Asymmetrical PN junction thermoelectric couple structure and its parameter determination method
11600758 · 2023-03-07
Assignee
Inventors
- Ruochen Wang (Zhenjiang, CN)
- Ding Luo (Zhenjiang, CN)
- Wei Yu (Zhenjiang, CN)
- Weiqi Zhou (Zhenjiang, CN)
- Long CHEN (Zhenjiang, CN)
Cpc classification
H10N10/17
ELECTRICITY
International classification
Abstract
The present invention discloses an asymmetrical PN junction thermoelectric couple structure and its parameter determination method. By changing the structural parameters of p-type semiconductor or n-type semiconductor, the current generated by p-type semiconductor is equal to the current generated by the n-type semiconductor, so that the high-efficiency output of PN junction thermoelectric couple can be realized. Meanwhile, the present invention provides a method for determining the parameters of PN junction based on the numerical solution method. Finally, the optimal size parameters of PN junction are obtained.
Claims
1. A method for determining the parameters of an asymmetric PN junction thermoelectric couple structure, comprising the following steps: calculating an integral mean value of electrical resistivity of a p-type semiconductor
2. The method for determining the parameters of the asymmetric PN junction thermoelectric couple structure according to claim 1, further comprising the step: if
3. The method for determining the parameters of asymmetric PN junction thermoelectric couple structure according to claim 2, wherein the method of determining the length of the p-type semiconductor and the n-type semiconductor when
4. The method for determining the parameters of the asymmetric PN junction thermoelectric couple structure according to claim 1, wherein the boundary conditions for calculating Peltier heat are as follows: wherein a bottom contact surface of the p-type semiconductor is in contact with a first bottom copper electrode, and a bottom contact surface of the n-type semiconductor is in contact with a second bottom copper electrode, the temperature of the first and second bottom copper electrodes equals the temperature of the p-type semiconductor and the n-type semiconductor, that is T.sub.co|.sub.z=H.sub.
5. The method for determining the parameters of the asymmetric PN junction thermoelectric couple structure according to claim 1, wherein the current boundary conditions are: on a left end surface of the first bottom copper electrode and a left end surface of a resistance, both surfaces are set to be grounded, that is, the voltage is zero; on a right end surface of the second bottom copper electrode and a right end surface of the resistance, both surfaces are set to be connected electrically, that is, the voltages are equal.
6. The method for determining the parameters of the asymmetric PN junction thermoelectric couple structure according to claim 1, wherein the temperature boundary conditions are: the contact surfaces of the PN junction thermoelectric couple with the environment are set as an adiabatic boundary; a bottom surface of a bottom ceramic plate is set as high temperature boundary, and a top surface of a top ceramic plate is set as low temperature boundary.
7. The method for determining the parameters of the asymmetric PN junction thermoelectric couple structure according to claim 1, wherein the asymmetric PN junction thermoelectric couple structure, comprises ceramic plates in opposite arrangement, the copper electrodes, and the p-type semiconductor and the n-type semiconductor with the same height, wherein the top and bottom contact surfaces of the p-type semiconductor and the n-type semiconductor are connected in series by copper electrodes, and are sandwiched between the top and bottom ceramic plates, wherein the sum of length of the p-type semiconductor L.sub.p and the length of n-type semiconductor L.sub.n is 2L, and L is the initial length of p-type semiconductor and n-type semiconductor.
8. The method for determining the parameters of the asymmetric PN junction thermoelectric couple structure according to claim 7, wherein the length of the p-type semiconductor L.sub.p is L±i×Δl, and the length of the n-type semiconductor L.sub.n is L∓i×Δl, wherein i is the number of iterations to be determined, and Δl is the length change value of the p-type semiconductor and the n-type semiconductor in each iteration calculation.
9. The method for determining the parameters of the asymmetric PN junction thermoelectric couple structure according to claim 8, wherein the total length of copper electrodes in contact with the top contact surfaces of the p-type semiconductor and the n-type semiconductor is 2L+L.sub.s, where L.sub.s is the distance between the p-type semiconductor and the n-type semiconductor.
10. The method for determining the parameters of the asymmetric PN junction thermoelectric couple structure according to claim 9, the length of the copper electrode in contact with the bottom end of the p-type semiconductor is L.sub.p+L.sub.s/2, and the length of the copper electrode in contact with the bottom end of the n-type semiconductor is L.sub.n+L.sub.s/2.
11. An asymmetric PN junction thermoelectric couple structure comprising top and bottom ceramic plates in opposite arrangement, copper electrodes, and a p-type semiconductor and an n-type semiconductor with the same height, wherein top and bottom contact surfaces of the p-type semiconductor and the n-type semiconductor are connected in series by the copper electrodes, and are sandwiched between the top and bottom ceramic plates, wherein the sum of length of the p-type semiconductor L.sub.p and the length of n-type semiconductor L.sub.n is 2L, and L is the initial length of p-type semiconductor and n-type semiconductor.
12. The asymmetric PN junction thermoelectric couple structure according to claim 11, wherein the length of the p-type semiconductor L.sub.p is L±i×Δl, and the length of the n-type semiconductor L.sub.n is L∓i×Δl, wherein i is the number of iterations to be determined, and Δl is the length change value of the p-type semiconductor and the n-type semiconductor in each iteration calculation.
13. The asymmetric PN junction thermoelectric couple structure according to claim 12, wherein the total length of copper electrodes in contact with the top contact surfaces of the p-type semiconductor and the n-type semiconductor is 2L+L.sub.s, wherein L.sub.s is the distance between the p-type semiconductor and the n-type semiconductor.
14. The asymmetric PN junction thermoelectric couple structure according to claim 13, wherein the length of the copper electrode in contact with the bottom end of the p-type semiconductor is L.sub.p+L.sub.s/2, and the length of the copper electrode in contact with the bottom end of the n-type semiconductor is L.sub.n+L.sub.s/2.
15. The asymmetric PN junction thermoelectric couple structure according to claim 11, wherein the method for determining the parameters of the asymmetric PN junction thermoelectric couple structure comprises the following steps: calculating an integral mean value of electrical resistivity of a p-type semiconductor
Description
DESCRIPTION OF DRAWINGS
(1)
(2)
(3)
(4)
(5)
(6)
EMBODIMENT
(7) The technical schemes of the present invention are described below in combination with the drawings, the specific structure of PN junction thermoelectric couple and its material parameters.
(8) As shown in
(9) As shown in
(10) Step 1, calculating the integral mean value of electrical resistivity of the p-type semiconductor (
(11) (1) Calculating the integral mean value of electrical resistivity of the p-type semiconductor
(12)
where T.sub.h and T.sub.c are the hot-end and cold-end temperature of the PN junction thermoelectric couple respectively, and ρ.sub.p(T) is the electrical resistivity of the p-type semiconductor;
(13) (2) Calculating the integral mean value of electrical resistivity of the n-type semiconductor
(14)
where ρ.sub.n(T) is the electrical resistivity of the n-type semiconductor;
(15) (3) If
(16) Step 2, establishing the differential equations of the PN junction thermoelectric couple;
(17) (1) The energy conservation equation of the p-type semiconductor is:
∇.Math.(λ.sub.p(T)∇T.sub.p)=−ρ.sub.p(T)
where
(18) (2) The energy conservation equation of the n-type semiconductor is:
∇.Math.(λ.sub.n(T)∇T.sub.n)=−ρ.sub.n(T)
where T.sub.n is the temperature of the n-type semiconductor;
(19) (3) The energy conservation equation of the copper electrodes is:
∇.Math.(λ.sub.co∇T)=−ρ.sub.co
where λ.sub.0 and ρ.sub.co are the thermal conductivity and electrical resistivity of the copper electrodes respectively;
(20) (4) The energy conservation equation of the ceramic plates is:
∇.Math.(λ.sub.ce∇T)=0 (6)
where λ.sub.ce is the thermal conductivity of the ceramic plates;
(21) (5) In addition, the electrical field density vector of the p-type semiconductor and the n-type semiconductor is:
Ē=−∇ϕ+α∇T (7)
where Ē is the electrical field density vector, ϕ is the electric potential difference, and α is the Seebeck coefficient;
(22) (6) p-type semiconductor, n-type semiconductor, copper electrodes, and resistance follow the current conservation equations, which are:
(23)
where ρ is the material electrical resistivity;
(24) Step 3, as shown in
(25) (1) On the contact surface B between the p-type semiconductor and the bottom copper electrode and the contact surface F between the n-type semiconductor and the bottom copper electrode, the following equations are satisfied:
(26) The temperature of the bottom copper electrodes equals the temperature of the p-type semiconductor and the n-type semiconductor, that is:
T.sub.co|.sub.z=H.sub.
The heat conduction of the bottom copper electrodes equals the heat conduction of the p-type semiconductor and n-type semiconductor plus the Peltier heat of the p-type semiconductor and n-type semiconductor, that is:
(27)
where z=H.sub.1+H.sub.2 represents the coordinate axis positions of the contact surfaces B and F;
(28) (2) On the contact surface C between the p-type semiconductor and the top copper electrode and the contact surface E between the n-type semiconductor and the top copper electrode, the following equations are satisfied:
(29) The temperature of the top copper electrodes equals the temperature of the p-type semiconductor and n-type semiconductor, that is:
T.sub.co|.sub.z=H.sub.
The heat conduction of the top copper electrodes equals the heat conduction of the p-type semiconductor and n-type semiconductor plus the Peltier heat of the p-type semiconductor and n-type semiconductor, that is:
(30)
where z=H.sub.1+H.sub.2+H.sub.3 represents the coordinate axis positions of the contact surfaces C and E;
(31) (3) The current boundary conditions about the connection between the load resistance and the copper electrodes are:
(32) On the left end surface of the bottom copper electrode A and the left end surface of the resistance J, both A and J are set to be grounded, that is, the voltage is zero; on the right end surface of the bottom copper electrode G and the right end surface of the resistance I, G and I are set to be connected electrically, that is, the voltages are equal;
(33) (4) The temperature boundary conditions are:
(34) The contact surfaces of the PN junction thermoelectric couple with the environment are set as adiabatic boundary; the bottom surface of the bottom ceramic plate H is set as high temperature boundary, that is, the temperature of surface H is T.sub.H; and the top surface of the top ceramic plate D is set as low temperature boundary, that is, the temperature of surface D is T.sub.C.
(35) Step 4, determining an appropriate Δl which meets the condition of Δl<L/10; according to above differential equations and the settings of boundary conditions, the output voltage on both ends of the load resistance U.sub.L can be computed with the help of finite element software ANSYS; according to equation P=U.sub.L.sup.2/R.sub.L, calculating the overall output power of the PN junction thermoelectric couple P.sub.0 and P.sub.1 when i=0 and i=1; judging whether P.sub.0<P.sub.1, if so, i=i+1, returning to recalculate the overall output power of the PN junction thermoelectric couple P.sub.i, and judging whether P.sub.i<P.sub.i+1 again, ending the loop until P.sub.i≥P.sub.i+1; obtaining that when
(36) The used thermoelectric material of the PN junction thermoelectric couple in this example is BiSbTeSe based material, and the parameters of BiSbTeSe-based thermoelectric material of p-type semiconductor and n-type semiconductor are listed in Table 1.
(37) TABLE-US-00001 TABLE 1 Parameters of BiSbTeSe-based thermoelectric material of p-type semiconductor and n-type semiconductor parameter p-type semiconductor n-type semiconductor Seebeck 3.064 × 10.sup.−7T.sup.4 1.055 × 10.sup.−7T.sup.4 coefficient −4.976 × 10.sup.−4T.sup.3 + −1.639 × 10.sup.−4T.sup.3 + (μν/K) 0.287 × T.sup.2 9.549 × 10.sup.−2T.sup.2 −69.799 × T + 6253.741 −24.881T + 2303.862 Thermal 3.612 × 10.sup.−10T.sup.4 −2.469 × 10.sup.−10T.sup.4 conductivity −5.247 × 10.sup.−7T.sup.3 + +3.907 × 10.sup.−7T.sup.3 − (w/m .Math. K) 2.636 × 10.sup.−4T.sup.2 2.241 × 10.sup.−4T.sup.2 −5.156 × 10.sup.−2T + 3.420 +5.413 × 10.sup.−2T − 3.804 Electrical 4.429 × 10.sup.−8T.sup.4 1.317 × 10.sup.−8T.sup.4 resistivity −9.118 × 10.sup.−5T.sup.3 + −2.087 × 10.sup.−5T.sup.3 + (10.sup.−6Ω .Math. m) 6.777 × 10.sup.−2T.sup.2 1.236 × 10.sup.−2T.sup.2 −21.579T + 2526.630 −3.204T + 315.218
(38) In addition, the relative size parameters of PN junction and other parameters are listed in Table 2.
(39) TABLE-US-00002 TABLE 2 Size parameters of PN junction and other parameters Parameter value Height of ceramic plates H.sub.1 (mm) 0.8 Height of cooper electrodes H.sub.2 (mm) 0.2 Height of p-type and n-type semiconductors H.sub.3 1.4 (mm) Initial length of p-type and n-type semiconductors L 1.7 (mm) Spacing between p-type and n-type semiconductors 0.8 L.sub.s (mm) Width W (mm) 1.7 Length × Width × Height of load resistance (mm) 5 * 1 * 1 Thermal conductivity of ceramic plates λ.sub.ce (w/m .Math. K) 18 Thermal conductivity of copper electrodes λ.sub.co 397 (w/m .Math. K) Electrical resistivity of copper electrodes ρ.sub.co (Ω .Math. m) 1.75 × 10.sup.−8 Electrical resistivity of load resistance (Ω .Math. m) 1 × 10.sup.−5 Hot end temperature of PN junction T.sub.h (K) 500 Cold end temperature of PN junction T.sub.c (K) 300
(40) The integral mean value of electrical resistivity of the p-type semiconductor (
(41)
(42) The specific embodiment is described above in detail according to the technical schemes of the present invention. According to the technical schemes of the present invention, the person skilled in this art can propose a variety of mutually replaceable structure modes and implementation modes, without departing from the essence of the present invention. Therefore, the specific embodiment described above, and the drawings are only exemplary illustration of the technical solutions of the present invention, and should not be regarded as the whole of the present invention or as limitation to the technical schemes of the invention.