JP7709717B2 - Thermoelectric elements and thermoelectric devices - Google Patents

Description

The present invention relates to a thermoelectric element and a thermoelectric device equipped with a thermoelectric element.

A heat pump is a device that transports heat from low temperature to high temperature. Until now, heat pumps have been dominated by those that use a heat transfer medium, and perform heat exchange and heat transfer by heat of vaporization and heat of condensation. In recent years, alternative fluorocarbons that do not destroy the ozone layer have been used as heat transfer media. However, since alternative fluorocarbons have a much higher greenhouse effect than _CO2 , the Kigali Amendment enacted in 2016 requires a significant reduction in the use of alternative fluorocarbons. Therefore, there is an urgent need to develop a new heat pump mechanism to replace the current mechanism that uses alternative fluorocarbons as a heat transfer medium.

Research into using the thermoelectric effect in heat pumps has been ongoing since the 1950s. For example, Non-Patent Document 1 proposes a cooling device that uses the Peltier effect, which is the inverse process of the Seebeck effect, as a thermoelectric effect. In addition, a cooling device that uses the Ettingshausen effect, which is the inverse process of the Nernst effect, as another thermoelectric effect has also been proposed (see, for example, Non-Patent Documents 2 and 3).

T. Metzger, R.P. Huebener, “Modelling 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 to practical use. In particular, with the Peltier effect, the heat is transported in the same direction as the electric current, resulting in a complex, three-dimensional structure (see Figure 3) in which p-type and n-type semiconductors are arranged alternately, requiring a large number of PN junctions. As a result, current cooling devices using the Peltier effect have a low coefficient of performance (COP), an index of energy efficiency, of around 0.5.

The present invention was made in consideration of the above problems, and aims to provide an energy-efficient thermoelectric element and thermoelectric device that uses the Ettingshausen effect.

The thermoelectric element according to one embodiment of the present invention is made of a semimetal or a semiconductor with 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 perpendicular to the current, a temperature gradient is generated in a direction perpendicular to both the current and the magnetic field.

The thermoelectric device according to one embodiment of the present invention comprises a plurality of thermoelectric elements each extending in one direction. The thermoelectric elements are arranged so that their longitudinal directions are parallel to each other, and are made of a semimetal or a semiconductor with a band gap of 0.5 eV or less. When a current is passed along the longitudinal direction of each thermoelectric element and a magnetic field is applied in a direction perpendicular to the current, a temperature gradient is generated in a direction perpendicular to both the current and the magnetic field.

According to the present invention, a thermoelectric element made of a semimetal or a semiconductor with a band gap of 0.5 eV or less exhibits the Ettingshausen effect, making it possible to improve energy efficiency.

FIG. 1 is a schematic diagram for explaining the Nernst effect. FIG. 1 is a schematic diagram for explaining the Seebeck effect. FIG. 1 is a cross-sectional view showing a schematic configuration of a conventional heat pump using the Peltier effect. 1 is a perspective view of a thermoelectric device according to a first embodiment. 4B is a perspective view showing an arrangement of a plurality of thermoelectric elements constituting the thermoelectric device shown in FIG. 4A. 4B is a plan view showing an arrangement of a plurality of thermoelectric elements constituting the thermoelectric device shown in FIG. 4A. 4 is a graph showing the current dependency of the amount of heat absorption for each temperature difference for the thermoelectric device according to the first embodiment including a thermoelectric element made of Cd ₃ As ₂ . 4 is a graph showing the current dependence of COP for each temperature difference for the thermoelectric device according to the first embodiment including a thermoelectric element made of Cd ₃ As ₂ . FIG. 5 is a schematic diagram showing a configuration of a thermoelectric device according to a second embodiment. FIG. 11 is a schematic diagram illustrating the arrangement of thermoelectric elements and permanent magnets in a thermoelectric device according to a modified example of the second embodiment. FIG. 13 is a schematic diagram showing a configuration of a thermoelectric device according to a third embodiment. 13 is a schematic diagram showing the shape of a thermoelectric element according to a modified example of the third embodiment. FIG. 11 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 . 1 is a graph showing the relationship between the dimensionless figure of merit and the Carnot efficiency for a conventional Peltier element and each thermoelectric element according to each embodiment (new technology).

Exemplary embodiments of the present invention will now be described with reference to the accompanying drawings.
In the drawings, the same or similar components are given the same reference symbols. The drawings are schematic, and the relationship between planar dimensions and thickness, and the thickness ratio of each component differ from the actual ones. In addition, the drawings include parts whose dimensional relationships and ratios differ from each other.

First, we will explain the Nernst effect and the Seebeck effect with reference to Figures 1 and 2.

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 of a rectangular thermoelectric element (depth l, width w, thickness t), the magnetization M in the width direction of the thermoelectric element bends the carrier movement direction, and an electromotive force V is generated in a direction perpendicular to both the magnetization M and the heat flow. If the Nernst coefficient of the thermoelectric element is S _N , 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.

On the other hand, the Seebeck effect is a phenomenon in which, when a heat flow passes through a thermoelectric element, carriers move along the heat flow, generating an electromotive force in the direction of the heat flow. For example, as shown in Figure 2, when a heat flow (∝ temperature difference ΔT) passes through a rectangular thermoelectric element (depth l, width w, thickness t) in the thickness direction, an electromotive force V is generated parallel to the heat flow. If the Seebeck coefficient of the thermoelectric element is S, then the electromotive force V is SΔT.

Next, we will explain the mechanism of a conventional heat pump (hereafter referred to as a Peltier cooling device) that uses the Peltier effect, which is the reverse process of the Seebeck effect.

Figure 3 shows the schematic configuration of a conventional Peltier cooling device 1. In the Peltier 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 adjacent p-type semiconductors 5p and n-type semiconductors 5n are joined by metal electrodes 7. When a DC voltage V is applied as shown in Figure 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, and heat is absorbed at the electrode on the substrate 3a side and dissipated 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).

If the heat dissipation side temperature is T _h , the heat absorption side temperature is T _c , the resistance of a pair of adjacent p-type and n-type semiconductors (hereinafter referred to as Peltier elements) is R, the thermal conductance is K, and the Seebeck coefficient is S, the amount of heat dissipation Q _h on the high-temperature side and the amount of heat absorption Q _c on the low-temperature side of the Peltier element are expressed by equations (1) and (2), respectively.

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

If the width in the x direction of each of the p-type and n-type semiconductors that make up the Peltier element is w, the depth in the y direction is l, and the thickness (height) in the z direction is t, and the electrical resistivity of the Peltier element is ρ and the thermal conductivity is κ, the resistance R and thermal conductance K of the Peltier element can be expressed as shown in Equation (3).

For example, a module measuring 40 mm×40 mm×4 _mm is prepared, which is composed of 120 Peltier elements (i.e., 120 pairs of p-type and n-type semiconductors) each of which is ₁ mm×1 mm×1 mm in size, with each Peltier element being made of Bi2Te3. If the electrical resistivity ρ of each Peltier 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 K _tot , and Seebeck coefficient S _tot of the entire module are about 3 Ω, about 0.5 W/K, and about 0.05 V/K, respectively.

The total heat absorption amount of the entire module is denoted as _{Qc_tot} . If a current I of 1 A is passed through the module and the resulting temperature difference ΔT (=T _h -T _c ) is 2°C, of the total heat absorption amount _{Qc_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 (thermal conduction) is about 1 W.

The maximum COP, COP _max, of the entire module made up of the above-mentioned Peltier elements is approximately 4, as shown in formula (4).

As described above, the Peltier cooling device 1 requires a large number of PN junctions, which results in a low COP and a decrease in element performance. It is also found that the COP decreases significantly when the current I or temperature difference ΔT (=T _h -T _c ) increases. As described above, the COP of current Peltier cooling devices is approximately 0.5.

Next, with reference to Figures 4A to 12, we will explain the first, second, and third embodiments of the present invention, which use the Ettingshausen effect, which is the reverse process of the Nernst effect.

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

Thermoelectric device 100 is a heat pump that uses the Ettingshausen effect, and includes multiple rectangular thermoelectric elements 104 that extend in one direction (y direction). As shown in Figures 4A to 4C, the multiple thermoelectric elements 104 are arranged in parallel on the substrate 102 in a direction perpendicular to the longitudinal direction (x direction) so that their longitudinal directions (y direction) are parallel to each other.

As shown in FIG. 4C, the +y side of a thermoelectric element 104 of interest is connected to the -y side of the thermoelectric element 104 adjacent to the +x side by copper wiring 106, and 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 copper wiring 106. In this way, multiple 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 with a band gap of 0.5 eV or less, and is made of a material that has a higher mobility (inversely proportional to the electrical resistivity ρ) and a smaller thermal conductivity κ than conventional Peltier elements at the operating temperature. Examples of gapless semimetals include the Dirac semimetal Cd ₃ As ₂ , Ag ₂ Se, Ag ₂ Te, etc. Examples of semiconductor materials include InSb, Bi _0.5 Sb _1.5 Te ₃ , AgCuSe, simple Te, Ag ₈ SiSe ₆ , or Ag ₈ SnSe ₆ .

In addition, the Mn ₃ Sn-based, full Heusler-based Co ₂ MnGa-based, and Fe ₃ Ga-based thermoelectric materials in which the present inventors have observed the anomalous Nernst effect are also promising candidates for heat pump materials using the Ettingshausen effect.

The anomalous Nernst effect of Mn ₃ Sn-based 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 effect of full-Heusler Co ₂ MnGa and Fe ₃ Ga-based thermoelectric materials is disclosed in WO 2019/009308 and PCT/JP2020/018010, respectively.

As shown in FIG. 4A, a heat sink 110 (heat sink) made of a metal material with high thermal conductivity such as aluminum, iron, or copper is provided on the heat dissipation side of the multiple thermoelectric elements 104, and dissipates heat from the multiple thermoelectric elements 104. Although only a portion of the heat sink 110 is shown in FIG. 4A, the actual heat sink 110 is provided to cover the entire multiple thermoelectric elements 104. In order to improve the heat dissipation efficiency of the heat sink 110, a shape that increases the surface area is adopted; for example, in addition to a structure with multiple protrusions as shown in FIG. 4A, there are also bellows-shaped structures.

When a current I is passed through multiple thermoelectric elements 104 in the +y direction along the longitudinal direction of each element, and a magnetic field H is applied in the +x direction perpendicular to the current I, each thermoelectric element 104 is magnetized in the +x direction, a temperature gradient is generated in the z direction perpendicular 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) (in the +z direction).

4B, each thermoelectric element 104 has a width w in the x direction, a length l in the y direction, and a thickness t in the z direction. If the heat radiation side temperature of each thermoelectric element 104 is T _h , the heat absorption side temperature is T _c , the resistance is R, the thermal conductance is K, and the Nernst coefficient is S _N , the heat radiation amount Q _h and heat absorption amount Q _c of each thermoelectric element 104 are expressed by equations (5) and (6), respectively.

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

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

As shown in FIG. 4C, a sample is prepared in which multiple thermoelectric elements 104 with thickness t = 0.5 mm, width w = 0.5 mm, and length l = 40 mm are arranged in parallel in an area of 40 mm x 40 mm on a substrate 102 with dimensions of 50 mm x 50 mm. Here, 20 thermoelectric elements 104 are arranged so that the total length l of the multiple thermoelectric elements 104 is 0.8 m.

The total heat absorption amount 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. If a magnetic field H of 0.5 T is applied to the sample and a current I of 1 A is passed through it, and the temperature difference ΔT (= T _h - _{T c} ) is 2°C, then of the total heat absorption amount Q _{c_tot} , the first term (Ettingshausen effect) of formula (6) is about 96 W, the second term (Joule heat) is about 1.5 W, and the third term (thermal conduction) is about 24 W. If the resistance of the entire sample is denoted as R _tot , the COP of the entire sample is a large value of about 15 as shown in formula (8).

5 shows the current dependency of the heat absorption amount _Qc for each temperature difference ΔT when a magnetic field of 0.5 T is applied to a sample (FIG. _4C ) in which each thermoelectric element 104 is made of _Cd3As2 and has the above-mentioned size. As shown in FIG. 5, for the same current I, the smaller the temperature difference ΔT, the larger the heat absorption amount _Qc , while the larger the temperature difference ΔT, the smaller the heat absorption amount _Qc , making it difficult to transport heat from a low temperature to a high temperature. It can also be seen that the heat absorption amount _Qc reaches its maximum value when the current I is 10 A, even with the same temperature difference ΔT. With this sample, a temperature difference of approximately 70°C can be achieved at the maximum.

Figure 6 shows the current dependence of COP for this sample for each temperature difference ΔT. As shown in Figure 6, the smaller the temperature difference ΔT, the higher the COP, and at ΔT = 1K, the COP exceeds 30.

As described above, the thermoelectric device 100 using the Ettingshausen effect allows the cooling performance of the thermoelectric device 100 to be controlled by the shape factor l/t of the thermoelectric element 104. This makes it possible to achieve high conversion efficiency that could not be achieved with conventional Peltier elements.

Second Embodiment
Next, a second embodiment of the present invention will be described with reference to FIGS.

In the first embodiment, the multiple thermoelectric elements 104 arranged with their longitudinal directions parallel to each other were electrically connected in series so that the current I flowed in the same direction, but a circuit configuration may be adopted in which the currents flow in opposite directions between adjacent thermoelectric elements.

Figure 7 shows a schematic configuration of a thermoelectric device 200A according to the second embodiment. As shown in Figure 7, the thermoelectric device 200A includes a plurality of first thermoelectric elements 204a and a plurality of second thermoelectric elements 204b that are rectangular and of the same size, and the first thermoelectric elements 204a and the second thermoelectric elements 204b are arranged alternately so that their longitudinal directions (y direction) are parallel to each other. 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.

Although not shown in FIG. 7, the thermoelectric device 200A, like the thermoelectric device 100 (FIG. 4A) according to the first embodiment, has a substrate on the heat absorption side (cold) of the multiple first thermoelectric elements 204a and the multiple second thermoelectric elements 204b, and a heat sink on the heat dissipation side (hot). The same is true for the thermoelectric device 200B (FIG. 8) described below.

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 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 copper wiring 206. In this way, the multiple thermoelectric elements are electrically connected in series such that the current I flows in opposite directions through adjacent thermoelectric elements, with the structure in which the connections between the +y sides and the connections between the -y sides are repeated alternately. FIG. 7 shows an example in which the current I flows in the +y direction through the first thermoelectric element 204a, and the current I flows in the -y direction through the second thermoelectric element 204b.

Since the current I flows in the first thermoelectric element 204a and the second thermoelectric element 204b in opposite directions, 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 these thermoelectric elements. For example, as shown in FIG. 7, if the direction from the heat absorption side (cold) to the heat dissipation side (hot) is +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. In other words, alternating magnetic fields in opposite directions are applied to adjacent thermoelectric elements.

As described above, since the multiple first thermoelectric elements 204a and multiple second thermoelectric elements 204b constituting the thermoelectric device 200A are in the same plane, it is necessary to apply alternating magnetic fields H1 and H2 in the same plane. However, structurally, it is not easy to apply alternating magnetic fields of opposite directions to adjacent thermoelectric elements in the same plane. Therefore, if the first thermoelectric elements and the second thermoelectric elements are arranged in different planes, it is possible to apply magnetic fields in the same direction in the same plane.

Specifically, as shown in the thermoelectric device 200B in FIG. 8, a plurality of first thermoelectric elements 224a and a plurality of second thermoelectric elements 224b of the same size and rectangular parallelepiped shape are provided, and the plurality of first thermoelectric elements 224a are arranged in odd-numbered rows (first row, third row, ...) in the +z direction and odd-numbered rows (first row, third row, ...) in the +x direction, and the plurality of second thermoelectric elements 224b are arranged in even-numbered rows (second row, fourth row, ...) in the +z direction and even-numbered rows (second row, fourth row, ...) in the +x direction. That is, the first thermoelectric elements 224a and the second thermoelectric elements 224b are arranged so 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. 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 flow in opposite directions along the longitudinal direction in the first thermoelectric element 224a and the second thermoelectric element 224b. For example, current I flows in the +y direction in the first thermoelectric element 224a, and 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 magnetized in the +x direction can be placed between two first thermoelectric elements 224a adjacent in the x direction, and a permanent magnet 226 magnetized in the -x direction can be placed between two second thermoelectric elements 224b adjacent in the x direction. By placing 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 with a greater coercive force than the first thermoelectric element 224a and the second thermoelectric element 224b. In order to homogenize the thermal conductivity in the direction in which the temperature gradient occurs (z direction), each permanent magnet 226 is preferably made of a material with 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 magnetic field direction is aligned in the same plane, magnetization in the same plane is stabilized.

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

Non-Patent Document 1 discloses that cooling performance can be enhanced by stacking plate-shaped blocks made of Peltier elements in the direction in which a temperature gradient occurs, and configuring them in a stepped manner with the heat dissipation side blocks wider than the heat absorption side blocks. However, as mentioned above, the Peltier effect causes extremely high losses due to the numerous PN junctions, which leads to a decrease in element performance. Therefore, when multiple blocks are multiple-connected as in Non-Patent Document 1, there is a problem that the losses due to the PN junctions become even greater.

On the other hand, the Ettingshausen effect does not require a PN junction, so it is believed that the element performance can be fully demonstrated even if plate-shaped thermoelectric elements are stacked as described above. Therefore, in the third embodiment, a structure in which multiple thermoelectric elements that exhibit 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 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 in which a temperature gradient occurs (x direction), and all of these thermoelectric elements are 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.

The multiple 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 same length l in the direction in which the current I flows (z direction; longitudinal direction), but differ from each other in width in the direction in which the magnetic field H is applied (y direction). 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 symmetrical stepped shape.

When a current I is passed through each thermoelectric element constituting the thermoelectric device 300A in the +z direction along the longitudinal direction of each element, and a magnetic field H is applied in the +y direction perpendicular to the current I, each thermoelectric element is magnetized in the +y direction, a temperature gradient is generated in the x direction perpendicular 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) (in the +x direction).

The position x on the heat absorption side of the m-th thermoelectric element 310_m (m=1, 2, ..., N) is (m-1)Δx. The width in the y direction of the thermoelectric element at this position x is y(x). If the electrical resistivity, thermal conductivity, and Nernst coefficient of each thermoelectric element are ρ, κ, and S _N , respectively, the amount of heat absorption Q _c ^m (x) and the amount of heat dissipation Q _h ^m (x+Δx) of the m-th thermoelectric element 310_m are expressed by equations (9) and (10), respectively.

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

A structure in which many thermoelectric elements with a small thickness Δx are stacked is equivalent to a structure in which one thermoelectric element 300B increases in 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.

Non-Patent Document 2 shows that the optimal shape for a thermoelectric element that exhibits the Ettingshausen effect to produce the maximum temperature difference is one in which the width increases exponentially from the heat absorption side (cold) to the heat dissipation side (hot). Therefore, it is considered that the thermoelectric element 300B should 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 thermoelectric element 300B is X, the width on cooling surface 320 at x=0 is _yc , and the width on heat dissipation surface 330 at x=X is _yh ( _yc < _yh ). In order to obtain thermoelectric element 300B with an optimal shape, the width y(x) of thermoelectric element 300B at position x in the direction in which the temperature gradient occurs may be defined as in equation (12).

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 S _N of the thermoelectric element 300B is set to 200 μV / K, the electrical resistivity ρ is set to 100 μΩ cm, the thermal conductivity κ is set to 15 W / Km, and the heat dissipation side temperature T _h is fixed to 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, a larger temperature difference can be realized by adopting a shape in which the width y (x) increases exponentially from the heat absorption side to the heat dissipation side as shown in formula (12) for materials with the same performance.

As described above, the thermoelectric elements according to the first to third embodiments have a simpler element structure than a Peltier element, and there is more freedom in the shape. In particular, by adopting a shape such as that shown in FIG. 10, the cooling performance can be further improved.

Next, the relationship between the dimensionless figure of merit and the Carnot efficiency will be described. The dimensionless figure of merit of the conventional Peltier 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). FIG. 12 shows the relationship between the dimensionless figures of merit ZT and _ZNT and the Carnot efficiency. From FIG. 12, it can be seen that the increase rate of the Carnot efficiency with respect to _ZNT is greater than the increase rate with respect to ZT. Specifically, the conventional Peltier 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 800K and the low temperature is 300K.

In this way, the thermoelectric elements exhibiting the Ettingshausen effect according to the first to third embodiments have a Carnot efficiency that is significantly better than that of a Peltier element.

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

Claims (3)

A thermoelectric device comprising a plurality of thermoelectric elements each extending in one direction,
The plurality of thermoelectric elements include
They are arranged so that their longitudinal directions are parallel to each other,
Made of a semimetal or a semiconductor with a band gap 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 perpendicular to the current, a temperature gradient is generated in a direction perpendicular to both the current and the magnetic field,
the plurality of thermoelectric elements includes a first thermoelectric element and a second thermoelectric element;
The first thermoelectric element and the second thermoelectric element are
The positions of the first and second electrodes in a first direction perpendicular to the longitudinal direction are different from each other, and the positions of the first and second electrodes in a second direction perpendicular to both the longitudinal direction and the first direction are different from each other.
A thermoelectric device, wherein when currents are passed through the first thermoelectric element and the second thermoelectric element in opposite directions along the longitudinal direction and alternating magnetic fields are applied in opposite directions along the second direction, a temperature gradient is generated in each of the first thermoelectric element and the second thermoelectric element along the first direction. A thermoelectric device comprising a plurality of thermoelectric elements each extending in one direction,
The plurality of thermoelectric elements include
They are arranged so that their longitudinal directions are parallel to each other,
Made of a semimetal or a semiconductor with a band gap 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 perpendicular to the current, a temperature gradient is generated in a direction perpendicular to both the current and the magnetic field,
The plurality of thermoelectric elements are plate-shaped and stacked in a direction in which the temperature gradient occurs,
A thermoelectric device, wherein the thermoelectric element on the heat dissipation side is wider in the direction in which the magnetic field is applied than the thermoelectric element on the heat absorption side. The semimetal or the semiconductor is Cd ₃ A.S. 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 , Mn ₃ Sn-based materials, full Heusler Co ₂ MnGa or Fe ₃ The thermoelectric device according to claim 1 or 2, which is made of a Ga-based material.