AN ASYMMETRICAL PN JUNCTION THERMOELECTRIC COUPLE STRUCTURE AND ITS PARAMETER DETERMINATION METHOD

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 .sub.p and an integral mean value of electrical resistivity of a n-type semiconductor .sub.n; determining a length relationship between the p-type semiconductor and the n-type semiconductor; establishing differential equations of PN junction thermoelectric couple structure; setting boundary conditions to calculate the Peltier heat of the p-type semiconductor and the n-type semiconductor; setting current boundary conditions to connect load resistance with copper electrodes; setting temperature boundary conditions to load the temperature, and calculating an output voltage at both ends of the load resistance to get an output power of the PN junction thermoelectric couple.

2. The method for determining the parameters of the asymmetric PN junction thermoelectric couple structure according to claim 1, further comprising the step: if .sub.p>.sub.n, setting the length of the p-type semiconductor L.sub.p as L+il and setting the length of the n-type semiconductor L.sub.n as Lil; if .sub.p<.sub.n, setting the length of the p-type semiconductor L.sub.p as Lil and setting the length of the n-type semiconductor L.sub.n as Lil; if .sub.p=.sub.n, setting the length of p-type semiconductor as being equal to the length of n-type semiconductor, i.e., L.sub.p=L.sub.p=L.

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 .sub.p>.sub.n and .sub.p<.sub.n includes selecting a value of l to meet the condition of l<L/10, calculating the overall output powers of the PN junction thermoelectric couple P.sub.0 and P.sub.1 when i=0, 1; determining whether P.sub.0<P.sub.1, and if so, i=i+1, returning to recalculate the overall output power of PN junction thermoelectric couple P.sub.i, and determining whether P.sub.i<P.sub.i+1 again, ending the loop until P.sub.iP.sub.i+1.

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 the a second bottom copper electrodes, 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|z=H.sub.1.sub.+H.sub.2=T.sub.P,N|z=H.sub.1.sub.+H.sub.2; the heat conduction of the first and second bottom copper electrodes equals the heat conduction of the p-type semiconductor and the n-type semiconductor plus the Peltier heat of the p-type semiconductor and n-type semiconductor, that is, $-{}_{\mathrm{co}}\frac{T_{\mathrm{co}}}{Z}{|}_{z=H_1+H_2}=-{}_{P,N}\frac{T_{P,N}}{Z}{.Math.}_{z=H_1+H_2}+{}_{P,N}T\stackrel{\_}{J_z}{|}_{z=H_1+H_2,}$ where z=H.sub.1+H.sub.2 represents the coordinate axis positions of the bottom contact surface of the p-type semiconductor and the bottom contact surface of the n-type semiconductor; on a top contact surface f the p-type semiconductor and a top contact surface of the n-type semiconductor, both in contact with a top copper electrodes, the temperature of the top copper electrodes equals the temperature of the p-type semiconductor and the n-type semiconductor, that is T.sub.co|z=H.sub.1.sub.+H.sub.2.sub.+H.sub.3=T.sub.P,N|z=H.sub.1.sub.+H.sub.2.sub.H.sub.3; the heat conduction of the top copper electrodes equals the heat conduction of the p-type semiconductor and the n-type semiconductor plus the Peltier heat of the p-type semiconductor and n-type semiconductor, that is, $-{}_{P,N}\frac{T_{P,N}}{Z}{|}_{z=H_1+H_2+H_3}+{}_{P,N}T\stackrel{\_}{J_z}{|}_{z=H_1+H_2+H_3}=-{}_{\mathrm{co}}\frac{T_{\mathrm{co}}}{Z}{|}_{z=H_1+H_2+H_3},$ where z=H.sub.1+H.sub.2+H.sub.3 represents the coordinate axis positions of the top contact surface of the p-type semiconductor and the top contact surface of the n-type semiconductor.

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 Lil, and the length of the n-type semiconductor L.sub.n is Lil, wherein t is the number of iterations to be determined, and l 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 is L.sub.s 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, 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.

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+il, and the length of the n-type semiconductor L.sub.n is Lil, wherein i is the number of iterations to be determined, and l 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.pL.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 .sub.p and an integral mean value of electrical resistivity of a n-type semiconductor .sub.n; determining a length relationship between the p-type semiconductor and the n-type semiconductor; establishing differential equations of PN junction thermoelectric couple structure; setting boundary conditions to calculate the Peltier heat of the p-type semiconductor and the n-type semiconductor; setting current boundary conditions to connect load resistance with copper electrodes; setting temperature boundary conditions to load the temperature, and calculating an output voltage at both ends of the load resistance to get an output power of the PN junction thermoelectric couple.

Description

DESCRIPTION OF DRAWINGS

[0017] FIG. 1 shows schematic diagram of the asymmetric PN junction thermoelectric couple structure;

[0018] FIG. 2 shows parameter calculation flow diagram of the asymmetric PN junction thermoelectric couple structure;

[0019] FIG. 3 shows diagram for defining the surface boundary conditions;

[0020] FIG. 4 shows relation diagram of the output current of PN junction thermoelectric couple with the length of semiconductor;

[0021] FIG. 5 shows relation diagram of the output voltage of PN junction thermoelectric couple with the length of semiconductor;

[0022] FIG. 6 shows relation diagram of the output power of PN junction thermoelectric couple with the length of semiconductor.

EMBODIMENT

[0023] 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.

[0024] As shown in FIG. 1, an asymmetric PN junction thermoelectric couple structure includes ceramic plates, copper electrodes, p-type semiconductor, and n-type semiconductor; the p-type semiconductor and the n-type semiconductor are connected in series by copper electrodes and sandwiched between two ceramic plates; the heights of ceramic plates, copper electrodes, and p-type semiconductor are H.sub.1, H.sub.2 and H.sub.3, respectively, and the height of n-type semiconductor is equal to the height of p-type semiconductor; said ceramic plates, copper electrodes, p-type semiconductor, and n-type semiconductor possess the same width of w; the length of the ceramic plates is 2L+2L.sub.s, where L.sub.s is the distance between the p-type semiconductor and the n-type semiconductor; the length of top copper electrode is 2L+L.sub.s, the length of the p-type semiconductor L.sub.p equals L+il, the length of the n-type semiconductor L.sub.n equals Lil, and the lengths of the two copper electrodes at the bottom end equal the length of the connected semiconductor plus L.sub.s/2, respectively; where L is the initial length of the p-type semiconductor and the n-type semiconductor, i is the number of iterations to be determined, and l is the length change value of the p-type semiconductor and the n-type semiconductor in each iteration calculation.

[0025] As shown in FIG. 2, specific processes of the method for determining the parameters of asymmetric PN junction thermoelectric couple structure are as follows:

[0026] Step 1, calculating the integral mean value of electrical resistivity of the p-type semiconductor (.sub.p) and the n-type semiconductor (.sub.n) and determining the length relationship between the p-type semiconductor and the n-type semiconductor;

[0027] (1) Calculating the integral mean value of electrical resistivity of the p-type semiconductor .sub.p;

[00003]$\begin{array}{cc}\stackrel{\_}{{}_p}=\frac{{}_{T_c}^{T_h}{}_p\left(T\right)\mathrm{dT}}{T_h-T_c}& \left(1\right)\end{array}$

where T.sub.h and T.sub.c are the hot-end and cold-end temperature of the PN junction thermoelectric couple respectively, and .sub.p(T) is the electrical resistivity of the p-type semiconductor;

[0028] (2) Calculating the integral mean value of electrical resistivity of the n-type semiconductor .sub.n;

[00004]$\begin{array}{cc}\stackrel{\_}{{}_n}=\frac{{}_{T_c}^{T_h}{}_n\left(T\right)\mathrm{dT}}{T_h-T_c}& \left(2\right)\end{array}$

where .sub.n(T) is the electrical resistivity of the n-type semiconductor; [0029] (3) If .sub.p>.sub.n, the length of the p-type semiconductor L.sub.p is set as L+il, and the length of the n-type semiconductor L.sub.n is set as Lil; if .sub.p<.sub.n, the length of the p-type semiconductor L.sub.p is set as Lil, and the length of the n-type semiconductor L.sub.n is set as L+il; if .sub.p=.sub.n, the length of p-type semiconductor is set to be equal to the length of the n-type semiconductor, i.e., L.sub.p=L.sub.p=L.

[0030] Step 2, establishing the differential equations of the PN junction thermoelectric couple;

[0031] (1) The energy conservation equation of the p-type semiconductor is:

.Math.(.sub.p(T)T.sub.p)=.sub.p(T)J.sup.2+.sub.p(T)JT.sub.p(3)

where J is the current density vector, T is the temperature, and T.sub.p is the temperature of the p-type semiconductor;

[0032] (2) The energy conservation equation of the n-type semiconductor is:

.Math.(.sub.n(T)T.sub.n)=.sub.n(T)J.sup.2+.sub.n(T)JT.sub.n(4)

where T.sub.n is the temperature of the n-type semiconductor;

[0033] (3) The energy conservation equation of the copper electrodes is:

.Math.(.sub.coT)=.sub.coJ.sup.2(5)

where .sub.0 and .sub.co are the thermal conductivity and electrical resistivity of the copper electrodes respectively;

[0034] (4) The energy conservation equation of the ceramic plates is:

.Math.(.sub.ceT)=0(6)

where .sub.ce is the thermal conductivity of the ceramic plates;

[0035] (5) In addition, the electrical field density vector of the p-type semiconductor and the n-type semiconductor is:

=+T(7)

where is the electrical field density vector, is the electric potential difference, and is the Seebeck coefficient;

[0036] (6) p-type semiconductor, n-type semiconductor, copper electrodes, and resistance follow the current conservation equations, which are:

[00005]$\begin{array}{cc}\stackrel{\_}{J}=\frac{1}{}\stackrel{\_}{E}& \left(8\right)\\ \stackrel{\_}{J}=0& \left(9\right)\end{array}$

where is the material electrical resistivity;

[0037] Step 3, as shown in FIG. 3, setting the boundary conditions for the surfaces A, B, C, D, E, F, G, H, I, J of the PN junction thermoelectric couple, where surfaces A, G, I, J are the voltage boundary and connect the thermoelectric couple with the load resistance in series; surfaces B, C, E, F are the Peltier heat boundary, the Peltier heat on the contact surfaces between the p-type semiconductor, the n-type semiconductor and the copper electrodes is calculated, and surfaces D, H are the temperature boundary, on two ends of which the temperature load is imposed;

[0038] (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:

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|z=H.sub.1.sub.+H.sub.2=T.sub.P,N|z=H.sub.1.sub.+H.sub.2(10)

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:

[00006]$\begin{array}{cc}-{}_{\mathrm{co}}\frac{T_{\mathrm{co}}}{Z}{|}_{z=H_1+H_2}=-{}_{P,N}\frac{T_{P,N}}{Z}{|}_{z=H_1+H_2}+{}_{P,N}T\stackrel{\_}{J_z}{|}_{z=H_1+H_2}& \left(11\right)\end{array}$

where z=H.sub.1+H.sub.2 represents the coordinate axis positions of the contact surfaces B and F;

[0039] (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:

The temperature of the top copper electrodes equals the temperature of the p-type semiconductor and n-type semiconductor, that is:

T.sub.co|z=H.sub.1.sub.+H.sub.2.sub.H.sub.3=T.sub.P,N|z=H.sub.1.sub.+H.sub.2.sub.H.sub.3(12)

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:

[00007]$\begin{array}{cc}-{}_{\mathrm{co}}\frac{T_{\mathrm{co}}}{Z}{|}_{z=H_1+H_2+H_3}=-{}_{P,N}\frac{T_{P,N}}{Z}{|}_{z=H_1+H_2+H_3}+{}_{P,N}T\stackrel{\_}{J_z}{|}_{z=H_1+H_2+H_3}& \left(13\right)\end{array}$

where z=H.sub.1+H.sub.2+H.sub.3 represents the coordinate axis positions of the contact surfaces C and E;

[0040] (3) The current boundary conditions about the connection between the load resistance and the copper electrodes are:

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;

[0041] (4) The temperature boundary conditions are:

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.

[0042] Step 4, determining an appropriate l which meets the condition of l<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.iP.sub.i+1; obtaining that when .sub.p>.sub.n, the length of the p-type semiconductor is L.sub.p=L+il, and the length of the n-type semiconductor is L.sub.n=Lil, or when .sub.p<.sub.n, the length of the p-type semiconductor is L.sub.p=Lil, and the length of the n-type semiconductor is L.sub.n=L+il.

[0043] 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.

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.7 T.sup.4 1.055 10.sup.7 T.sup.4 coefficient 4.976 10.sup.4 T.sup.3 + 0.287 T.sup.2 1.639 10.sup.4 T.sup.3 + 9.549 10.sup.2 T.sup.2 (v/K) 69.799 T + 6253.741 24.881T + 2303.862 Thermal .sub.3.612 10.sup.10 T.sup.4 2.469 10.sup.10 T.sup.4 conductivity 5.247 10.sup.7 T.sup.3 + 2.636 10.sup.4 T.sup.2 +3.907 10.sup.7 T.sup.3 2.241 10.sup.4 T.sup.2 (w/m .Math. K) 5.156 10.sup.2 T + 3.420 +5.413 10.sup.2 T 3.804 Electrical 4.429 10.sup.8 T.sup.4 1.317 10.sup.8 T.sup.4 resistivity 9.118 10.sup.5 T.sup.3 + 6.777 10.sup.2 T.sup.2 2.087 10.sup.5 T.sup.3 + 1.236 10.sup.2 T.sup.2 (10.sup.6 .Math. m) 21.579T + 2526.630 3.204T + 315.218

[0044] In addition, the relative size parameters of PN junction and other parameters are listed in Table 2.

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 (mm) 1.4 Initial length of p-type and n-type semiconductors L (mm) 1.7 Spacing between p-type and n-type semiconductors L.sub.s 0.8 (mm) Width W (mm) 1.7 Length Width Height of load resistance (mm) 5*1*1 Thermal conductivity of ceramic plates .sub.ce (w/m .Math. K) 18 Thermal conductivity of copper electrodes .sub.co (w/m .Math. K) 397 Electrical resistivity of copper electrodes .sub.co ( .Math. m) 1.75 10.sup.8 Electrical resistivity of load resistance ( .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

[0045] The integral mean value of electrical resistivity of the p-type semiconductor (.sub.p) and the n-type semiconductor (.sub.n) can be computed by equation (1) and equation (2) respectively; the calculation results are: .sub.p=4.1110.sup.5 .Math.m and .sub.n=1.3610.sup.5 .Math.m; because .sub.p>.sub.n, the length of the p-type semiconductor is L.sub.p=L+il, and the length of the n-type semiconductor is L.sub.n=Lil; l is selected as 0.1 mm for calculating the output parameters of the PN junction and further determining the length of the p-type semiconductor and n-type semi conductor.

[0046] FIG. 4, FIG. 5, and FIG. 6 show the relation diagrams of output current, output voltage, and output power of the PN junction thermoelectric couple with the length of the semiconductor, respectively. It can be observed that when i=5, the condition of P.sub.5P.sub.6 is satisfied, and the loop is ended. At this time, the output power of PN junction thermoelectric couple reaches the maximum value, that is, the finally determined length of the p-type semiconductor is L.sub.p=2.2 mm, and the length of the n-type semiconductor is L.sub.n=1.2 mm. Compared with the traditional PN junction thermoelectric couple structure (i=0), the output current and output voltage of the optimized PN junction are increased by 2.33%, and the output power of the optimized PN junction is increased by 4.71%, under the same amount of used thermoelectric materials.

[0047] 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.