Thermoelectric element and thermoelectric device

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

Technical Field

[0001] The present invention relates to a thermoelectric element and a thermoelectric device including the thermoelectric element.

Background Art

[0002] A heat pump is a device that transports heat from a low temperature to a high temperature. Conventionally, heat pumps that use a heat medium have been dominant, and heat exchange and heat transport are performed using the latent heat of vaporization and condensation heat. In recent years, alternative refrigerants that do not deplete the ozone layer have been used as heat media. However, since alternative refrigerants have a much higher greenhouse effect than CO2, the Kigali Amendment enacted in 2016 requires a significant reduction in the amount of alternative refrigerants used. Therefore, it is urgent to develop a new heat pump mechanism to replace the current mechanism using alternative refrigerants as heat media.

[0003] Research on using the thermoelectric effect in heat pumps has been ongoing since the 1950s. For example, in Non-Patent Document 1, a cooling device using the Peltier effect, which is the reverse process of the Seebeck effect as a thermoelectric effect, has been proposed. Also, as another thermoelectric effect, a cooling device using the Ettingshausen Effect, which is the reverse process of the Nernst effect, has been proposed (see, for example, Non-Patent Documents 2 and 3).

Prior Art Documents

Non-Patent Documents

[0004]

Non-Patent Document 1

Non-Patent Document 2

[0005] However, heat pumps using the thermoelectric effect have hardly been put into practical use. In particular, in the Peltier effect, since the direction of heat transport and the electric current are in the same direction, a three-dimensional and complex 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 required. As a result, the current cooling devices using the Peltier effect have a low coefficient of performance (COP), which is an energy efficiency index, of about 0.5.

[0006] The present invention has been made in view of the above problems, and an object thereof is to provide a highly energy-efficient thermoelectric element and a thermoelectric device using the Ettingshausen effect. [Means for Solving the Problems]

[0007] The thermoelectric element according to an embodiment of the present invention is made of a half-metal or a semiconductor having a band gap of 0.5 eV or less. When an electric current is passed in one direction and a magnetic field is applied in a direction orthogonal to the electric current, a temperature gradient is generated in a direction orthogonal to both the electric current and the magnetic field.

[0008] A thermoelectric device according to an 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 such that their longitudinal directions are parallel, and are made of a half-metal or a semiconductor having a bandgap of 0.5 eV or less. When an electric current is passed along each longitudinal direction and a magnetic field is applied in a direction orthogonal to the electric current, a temperature gradient is generated in a direction orthogonal to both the electric current and the magnetic field.

Advantages of the Invention

[0009] According to the present invention, by virtue of the fact that a thermoelectric element made of a half-metal or a semiconductor having a bandgap of 0.5 eV or less exhibits the Ettingshausen effect, it becomes possible to improve the energy efficiency.

Brief Description of the Drawings

[0010]

Figure 1

Figure 2

Figure 3

Figure 4A

Figure 4B

Figure 4C

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Mode for Carrying Out the Invention

[0011] 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 denoted by the same reference numerals. The drawings are schematic, and the relationship between the planar dimensions and the thickness, and the ratio of the thicknesses of the respective members are different from the actual ones. Also, it goes without saying that there are portions where the dimensional relationships and ratios are different between the drawings.

[0012] First, with reference to FIGS. 1 and 2, the Nernst effect and the Seebeck effect will be described respectively.

[0013] The Nernst effect is a phenomenon in which when a heat current flows through a thermoelectric element, an electromotive force is generated in a direction perpendicular to both the heat current and the magnetization of the thermoelectric element. For example, as shown in FIG. 1, when a heat current (∝ temperature difference ΔT) flows in the thickness direction in a rectangular parallelepiped thermoelectric element (depth l, width w, thickness t), the movement direction of carriers is bent by the magnetization M in the width direction of the thermoelectric element, and an electromotive force V is generated in a direction perpendicular to both the magnetization M and the heat current. Let the Nernst coefficient of the thermoelectric element be S N Then, the electromotive force V is S N ΔT(l / t). Thus, the electromotive force V generated by the Nernst effect is proportional to the shape factor l / t of the thermoelectric element.

[0014] On the one hand, the Seebeck effect is a phenomenon in which when a heat current flows through a thermoelectric element, carriers move along the heat current and an electromotive force is generated in the direction of the heat current. For example, as shown in FIG. 2, when a heat current (∝ temperature difference ΔT) flows in the thickness direction in a rectangular parallelepiped-shaped thermoelectric element (depth l, width w, thickness t), an electromotive force V is generated parallel to the heat current. If the Seebeck coefficient of the thermoelectric element is S, the electromotive force V is SΔT.

[0015] Next, the mechanism of a conventional heat pump (hereinafter referred to as a Peltier cooling device) using the Peltier effect, which is the reverse process of the Seebeck effect, will be described.

[0016] FIG. 3 shows a schematic configuration of a conventional Peltier cooling device 1. In the Peltier cooling device 1, a rod-shaped p-type semiconductor 5p and an n-type semiconductor 5n are alternately connected between two insulating substrates 3a and 3b, and the adjacent p-type semiconductor 5p and n-type semiconductor 5n are joined by a metal electrode 7. When a DC voltage V is applied as shown in FIG. 3, 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, heat absorption occurs at the electrode on the substrate 3a side, and heat dissipation occurs at the electrode on the substrate 3b side. In this way, heat is transported from the heat absorption side (cold) to the heat dissipation side (hot).

[0017] Let the heat dissipation side temperature be T h and the heat absorption side temperature be T c . Assuming that the resistance of a pair of adjacent p-type and n-type semiconductors (hereinafter referred to as a Peltier element) is R, the thermal conductance is K, and the Seebeck coefficient is S, the heat dissipation amount Q h on the high-temperature side and the heat absorption amount Q c on the low-temperature side of the Peltier element are expressed as in equations (1) and (2), respectively.

Equation

[0018] The first, second, and third terms on the right-hand sides of equations (1) and (2) represent the Peltier effect, Joule heat, and heat conduction (heat inflow from high temperature), respectively.

[0019] Let the width of each of the p-type and n-type semiconductors constituting the Peltier element in the x direction be w, the depth in the y direction be l, and the thickness (height) in the z direction be t. Let the electrical resistivity of the Peltier element be ρ and the thermal conductivity be κ. Then, the resistance R and the thermal conductance K of the Peltier element are expressed as in Equation (3).

Equation

[0020] For example, assuming that each Peltier element is made of Bi2Te3, a module with a size of 40 mm × 40 mm × 4 mm composed of 120 sets of Peltier elements (i.e., 120 sets of p-type and n-type semiconductors) with a size of 1 mm × 1 mm × 1 mm per set is prepared. When the electrical resistivity ρ of each Peltier element is about 10 3 μΩcm, the thermal conductivity κ is about 2 W / Km, and the Seebeck coefficient S is about 200 μV / K, the resistance R tot , the thermal conductance Κ tot , and the Seebeck coefficient S tot of the entire module are about 3 Ω, about 0.5 W / K, and about 0.05 V / K, respectively.

[0021] Let the total heat absorption of the entire module be denoted as Q c_tot . When a current I of 1 A is passed through the module and the resulting temperature difference ΔT (= T h - T c ) is 2 °C, among the total heat absorption Q c_tot , the first term (Peltier effect) in Equation (2) is about 14 W, the second term (Joule heat) is about 1.5 W, and the third term (heat conduction) is about 1 W.

[0022] COP max , which is the maximum value of the COP of the entire module composed of the above Peltier elements, is about 4 as shown in Equation (4).

Equation

[0023] Thus, since the Peltier cooling device 1 needs to be provided with a large number of PN junctions, it can be seen that the COP is low, leading to a decrease in element performance. Also, it can be seen that when the current I or the temperature difference ΔT (= T h - T c ) becomes large, the COP decreases significantly. Note that, as described above, the current Peltier cooling device has a COP of about 0.5.

[0024] 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.

[0025] <First Embodiment> First, with reference to FIGS. 4A to 6, the first embodiment of the present invention will be described. FIGS. 4A to 4C show a schematic configuration of a thermoelectric device 100 according to the first embodiment.

[0026] 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 in a direction (x direction) perpendicular to the longitudinal direction on a substrate 102 such that their longitudinal directions (y direction) are parallel.

[0027] As shown in FIG. 4C, the +y side of the thermoelectric element 104 of interest is connected by a copper wiring 106 to the -y side of the thermoelectric element 104 adjacent to the +x side, and the -y side of the thermoelectric element 104 of interest is connected by a copper wiring 106 to the +y side of the thermoelectric element 104 adjacent to the -x side. 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).

[0028] The thermoelectric element 104 is made of a half-metal or a semiconductor with a bandgap of 0.5 eV or less, and at the operating temperature, it is made of a material with a higher mobility (inversely proportional to the electrical resistivity ρ) and a lower thermal conductivity κ than a conventional Peltier element. Examples of gapless half-metals include Cd3As2, which is a Dirac semimetal, as well as Ag2Se, Ag2Te, etc. Examples of semiconductor materials include InSb, Bi 0.5 Sb 1.5 Te3, AgCuSe, elemental Te, Ag8SiSe6, or Ag8SnSe6, etc.

[0029] In addition, regarding the thermoelectric materials of the Mn3Sn system, the full-Heusler system Co2MnGa, and the Fe3Ga system, in which the inventors of the present application observed the anomalous Nernst effect, they can also be expected as candidate materials for a heat pump using the Ettingshausen effect.

[0030] The anomalous Nernst effect of the thermoelectric material of the Mn3Sn system 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 the full-Heusler system Co2MnGa and Fe3Ga thermoelectric materials are disclosed in International Publication No. 2019 / 009308 and PCT / JP2020 / 018010, respectively.

[0031] As shown in FIG. 4A, a heat dissipation plate 110 (heat sink) made of a metal material having high thermal conductivity such as aluminum, iron, or copper is provided on the heat dissipation side of the plurality of thermoelectric elements 104, and the heat from the plurality of thermoelectric elements 104 is dissipated. In FIG. 4A, only a part of the heat dissipation plate 110 is shown, but the actual heat dissipation plate 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 dissipation plate 110, a shape with 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-like structure.

[0032] When an electric current I is passed through the plurality of thermoelectric elements 104, for example, in the +y direction along their respective longitudinal directions, and a magnetic field H is applied in the +x direction orthogonal to the electric current I, each thermoelectric element 104 is magnetized in the +x direction, and a temperature gradient is generated in the z direction orthogonal to both the electric current I and the magnetic field H, and heat is transported from the heat absorption side (cold) to the heat dissipation side (hot) in the (+z direction).

[0033] As shown in FIG. 4B, each thermoelectric element 104 is assumed to have 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. Let the temperature on the heat dissipation side of each thermoelectric element 104 be T h , the temperature on the heat absorption side be T c , the resistance be R, the thermal conductance be K, and the Nernst coefficient be S N . Then, the heat dissipation amount Q h and the heat absorption amount Q c of each thermoelectric element 104 are respectively expressed as in Equations (5) and (6).

Equation

[0034] 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 a high temperature), respectively. The first term representing the Ettingshausen effect is proportional to the shape factor l / t of each thermoelectric element 104.

[0035] The resistance R and the thermal conductance K of each thermoelectric element 104 are expressed as in Equation (7).

Equation

[0036] As shown in FIG. 4C, a sample is prepared in which a plurality of thermoelectric elements 104 with a thickness t = 0.5 mm, a width w = 0.5 mm, and a length l = 40 mm are arranged in parallel in a 40 mm × 40 mm region of a substrate 102 with a size of 50 mm × 50 mm. 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.

[0037] The total heat absorption of the entire sample is denoted 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 S N is 200 μV / K. When a magnetic field H of 0.5 T is applied to the sample and a current I of 1 A is passed through, the temperature difference ΔT (= T h - T c ) is set to 2 °C, then among the total heat absorption Q c_tot , the first term (Ettinghausen effect) of Equation (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 denoted as R tot , the COP of the entire sample takes a large value of about 15 as shown in Equation (8).

Equation

[0038] FIG. 5 shows the current dependence of the heat absorption Q c when a magnetic field of 0.5 T is applied to the sample (FIG. 4C) in which each thermoelectric element 104 is made of Cd3As2 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 Q c , while the larger the temperature difference ΔT, the smaller the heat absorption Q c , indicating that heat transport from low temperature to high temperature becomes difficult. Also, even for the same temperature difference ΔT, when the current I is 10 A, the heat absorption Qc It can be seen that it takes the maximum value. In this sample, a temperature difference of about 70 °C can be applied at most.

[0039] For this sample, Fig. 6 shows the current dependence of the COP for each temperature difference ΔT. As shown in Fig. 6, the smaller the temperature difference ΔT, the higher the COP, and it can be seen that the COP exceeds 30 at ΔT = 1K.

[0040] 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. Thereby, it becomes possible to realize a high conversion efficiency that could not be achieved with conventional Peltier elements.

[0041] <Second Embodiment> Next, with reference to Figs. 7 and 8, a second embodiment of the present invention will be described.

[0042] In the first embodiment, the plurality of thermoelectric elements 104 arranged such that their longitudinal directions are parallel are electrically connected in series so that currents I in the same direction flow, but a circuit configuration may be adopted in which currents in opposite directions flow in adjacent thermoelectric elements.

[0043] Fig. 7 shows a schematic configuration of a 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 that are rectangular parallelepiped and of the same size, and the first thermoelectric elements 204a and the second thermoelectric elements 204b are alternately arranged such that their longitudinal directions (y direction) are parallel. The first thermoelectric elements 204a and the second thermoelectric elements 204b are made of the same material as the thermoelectric element 104 according to the first embodiment.

[0044] Although not shown in FIG. 7, the thermoelectric device 200A also includes a substrate on the heat absorption side (cold) of a plurality of first thermoelectric elements 204a and a plurality of second thermoelectric elements 204b, and a heat sink on the heat dissipation side (hot), similar to the thermoelectric device 100 (FIG. 4A) according to the first embodiment. The same applies to the thermoelectric device 200B (FIG. 8) described later.

[0045] 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 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 the copper wiring 206. In this way, the plurality of thermoelectric elements are electrically connected in series such that currents I flow in opposite directions in adjacent thermoelectric elements due to a structure in which connections between +y sides and connections between -y sides are alternately repeated. In FIG. 7, an example is shown 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.

[0046] Since currents I flow in opposite directions in 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, it is necessary to apply magnetic fields in opposite directions to these thermoelectric elements. For example, as shown in FIG. 7, assuming that the direction from the heat absorption side (cold) to the heat dissipation 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, and a magnetic field H2 in the -x direction is applied to the second thermoelectric element 204b by a permanent magnet, thereby magnetizing the first thermoelectric element 204a in the +x direction and magnetizing the second thermoelectric element 204b in the -x direction. That is, alternating magnetic fields in opposite directions are applied to adjacent thermoelectric elements.

[0047] 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 not easy structurally to apply reverse alternating magnetic fields to adjacent thermoelectric elements in the same plane. Therefore, if the first thermoelectric elements and the second thermoelectric elements are arranged in separate planes, a magnetic field in the same direction can be applied in the same plane.

[0048] 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 parallelepiped shape and the same size are provided. The plurality of first thermoelectric elements 224a are arranged in odd rows (+z direction, 1st row, 3rd row,...) and odd columns (+x direction, 1st column, 3rd column,...), and the plurality of second thermoelectric elements 224b are arranged in even rows (+z direction, 2nd row, 4th row,...) and even columns (+x direction, 2nd column, 4th column,...). That is, the first thermoelectric elements 224a and the second thermoelectric elements 224b are arranged such that their positions in the first direction (z direction) perpendicular to the longitudinal direction (y direction) are different from each other, and their positions in the second direction (x direction) perpendicular to both the longitudinal direction and the first direction are also different from each other. Note that the first thermoelectric elements 224a and the second thermoelectric elements 224b are also made of the same material as the thermoelectric element 104 according to the first embodiment.

[0049] Currents flowing in opposite directions to each other along the longitudinal direction flow through the first thermoelectric element 224a and the second thermoelectric element 224b. For example, current I flows in the +y direction through the first thermoelectric element 224a, and current I flows in the -y direction through the second thermoelectric element 224b.

[0050] 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 magnetized in the +x direction may be disposed between two adjacent first thermoelectric elements 224a in the x direction, and a permanent magnet 226 magnetized in the -x direction may be disposed between two adjacent second thermoelectric elements 224b in the x direction. By disposing 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.

[0051] Note that each permanent magnet 226 is made of a material having a coercive force larger than that of the first thermoelectric element 224a and the second thermoelectric element 224b. Further, in order to make the thermal conductivity uniform in the direction (z direction) in which the temperature gradient occurs, 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.

[0052] As described above, by disposing the permanent magnets 226 so as to align the directions of the magnetic fields in the same plane, the magnetization in the same plane is stabilized.

[0053] <Third Embodiment> Next, a third embodiment of the present invention will be described with reference to FIGS. 9 to 11.

[0054] Non-Patent Document 1 discloses that by stacking plate-like blocks made of Peltier elements in the direction in which a temperature gradient occurs and configuring them in a stepped shape in which the block on the heat dissipation side is wider than the block on the heat absorption side, the cooling performance is enhanced. However, as described above, in the Peltier effect, the loss due to a large number of PN junctions is extremely high, leading to a decrease in element performance. Therefore, when a plurality of blocks are multiply connected as in Non-Patent Document 1, there is a problem that the loss due to PN junctions becomes even larger.

[0055] On the other hand, in the Ettingshausen effect, since a PN junction is not required, it is considered that even if plate-shaped thermoelectric elements are stacked as described above, the element performance can be fully exhibited. 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.

[0056] As shown in FIG. 9, the thermoelectric device 300A according to the third embodiment includes a plurality of plate-shaped thermoelectric elements 310_1, 310_2, …, 310_N (N is an integer of 2 or more) stacked in the direction (x direction) in which a temperature gradient occurs. These thermoelectric elements are all made of the same material as the thermoelectric element 104 according to the first embodiment. Note that the number of thermoelectric elements constituting the thermoelectric device 300A is not particularly limited.

[0057] The plurality of thermoelectric elements 310_1, 310_2, …, 310_N all have the same thickness Δx in the direction (x direction) in which a temperature gradient occurs and the same length l in the direction (z direction; longitudinal direction) in which the current I flows, but their 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 heat absorption side (cold), and the cross section in the x-y plane has a symmetric stepped shape.

[0058] When a current I is passed through each thermoelectric element constituting the thermoelectric device 300A in the +z direction along its longitudinal direction 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 occurs in the x direction orthogonal to both the current I and the magnetic field H, and heat is transported from the heat absorption side (cold) to the heat dissipation side (hot) (+x direction).

[0059] The position x of the heat absorption side of the m-th thermoelectric element 310_m (m = 1, 2, …, N) is (m - 1)Δx. Let the width in the y direction of the thermoelectric element at this position x be y(x). Let the electrical resistivity, thermal conductivity, and Nernst coefficient of each thermoelectric element be ρ, κ, and S, respectively. N Then, the heat absorption amount Q c m (x) and the heat dissipation amount Q hm (x + Δx) are respectively expressed as in Formula (9) and Formula (10).

Number

[0060] In Formula (9) and Formula (10), i is the current density, and is defined as i = I / y(x)Δx. T m (x), T m (x + Δx) are respectively the temperature at the heat absorption side (x) and the temperature at the heat dissipation side (x + Δx) of the m-th thermoelectric element 310_m. t m (x) represents the temperature gradient in the m-th thermoelectric element 310_m and is defined as in Formula (11).

Number

[0061] The structure in which a large number of thermoelectric elements with a small thickness Δx are stacked is equivalent to a structure in which one thermoelectric element 300B has a wider width in the direction in which the magnetic field H is applied from the heat absorption side (cold) to the heat dissipation side (hot), as shown in FIG. 10.

[0062] Non-Patent Document 2 shows that for a thermoelectric element exhibiting the Ettingshausen effect, the optimal shape that brings about the maximum temperature difference is a shape in which the width exponentially increases from the heat absorption side (cold) to the heat dissipation side (hot). Therefore, it is considered that the thermoelectric element 300B may be in such a shape. Note that the thermoelectric element 300B is also made of the same material as the thermoelectric element 104 according to the first embodiment.

[0063] Here, let the thickness of the thermoelectric element 300B be X, the width at the cooling surface 320 where x = 0 be y c , and the width at the heat dissipation surface 330 where x = X be y h (y c < y h ). In order to obtain the thermoelectric element 300B with the optimal shape, the width y(x) of the thermoelectric element 300B at the position x in the direction in which the temperature gradient occurs may be defined as in Formula (12).

Number

[0064] In FIG. 11, the maximum temperature difference ΔT h / y c obtained when the value of y of the thermoelectric element 300B is changed is shown. Here, the Nernst coefficient S max of the thermoelectric element 300B is set to 200 μV / K, the electrical resistivity ρ is set to 100 μΩcm, the thermal conductivity κ is set to 15 W / Km, and the temperature T N on the heat dissipation side is fixed at 300 K. As shown in FIG. 11, as y h / y h increases, it can be seen that the maximum temperature difference ΔT c increases. Thus, for materials with the same performance, by adopting a shape in which the width y(x) increases exponentially as shown in Equation (12) from the heat absorption side to the heat dissipation side, a larger temperature difference can be realized. max As described above, each thermoelectric element according to the first to third embodiments has a simpler element structure and more freedom in shape than a Peltier element. In particular, by adopting the shape as shown in FIG. 10, the cooling performance can be further improved.

[0065] Next, the relationship between the dimensionless figure of merit and the Carnot efficiency will be described. Let the dimensionless figure of merit of a conventional Peltier element (FIG. 3) be ZT (= S

[0066] T / ρκ), and the dimensionless figure of merit of each thermoelectric element (new technology) shown in the first to third embodiments be Z 2 T (= S N T / ρκ). FIG. 12 shows the relationship between the dimensionless figure of merit ZT and Z N 2 T and the Carnot efficiency. From FIG. 12, it can be seen that the rate of increase in the Carnot efficiency with respect to Z N T is larger than the rate of increase with respect to ZT. Specifically, the conventional Peltier element exhibits the highest performance at ZT = ∞, and the thermoelectric elements according to the respective embodiments exhibit the highest performance at Z N T = 1. Here, Z N T = 1. Here, Z NThe Carnot efficiency at T = 1 is a value determined when the high temperature is 800 K and the low temperature is 300 K.

[0067] Thus, each thermoelectric element showing the Ettingshausen effect according to the first to third embodiments has a significantly better Carnot efficiency than a Peltier element.

Description of Reference Numerals

[0068] 100, 200A, 200B, 300A thermoelectric devices 102 substrate 104, 300B thermoelectric elements 106, 206 copper wirings 110 heat sink 204a, 224a first thermoelectric elements 204b, 224b second thermoelectric elements 226 permanent magnet 320 cooling surface 330 heat dissipation surface

Claims

1. A thermoelectric device comprising a plurality of thermoelectric elements each having a shape extending in one direction, wherein the plurality of thermoelectric elements, are arranged such that their longitudinal directions are parallel, are made of a half-metal or a semiconductor having a bandgap of 0.5 eV or less, 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 plurality of thermoelectric elements include a first thermoelectric element and a second thermoelectric element, the first thermoelectric element and the second thermoelectric element, are arranged such that their positions in a first direction perpendicular to the longitudinal direction are different from each other, and their positions in a second direction perpendicular to both the longitudinal direction and the first direction are different from each other, when currents flowing in opposite directions along the longitudinal direction are passed through the first thermoelectric element and the second thermoelectric element, and an alternating magnetic field flowing in opposite directions along the second direction is applied, a temperature gradient along the first direction is generated in each of the first thermoelectric element and the second thermoelectric element, a thermoelectric device.

2. A thermoelectric device comprising a plurality of thermoelectric elements each having a shape extending in one direction, wherein the plurality of thermoelectric elements, are arranged such that their longitudinal directions are parallel, are made of a half-metal or a semiconductor having a bandgap of 0.5 eV or less, 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 plurality of thermoelectric elements are plate-shaped and are stacked in the direction in which the temperature gradient is generated, a thermoelectric device in which the thermoelectric element on the heat dissipation side is wider than the thermoelectric element on the heat absorption side in the direction in which the magnetic field is applied.

3. The thermoelectric device according to claim 1 or 2, wherein the half-metal or the 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, Ag 8 SnSe 6, an Mn 3 Sn-based material, a full-Heusler-based Co 2 MnGa, or an Fe 3 Ga-based material.

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