1010-1012. R. T. Delves. “The prospects for Ettingshausen and Peltier cooling at low temperatures,” British Journal of Applied Physics, Volume 13, 1962, Pages 440-445.

However, heat pumps using the thermoelectric effect have hardly been put into practical use. In particular, in the Pelche effect, since the heat transport direction and the current are in the same direction, a three-dimensional and complicated structure in which p-type semiconductors and n-type semiconductors are alternately provided (see FIG. 3) is formed, and a large number of PN junctions are formed. I need. As a result, the current cooling device using the Perche effect has a low coefficient of performance (COP) of about 0.5, which is an energy efficiency index.

The present invention has been made in view of the above problems, and an object of the present invention is to provide an energy-efficient thermoelectric element and a thermoelectric device using the Ettingshausen effect.

The thermoelectric element according to the embodiment of the present invention is made of a semi-metal or a semiconductor having a band gap of 0.5 eV or less, and when a current is passed in one direction and a magnetic field is applied in a direction orthogonal to the current, both the current and the magnetic field are applied. A temperature gradient is generated in the direction orthogonal to.

The thermoelectric device according to the embodiment of the present invention includes a plurality of thermoelectric elements each having a shape extending in one direction. The plurality of thermoelectric elements are arranged so that their longitudinal directions are parallel to each other, and are made of a semi-metal or a semiconductor having a band gap of 0.5 eV or less. When a magnetic field is applied to, a temperature gradient is generated in the direction orthogonal to both the current and the magnetic field.

According to the present invention, a thermoelectric element made of a semimetal or a semiconductor having a bandgap of 0.5 eV or less exhibits an Ettingshausen effect, so that energy efficiency can be improved.

It is a schematic diagram for demonstrating the Nernst effect. It is a schematic diagram for demonstrating the Zeebeck effect. It is sectional drawing which shows the schematic structure of the conventional heat pump using the Pelche effect. It is a perspective view of the thermoelectric device which concerns on 1st Embodiment. It is a perspective view which shows the arrangement of the plurality of thermoelectric elements constituting the thermoelectric device shown in FIG. 4A. It is a top view which shows the arrangement of the plurality of thermoelectric elements constituting the thermoelectric device shown in FIG. 4A. 6 is a graph showing the current dependence of the amount of heat absorbed for each temperature difference in the thermoelectric device according to the first embodiment including the thermoelectric element composed of Cd ₃ As ₂ . 6 is a graph showing the current dependence of COP for each temperature difference in the thermoelectric device according to the first embodiment including the thermoelectric element composed of Cd ₃ As ₂ . It is a schematic diagram which shows the structure of the thermoelectric device which concerns on 2nd Embodiment. It is a schematic diagram explaining the arrangement of each thermoelectric element and a permanent magnet about the thermoelectric device which concerns on the modification of 2nd Embodiment. It is a schematic diagram which shows the structure of the thermoelectric device which concerns on 3rd Embodiment. It is a schematic diagram which shows the shape of the thermoelectric element which concerns on the modification of 3rd Embodiment. 6 is a graph showing the relationship between (width of heat dissipation surface) / (width of cooling surface) and maximum temperature difference for the thermoelectric element shown in FIG. 10. It is a graph showing the relationship between the dimensionless figure of merit and the Carnot efficiency for each conventional Pelche element and each thermoelectric element according to each embodiment (new technology).

Hereinafter, exemplary embodiments of the present invention will be described with reference to the accompanying drawings.
In the drawings, the same or similar components are designated by the same reference numerals. The drawings are schematic, and the relationship between the plane dimensions and the thickness and the ratio of the thickness of each member are different from the actual ones. In addition, it goes without saying that parts having different dimensional relationships and ratios are included between the drawings.

First, the Nernst effect and the Seebeck effect will be described with reference to FIGS. 1 and 2, respectively.

The Nernst effect is a phenomenon in which when a heat flow flows through a thermoelectric element, an electromotive force is generated in a direction perpendicular to both the heat flow and the magnetization of the thermoelectric element. For example, as shown in FIG. 1, when a heat flow (∝ temperature difference ΔT) flows in the thickness direction in a rectangular thermoelectric element (depth l, width w, thickness t), the carrier is subjected to magnetization M in the width direction of the thermoelectric element. The direction of movement is bent, and an electromotive force V is generated in a direction perpendicular to both the magnetization M and the heat flow. Assuming that the Nernst coefficient of the thermoelectric element is _SN , the electromotive force V is _SN ΔT (l / t). As described above, the electromotive force V generated by the Nernst effect is proportional to the shape factor l / t of the thermoelectric element.

On the other hand, the Zeebeck effect is a phenomenon in which when a heat flow flows through a thermoelectric element, carriers move along the heat flow and an electromotive force is generated in the heat flow direction. For example, as shown in FIG. 2, when a heat flow (∝ temperature difference ΔT) flows in the thickness direction in a rectangular parallelepiped thermoelectric element (depth l, width w, thickness t), an electromotive force V is generated in parallel with the heat flow. Assuming that the Seebeck coefficient of the thermoelectric element is S, the electromotive force V is SΔT.

Next, the mechanism of a conventional heat pump (hereinafter referred to as a Pelche cooling device) using the Pelche effect, which is the reverse process of the Zeebeck effect, will be described.

FIG. 3 shows a schematic configuration of the conventional Pelche cooling device 1. In the Pelche cooling device 1, rod-shaped p-type semiconductors 5p and n-type semiconductors 5n are alternately connected between two insulating substrates 3a and 3b, and the adjacent p-type semiconductors 5p and n-type semiconductors 5n are It is joined by a metal electrode 7. As shown in FIG. 3, when a DC voltage V is applied, a current I flows in the −z direction in the n-type semiconductor 5n and in the + z direction in the p-type semiconductor 5p, heat moves in the + z direction, and heat is absorbed by the electrode on the substrate 3a side. , Dissipation occurs at the electrode on the substrate 3b side. In this way, heat is transported from the endothermic side (cold) to the heat dissipation side (hot).

Let Th be the heat dissipation side temperature, T _c be the endothermic side temperature, R be the resistance of a pair of adjacent p-type and n-type semiconductors (hereinafter referred to as _Pelche elements), K be the thermal conductance, and S be the Zeebeck coefficient. The heat dissipation amount Q _h on the high temperature side and the endothermic amount Q _c on the low temperature side of the Pelche element are expressed as equations (1) and (2), respectively.

The first, second, and third terms on the right-hand side of equations (1) and (2) represent the Perche effect, Joule heat, and heat conduction (heat inflow from high temperature), respectively.

The width in the x direction of each of the p-type and n-type semiconductors constituting the Pelche element is w, the depth in the y direction is l, the thickness (height) in the z direction is t, the electrical resistivity of the Pelche element is ρ, and the heat. Assuming that the conductivity is κ, the resistivity R and the thermal conductance K of the Pelche element are expressed by the equation (3).

For example, it is assumed that each Pelche element is composed of Bi ₂ Te ₃ , and 40 mm × 40 mm each is composed of 120 sets of Pelche elements (that is, 120 sets of p-type and n-type semiconductors) having a size of 1 mm × 1 mm × 1 mm. Prepare a module with a size of × 4 mm. Assuming that the electrical resistivity ρ of ^each Pelche element is about 103 μΩcm, the thermal conductivity κ is about 2 W / Km, and the Seebeck coefficient S is about 200 μV / K, the resistance R _tot , thermal conductance Κ _tot , and Seebeck of the entire module The coefficients Shot are about _3Ω , about 0.5W / K, and about 0.05V / K, respectively.

The total amount of heat absorbed by the entire module is expressed as Q _{c_tot} . Assuming that a current I of 1 A is passed through the module and the generated temperature difference ΔT (= Th _{−T c} ) is 2 ° C., the first term (Perche effect) of the equation (2) is about in the total heat absorption Q _{c_tot} . 14W, the second term (Joule heat) is about 1.5W, and the third term (heat conduction) is about 1W.

The COP _max , which is the maximum value of the COP of the entire module composed of the above-mentioned Pelche element, is about 4 as shown in the equation (4).

As described above, it can be seen that the Pelche cooling device 1 needs to be provided with a large number of PN junctions, so that the COP is low and the element performance is deteriorated. Further, it can be seen that as the current I or the temperature difference ΔT (= Th _h −T _c ) increases, the COP decreases significantly. As described above, the current Pelche cooling device has a COP of about 0.5.

Next, with reference to FIGS. 4A to 12, the first, second and third embodiments of the present invention using the Ettingshausen effect, which is the reverse process of the Nernst effect, will be described.

<First Embodiment>
First, the first embodiment of the present invention will be described with reference to FIGS. 4A to 6. 4A to 4C show a schematic configuration of the thermoelectric device 100 according to the first embodiment.

The thermoelectric device 100 is a heat pump using the Ettingshausen effect, and includes a plurality of rectangular parallelepiped thermoelectric elements 104 extending in one direction (y direction). As shown in FIGS. 4A to 4C, the plurality of thermoelectric elements 104 are arranged in parallel on the substrate 102 in a direction perpendicular to the longitudinal direction (x direction) so that their respective longitudinal directions (y direction) are parallel. Have been placed.

As shown in FIG. 4C, the + y side of the thermoelectric element 104 of interest is connected to the −y side of the thermoelectric element 104 adjacent to the + x side by a copper wiring 106, and the −y side of the thermoelectric element 104 of interest is −. It is connected to the + y side of the thermoelectric element 104 adjacent to the x side by the copper wiring 106. In this way, the plurality of thermoelectric elements 104 are electrically connected in series so that the current I flows in the same direction (for example, the + y direction).

The thermoelectric element 104 is made of a semimetal or a semiconductor having a band gap of 0.5 eV or less, and has higher mobility (inversely proportional to the electrical resistivity ρ) and higher thermal conductivity κ than the conventional Pelche element at the operating temperature. It consists of a small material. Examples of the gapless semimetal include Cd ₃ As ₂ which is a Dirac semimetal, Ag ₂ Se, and Ag ₂ Te. Examples of the semiconductor material include InSb, Bi _0.5 Sb _1.5 Te ₃ , AgCuSe, simple substance Te, Ag ₈ SiSe ₆ , or Ag ₈ SnSe ₆ .

In addition, the Mn ₃ Sn-based, Full-Whisler-based Co ₂ Mn Ga, and Fe ₃ Ga-based thermoelectric materials in which the inventors of the present application have observed the anomalous Nernst effect are also expected as material candidates for heat pumps using the Ettingshausen effect. can do.

The anomalous Nernst effect of Mn ₃ Sn thermoelectric materials is disclosed in Japanese Patent No. 6611167 and the following papers.
Muhammad Ikhlas, Takahiro Tomita, Takashi Koretsune, Michi-To Suzuki, Daisuke Nishio-Hamane, Ryotaro Arita, Yoshichika Otani and Satoru Nakatsuji, “Large anomalous Nernst effect at room temperature in a chiral antiferromagnet.” Nature Physics volume 13, pages 1085- 1090 (2017).
The anomalous Nernst effects of full-Whisler-based Co ₂ Mn Ga and Fe ₃ Ga-based thermoelectric materials are disclosed in International Publication No. 2019/009308 and PCT / JP2020 / 018010, respectively.

As shown in FIG. 4A, a plurality of heat sinks 110 (heat sinks) made of a metal material having high thermal conductivity such as aluminum, iron, or copper are provided on the heat radiation side of the plurality of thermoelectric elements 104. Dissipate heat from the thermoelectric element 104. Although only a part of the heat sink 110 is shown in FIG. 4A, the actual heat sink 110 is provided so as to cover the entire plurality of thermoelectric elements 104. In order to improve the heat dissipation efficiency of the heat radiating plate 110, a shape having a large surface area is adopted. For example, in addition to the structure having a plurality of protrusions as shown in FIG. 4A, there is a bellows-shaped structure.

When a current I is passed through the plurality of thermoelectric elements 104 in the + y direction along their respective longitudinal directions and a magnetic field H is applied in the + x direction orthogonal to the current I, each thermoelectric element 104 is magnetized in the + x direction and the current is applied. A temperature gradient is generated in the z direction orthogonal to both I and the magnetic field H, and heat is transported from the heat absorbing side (cold) to the heat dissipation side (hot) (in the + z direction).

As shown in FIG. 4B, each thermoelectric element 104 has a width of w in the x direction, a length of l in the y direction, and a thickness of t in the z direction. Assuming that the heat dissipation side temperature of each thermoelectric element 104 is _Th , the heat absorption side temperature is T _c , the resistance is R, the thermal conductance is K, and the Nernst coefficient is _SN , the heat dissipation amount Q _h and the heat absorption amount Q of each thermoelectric element 104. _c is expressed as the formula (5) and the formula (6), respectively.

The first, second, and third terms on the right side of equations (5) and (6) represent the Ettingshausen effect, Joule heat, and heat conduction (heat inflow from high temperature), respectively. The first term representing the Ettingshausen effect is proportional to the shape factor l / t of each thermoelectric element 104.

The resistance R and the thermal conductance K of each thermoelectric element 104 are expressed by the equation (7).

As shown in FIG. 4C, a plurality of thermoelectric elements 104 having a thickness of t = 0.5 mm, a width of w = 0.5 mm, and a length of l = 40 mm are placed in a 40 mm × 40 mm region of a substrate 102 having a size of 50 mm × 50 mm. Prepare samples arranged in parallel. Here, it is assumed that 20 thermoelectric elements 104 are arranged so that the total length l of the plurality of thermoelectric elements 104 is 0.8 m.

The total amount of heat absorbed by the entire sample is expressed as Q _{c_tot} . The electrical resistivity ρ of each thermoelectric element 104 is 100 μΩcm, the thermal conductivity κ is 15 W / Km, and the Nernst coefficient _SN is 200 μV / K. Assuming that the temperature difference ΔT (= _Th −T _c ) generated when a magnetic field _H of 0.5 T is applied to the sample and a current I of 1 A is passed is 2 ° C. The first term (Ettingshausen effect) of 6) is about 96 W, the second term (Joule heat) is about 1.5 W, and the third term (heat conduction) is about 24 W. When the resistance of the entire sample is expressed as R _tot , the COP of the entire sample takes a large value of about 15 as shown in the equation (8).

_FIG . 5 shows the current dependence of the heat absorption amount Qc when a magnetic field of 0.5 T is applied to a sample of the above size (FIG. 4C) in which each thermoelectric element 104 is made of Cd ₃ As ₂ for each temperature difference ΔT. .. As shown in FIG. 5, for the same current I, the smaller the temperature difference ΔT, the larger the heat absorption amount Q _c , while the larger the temperature difference ΔT, the smaller the heat absorption amount Q _c , and heat transport from low temperature to high temperature. Turns out to be difficult. Further, it can be seen that even with the same temperature difference ΔT, the heat absorption amount Q _c takes the maximum value when the current I is 10 A. This sample can have a maximum temperature difference of about 70 ° C.

For this sample, FIG. 6 shows the current dependence of COP for each temperature difference ΔT. As shown in FIG. 6, it can be seen that the smaller the temperature difference ΔT, the higher the COP, and when ΔT = 1K, the COP exceeds 30.

As described above, according to the thermoelectric device 100 using the Ettingshausen effect, the cooling performance of the thermoelectric device 100 can be controlled by the shape factor l / t of the thermoelectric element 104. This makes it possible to realize high conversion efficiency that could not be realized by the conventional Pelche element.

<Second Embodiment>
Next, a second embodiment of the present invention will be described with reference to FIGS. 7 and 8.

In the first embodiment, the plurality of thermoelectric elements 104 arranged so that their longitudinal directions are parallel to each other are electrically connected in series so that a current I in the same direction flows, but they are adjacent thermoelectric elements. A circuit configuration may be adopted in which currents flowing in opposite directions to each other flow.

FIG. 7 shows a schematic configuration of the thermoelectric device 200A according to the second embodiment. As shown in FIG. 7, the thermoelectric device 200A includes a plurality of first thermoelectric elements 204a and a plurality of second thermoelectric elements 204b having a rectangular shape and the same size, and the respective longitudinal directions (y directions) are parallel to each other. The first thermoelectric element 204a and the second thermoelectric element 204b are alternately arranged. The first thermoelectric element 204a and the second thermoelectric element 204b are made of the same material as the thermoelectric element 104 according to the first embodiment.

Although not shown in FIG. 7, the thermoelectric device 200A also absorbs heat from the plurality of first thermoelectric elements 204a and the plurality of second thermoelectric elements 204b, similarly to the thermoelectric device 100 (FIG. 4A) according to the first embodiment. A substrate is provided on the cold side, and a heat sink is provided on the heat dissipation side (hot). The same applies to the thermoelectric device 200B (FIG. 8) described later.

As shown in FIG. 7, the + y side of the first thermoelectric element 204a of interest is connected to the + y side of the second thermoelectric element 204b adjacent to the + x side by a copper wiring 206, and-of the first thermoelectric element 204a of interest. The y side is connected to the −y side of the second thermoelectric element 204b adjacent to the −x side by the copper wiring 206. In this way, the plurality of thermoelectric elements are electrically connected in series so that the currents I flow in opposite directions to the adjacent thermoelectric elements due to the structure in which the + y side is connected to each other and the −y side is connected to each other alternately. It is connected to the. FIG. 7 shows an example in which a current I in the + y direction flows through the first thermoelectric element 204a and a current I in the −y direction flows through the second thermoelectric element 204b.

Since the current I flows in the opposite directions to the first thermoelectric element 204a and the second thermoelectric element 204b, in order to generate a temperature gradient in the same direction (+ z direction or −z direction) due to the Ettingshausen effect, these It is necessary to apply magnetic currents in opposite directions to the thermoelectric element. For example, as shown in FIG. 7, assuming that the direction from the heat absorbing side (cold) to the heat radiating side (hot) is the + z direction, a magnetic field H1 in the + x direction is applied to the first thermoelectric element 204a by a permanent magnet. By applying a magnetic field H2 in the −x direction to the second thermoelectric element 204b with a permanent magnet, the first thermoelectric element 204a is magnetized in the + x direction and the second thermoelectric element 204b is magnetized in the −x direction. That is, alternating magnetic fields in opposite directions are applied to adjacent thermoelectric elements.

As described above, since the plurality of first thermoelectric elements 204a and the plurality of second thermoelectric elements 204b constituting the thermoelectric device 200A are in the same plane, it is necessary to apply the alternating magnetic fields H1 and H2 in the same plane. However, it is structurally not easy to apply an alternating magnetic field in the opposite direction to adjacent thermoelectric elements in the same plane. Therefore, if the first thermoelectric element and the second thermoelectric element are arranged in separate planes, a magnetic field in the same direction can be applied in the same plane.

Specifically, as in the thermoelectric device 200B shown in FIG. 8, a plurality of first thermoelectric elements 224a and a plurality of second thermoelectric elements 224b having a rectangular shape and the same size are provided, and the plurality of first thermoelectric elements 224a are provided. Arranged in odd-numbered stages in the + z direction (1st stage, 3rd stage, ...) and odd-numbered rows in the + x direction (1st row, 3rd row, ...), and a plurality of second thermoelectric elements 224b are even numbers in the + z direction. It may be arranged in the columns (second column, fourth column, ...) And even columns in the + x direction (second column, fourth column, ...). That is, the first thermoelectric element 224a and the second thermoelectric element 224b have different positions in the first direction (z direction) perpendicular to the longitudinal direction (y direction), and are perpendicular to both the longitudinal direction and the first direction. The positions in the two directions (x direction) are also arranged so as to be different from each other. The first thermoelectric element 224a and the second thermoelectric element 224b are also made of the same material as the thermoelectric element 104 according to the first embodiment.

Currents flowing in opposite directions along the longitudinal direction flow through the first thermoelectric element 224a and the second thermoelectric element 224b. For example, the current I flows in the + y direction in the first thermoelectric element 224a, and the current I flows in the −y direction in the second thermoelectric element 224b.

In order to generate a temperature gradient in the same direction (+ z direction or −z direction) by the Ettingshausen effect, it is necessary to apply magnetic fields in opposite directions to the first thermoelectric element 224a and the second thermoelectric element 224b. For example, as shown in FIG. 8, a permanent magnet 226 having a magnetization of + x direction is arranged between two first thermoelectric elements 224a adjacent to each other in the x direction, and two second thermoelectric elements 224b adjacent to each other in the x direction. A permanent magnet 226 whose magnetization is in the −x direction may be placed between them. By arranging the permanent magnets 226 in this way, an alternating magnetic field is applied. As a result, the first thermoelectric element 224a is magnetized in the + x direction, and the second thermoelectric element 224b is magnetized in the −x direction.

Each permanent magnet 226 is made of a material having a larger coercive force than the first thermoelectric element 224a and the second thermoelectric element 224b. Further, in order to make the thermal conductivity in the direction in which the temperature gradient occurs (z direction) uniform, it is preferable that each permanent magnet 226 is made of a material having the same thermal conductivity as the first thermoelectric element 224a and the second thermoelectric element 224b. ..

As described above, by arranging the permanent magnets 226 so that the directions of the magnetic fields are aligned in the same plane, the magnetization in the same plane is stabilized.

<Third Embodiment>
Next, a third embodiment of the present invention will be described with reference to FIGS. 9 to 11.

In Non-Patent Document 1, the cooling performance is enhanced by stacking plate-shaped blocks made of Pelche elements in the direction in which the temperature gradient is generated and forming the blocks on the heat dissipation side in a stepped shape wider than the blocks on the endothermic side. It is disclosed that it will be done. However, as described above, in the Pelche effect, the loss due to a large number of PN junctions is extremely high, which causes a decrease in device performance. Therefore, as in Non-Patent Document 1, when a plurality of blocks are multiple-connected, there is a problem that the loss due to the PN junction becomes larger.

On the other hand, since the Ettingshausen effect does not require a PN junction, it is considered that the element performance can be sufficiently exhibited even if plate-shaped thermoelectric elements are stacked as described above. Therefore, in the third embodiment, a structure in which a plurality of thermoelectric elements exhibiting the Ettingshausen effect are stacked and a structure equivalent thereto will be described.

As shown in FIG. 9, the thermoelectric device 300A according to the third embodiment has a plurality of plate-shaped thermoelectric elements 310_1, 310_2, ..., 310_N (N is 2 or more) stacked in a direction (x direction) in which a temperature gradient is generated. The thermoelectric element is made of the same material as the thermoelectric element 104 according to the first embodiment. The number of thermoelectric elements constituting the thermoelectric device 300A is not particularly limited.

The plurality of thermoelectric elements 310_1, 310_2, ..., 310_N all have the same thickness Δx in the direction in which the temperature gradient occurs (x direction) and the length l in the direction in which the current I flows (z direction; longitudinal direction). The widths in the direction (y direction) in which the magnetic field H is applied are different from each other. Specifically, the thermoelectric element on the heat dissipation side (hot) is wider than the thermoelectric element on the endothermic side (cold), and the cross section in the xy plane has a symmetrical staircase shape.

When a current I is passed in the + z direction along the longitudinal direction of each thermoelectric element constituting the thermoelectric device 300A and a magnetic field H is applied in the + y direction orthogonal to the current I, each thermoelectric element is magnetized in the + y direction. A temperature gradient is generated in the x direction orthogonal to both the current I and the magnetic field H, and heat is transported from the heat absorbing side (cold) to the heat dissipation side (hot) (in the + x direction).

The endothermic side position x of the m-th thermoelectric element 310_m (m = 1, 2, ..., N) is (m-1) Δx. Let y (x) be the width of the thermoelectric element at this position x in the y direction. Assuming that the electrical resistivity, thermal conductivity, and Nernst coefficient of each thermoelectric element are ρ, κ, and _SN , respectively, the heat absorption amount Q ^cm (x) and the heat dissipation amount Q _h ^m of the mth thermoelectric element _{310_m} . (X + Δx) is expressed as Eq. (9) and Eq. (10), respectively.

In equations (9) and (10), i is the current density and is defined as i = I / y (x) Δx. T ^m (x) and T ^m (x + Δx) are the temperature on the endothermic side (x) and the temperature on the heat dissipation side (x + Δx) of the m-th thermoelectric element 310_m, respectively. t ^m (x) represents the temperature gradient in the m-th thermoelectric element 310_m, and is defined as in the equation (11).

As shown in FIG. 10, in the structure in which a large number of thermoelectric elements having a small thickness Δx are stacked, the direction in which the magnetic field H is applied from the endothermic side (cold) to the heat dissipation side (hot) of one thermoelectric element 300B. It is equivalent to the structure that widens the width in.

In Non-Patent Document 2, for a thermoelectric element exhibiting the Ettingshausen effect, the optimum shape that brings about the maximum temperature difference is a shape in which the width increases exponentially from the endothermic side (cold) to the heat dissipation side (hot). It is shown to be. Therefore, it is considered that the thermoelectric element 300B may have such a shape. The thermoelectric element 300B is also made of the same material as the thermoelectric element 104 according to the first embodiment.

Here, the thickness of the thermoelectric element 300B is X, the width of the cooling surface 320 at x = 0 is y _c , and the width of the heat dissipation surface 330 at x = X is y _h (y _c <y _h ). In order to obtain the thermoelectric element 300B having the optimum shape, the width y (x) of the thermoelectric element 300B at the position x in the direction in which the temperature gradient is generated may be defined as in the equation (12).

FIG. 11 shows the maximum temperature difference ΔT _max obtained when the value of y _h / y _c of the thermoelectric element 300B is changed. Here, the Nernst coefficient _SN of the thermoelectric element 300B was 200 μV / K, the electrical resistivity ρ was 100 μΩcm, the thermal conductivity κ was 15 W / Km, and the heat dissipation side temperature _Th was fixed at 300 K. As shown in FIG. 11, it can be seen that the maximum temperature difference ΔT _max increases as y _h / y _c increases. In this way, by adopting a shape in which the width y (x) increases exponentially from the endothermic side to the heat dissipation side as in equation (12) for materials with the same performance, a larger temperature difference can be obtained. It can be realized.

As described above, each thermoelectric element according to the first to third embodiments has a simpler element structure than the Pelche element and has a degree of freedom in shape. In particular, by adopting the shape as shown in FIG. 10, the cooling performance can be further improved.

Next, the relationship between the dimensionless figure of merit and Carnot efficiency will be described. The dimensionless figure of merit of the conventional Pelche element (FIG. 3) is ZT (= S ² T / _ρκ ), and the dimensionless figure of merit of each thermoelectric element (new technology) shown in the first to third embodiments is ZNT. (= S _N ² T / ρκ), and FIG. 12 shows the relationship between the dimensionless figure of merit ZT and _ZNT and the Carnot efficiency. From FIG. 12, it can be seen that the rate of increase in Carnot efficiency with respect to _ZNT is greater than the rate of increase with respect to ZT. Specifically, the conventional Pelche element shows the highest performance at ZT = ∞, and the thermoelectric element according to each embodiment shows the highest performance at _ZNT = 1. Here, the Carnot efficiency at _ZNT = 1 is a value determined when the high temperature is 800 K and the low temperature is 300 K.

As described above, each thermoelectric element exhibiting the Ettingshausen effect according to the first to third embodiments has much better Carnot efficiency than the Pelche element.

100, 200A, 200B, 300A Thermoelectric device 102 Board 104, 300B Thermoelectric element 106, 206 Copper wiring 110 Heat dissipation plate 204a, 224a First thermoelectric element 204b, 224b Second thermoelectric element 226 Permanent magnet 320 Cooling surface 330 Heat dissipation surface

Claims (10)

It consists of a metalloid or a semiconductor with a bandgap of 0.5 eV or less.
A thermoelectric element in which when a current is passed in one direction and a magnetic field is applied in a direction orthogonal to the current, a temperature gradient is generated in a direction orthogonal to both the current and the magnetic field. The thermoelectric element according to claim 1, which has a shape extending in one direction. The thermoelectric element according to claim 1 or 2, wherein the thermoelectric element has a shape in which the width increases in the direction in which the magnetic field is applied from the endothermic side to the heat dissipation side. The thermoelectric element according to claim 3, wherein the width in the direction in which the magnetic field is applied changes exponentially with respect to the direction in which the temperature gradient is generated. The metalloid or semiconductor is Cd ₃ As ₂ , Ag ₂ Se, Ag ₂ Te, InSb, Bi _0.5 Sb _1.5 Te ₃ , AgCuSe, Te, Ag ₈ SiSe ₆ , or Ag ₈ SnSe ₆ . , The thermoelectric element according to any one of claims 1 to 4. A thermoelectric device including a plurality of thermoelectric elements, each of which has a shape extending in one direction.
The plurality of thermoelectric elements are
Arranged so that their longitudinal directions are parallel,
It is made of the same material as the thermoelectric element according to any one of claims 1 to 5.
A thermoelectric device in which when a current is passed along each of the longitudinal directions and a magnetic field is applied in a direction orthogonal to the current, a temperature gradient is generated in a direction orthogonal to both the current and the magnetic field. The thermoelectric device according to claim 6, wherein the plurality of thermoelectric elements are electrically connected in series so that the current flows in the same direction, and the magnetic field is applied in the same direction orthogonal to the current. The plurality of thermoelectric elements are electrically connected in series so that the currents flowing in opposite directions to the adjacent thermoelectric elements flow.
The thermoelectric device according to claim 6, wherein an alternating magnetic field orthogonal to the current is applied to the adjacent thermoelectric elements. The plurality of thermoelectric elements include a first thermoelectric element and a second thermoelectric element.
The first thermoelectric element and the second thermoelectric element are
The positions in the first direction perpendicular to the longitudinal direction are different from each other, and the positions in the second direction perpendicular to both the longitudinal direction and the first direction are different from each other.
When the currents in opposite directions are passed along the longitudinal direction to the first thermoelectric element and the second thermoelectric element, and alternating magnetic fields in opposite directions are applied along the first direction. The thermoelectric device according to claim 6, wherein a temperature gradient is generated in each of the first thermoelectric element and the second thermoelectric element along the second direction. The plurality of thermoelectric elements have a plate shape and are stacked in the direction in which the temperature gradient is generated.
The thermoelectric device according to claim 6, wherein the thermoelectric element on the heat dissipation side has a wider width in the direction in which the magnetic field is applied than the thermoelectric element on the endothermic side.

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