JP7033292B2 - Thermoelectric property measuring device and thermoelectric property measuring method - Google Patents

Description

The present invention relates to a thermoelectric physical property measuring device and a thermoelectric physical property measuring method.

The Seebeck coefficient S as a thermoelectric property is obtained at both ends of the object to be measured when a temperature difference ΔT = Th—Tc (Th: temperature of the high temperature part, Tc: temperature of the low temperature part) is given to both ends of the object to be measured. Conventionally, the generated electromotive force is defined as Δv using the following equation.
S = Δv / ΔT ... (1)
Then, when the Seebeck coefficient S is obtained, a temperature difference ΔT is given to both ends of the object to be measured, the electromotive force Δv generated at both ends of the object to be measured is measured with a voltmeter, and the calculation is performed using the above equation (1). (See, for example, Patent Document 1).

Japanese Unexamined Patent Publication No. 2004-165233

However, the method of directly obtaining the Seebeck coefficient S from the electromotive force Δv has the following problems.
A voltmeter is used to measure the electromotive force Δv. The ideal condition for measuring the voltage between two points of an object to be measured with a voltmeter is that no current flows inside the voltmeter, that is, the two points are open ends. By increasing the internal resistance of the voltmeter, it is possible to reduce the current value so that it is close to the open end. However, the current value cannot be completely reduced to zero. Therefore, there is a limit to the measurement accuracy of the electromotive force Δv, and therefore there is a limit to the high accuracy of the calculation of the Seebeck coefficient S based on the above equation (1).

An object of the present invention is to provide a thermoelectric property measuring device and a thermoelectric property measuring method capable of obtaining a Seebeck coefficient S, that is, a thermoelectric property with higher accuracy.

The present invention provides the following in order to solve the above problems.
(1) Between a power source that applies a potential difference between one end and the other end of the object to be measured, a temperature difference generating portion that applies a temperature difference between the one end and the other end, and the one end and the other end. A current meter for measuring the value of the current flowing through the object, a voltmeter for measuring the voltage between the one end and the other end of the object to be measured, and a calculation unit, and the calculation unit is the object to be measured. When the length from the one end to the other end is l and the cross-sectional area orthogonal to the length direction is A, a potential difference ΔVA is added between the one end and the other end by the power _supply . Using the current _ΔIV ⁽²⁾ measured by the current meter at the time of calculation, the electric conductivity L ₁₁ ⁽²⁾ was obtained from the following equation.
L ₁₁ ⁽²⁾ = (l / A) (ΔIV ₍ ²⁾ / _ΔVA )
The voltage ΔV _V measured by the voltmeter when the potential difference ΔVA is applied _between the one end and the other end by the power supply and the current ΔIV _V ⁽⁴⁾ measured by the ammeter are used. Then, the electric conductivity L ₁₁ ⁽⁴⁾ was obtained from the following equation.
L ₁₁ ⁽⁴⁾ = (l / A) (ΔIV ₍ ⁴⁾ / ΔV _V )
Using the electric conductivity L ₁₁ ⁽²⁾ and the electric conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r was obtained from the following equation.
r = R ⁽²⁾ -R ⁽⁴⁾ = (1 / L ₁₁ ⁽²⁾ -1 / L ₁₁ ⁽⁴⁾ ) (l / A)
A current value measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generating portion without giving a potential difference between the one end and the other end. Using ΔIT ⁽²⁾ , obtain the _{thermoelectric} coefficient L ₁₂ ⁽²⁾ from the following equation.
L ₁₂ ⁽²⁾ = (l / A) (ΔIT ₍ ²⁾ / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected by using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation.
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Using the electric conductivity L ₁₁ ⁽⁴⁾ and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ , the Seebeck coefficient S is obtained from the following equation.
S = L ₁₂ ⁽⁴⁾ / L ₁₁ ⁽⁴⁾
Thermoelectric property measuring device.

As a further aspect, the present invention provides the following in order to solve the above problems.
( 2 ) Between a power source that applies a potential difference between one end and the other end of the object to be measured, a temperature difference generating portion that applies a temperature difference between the one end and the other end, and the one end and the other end. A current meter for measuring the value of the current flowing through the object, a voltmeter for measuring the voltage between the one end and the other end of the object to be measured, and a calculation unit, and the calculation unit is the object to be measured. When the length from the one end to the other end is l and the cross-sectional area orthogonal to the length direction is _A , a potential difference ΔVA is added between the one end and the other end by the power supply. Using the current _ΔIV ⁽²⁾ measured by the current meter at the time of calculation, the electric conductivity L ₁₁ ⁽²⁾ was obtained from the following equation.
L ₁₁ ⁽²⁾ = (l / A) ( _ΔIV ⁽²⁾ / _ΔVA )
The voltage ΔV _V measured by the voltmeter when the potential difference _ΔVA is applied between the one end and the other end by the power supply and the current ΔIV _V ⁽⁴⁾ measured by the ammeter are used. Then, the electric conductivity L ₁₁ ⁽⁴⁾ was obtained from the following equation.
L ₁₁ ⁽⁴⁾ = (l / A) (ΔIV ⁽⁴⁾ / _{ΔV V )}
Using the electric conductivity L ₁₁ ⁽²⁾ and the electric conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r was obtained from the following equation.
r = R ⁽²⁾ -R ⁽⁴⁾ = (1 / L ₁₁ ⁽²⁾ -1 / L ₁₁ ⁽⁴⁾ ) (l / A)
The current measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generating portion without giving a potential difference between the one end and the other end. Using the value _ΔIT ⁽² ), obtain the thermoelectric coefficient L ₁₂ ⁽²⁾ from the following equation.
L ₁₂ ⁽²⁾ = (l / A) ( _ΔIT ⁽²⁾ / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected by using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation.
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Thermoelectric property measuring device.

As another aspect, the present invention provides the following in order to solve the above problems.
( 3 ) Between a power source that applies a potential difference between one end and the other end of the object to be measured, a temperature difference generating portion that applies a temperature difference between the one end and the other end, and the one end and the other end. In a thermoelectric property measuring device including a current meter for measuring a current value flowing through a current meter and a voltmeter for measuring a voltage between the one end and the other end of the measurement object, the one end of the measurement object is provided. When the potential difference _ΔVA is applied between the one end and the other end by the power source when the length from the other end to the other end is l and the cross-sectional area orthogonal to the length direction is A. Using the current _ΔIV ⁽²⁾ measured by the current meter, the electric conductivity L ₁₁ ⁽²⁾ was obtained from the following equation.
L ₁₁ ⁽²⁾ = (l / A) ( _ΔIV ⁽²⁾ / _ΔVA )
The voltage ΔV _V measured by the voltmeter when the potential difference _ΔVA is applied between the one end and the other end by the power supply and the current ΔIV _V ⁽⁴⁾ measured by the ammeter are used. Then, the electric conductivity L ₁₁ ⁽⁴⁾ was obtained from the following equation.
L ₁₁ ⁽⁴⁾ = (l / A) (ΔIV ⁽⁴⁾ / _{ΔV V )}
Using the electric conductivity L ₁₁ ⁽²⁾ and the electric conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r was obtained from the following equation.
r = R ⁽²⁾ -R ⁽⁴⁾ = (1 / L ₁₁ ⁽²⁾ -1 / L ₁₁ ⁽⁴⁾ ) (l / A)
The current measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generating portion without giving a potential difference between the one end and the other end. Using the value _ΔIT ⁽² ), obtain the thermoelectric coefficient L ₁₂ ⁽²⁾ from the following equation.
L ₁₂ ⁽²⁾ = (l / A) ( _ΔIT ⁽²⁾ / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected by using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation.
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Using the electric conductivity L ₁₁ ⁽⁴⁾ and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ , the Seebeck coefficient S is obtained from the following equation.
S = L ₁₂ ⁽⁴⁾ / L ₁₁ ⁽⁴⁾
Thermoelectric property measurement method.

As another aspect, the present invention provides the following in order to solve the above problems.
(4) Between a power source that applies a potential difference between one end and the other end of the object to be measured, a temperature difference generating portion that applies a temperature difference between the one end and the other end, and the one end and the other end. In a thermoelectric property measuring device including a current meter for measuring a current value flowing through a current meter and a voltmeter for measuring a voltage between the one end and the other end of the object to be measured, from the one end of the object to be measured. When the length to the other end is l and the cross-sectional area orthogonal to the length direction is _A , and the potential difference ΔVA is applied between the one end and the other end by the power source. Using the current _ΔIV ⁽²⁾ measured by the current meter, the electric conductivity L ₁₁ ⁽²⁾ was obtained from the following equation.
L ₁₁ ⁽²⁾ = (l / A) ( _ΔIV ⁽²⁾ / _ΔVA )
The voltage ΔV _V measured by the voltmeter when the potential difference _ΔVA is applied between the one end and the other end by the power supply and the current ΔIV _V ⁽⁴⁾ measured by the ammeter are used. Then, the electric conductivity L ₁₁ ⁽⁴⁾ was obtained from the following equation.
L ₁₁ ⁽⁴⁾ = (l / A) (ΔIV ⁽⁴⁾ / _{ΔV V )}
Using the electric conductivity L ₁₁ ⁽²⁾ and the electric conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r was obtained from the following equation.
r = R ⁽²⁾ -R ⁽⁴⁾ = (1 / L ₁₁ ⁽²⁾ -1 / L ₁₁ ⁽⁴⁾ ) (l / A)
The current measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generating portion without giving a potential difference between the one end and the other end. Using the value _ΔIT ⁽² ), obtain the thermoelectric coefficient L ₁₂ ⁽²⁾ from the following equation.
L ₁₂ ⁽²⁾ = (l / A) ( _ΔIT ⁽²⁾ / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected by using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation.
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Thermoelectric property measurement method.

According to the present invention, it is possible to provide a thermoelectric property measuring device and a thermoelectric property measuring method capable of obtaining a Seebeck coefficient S, that is, a thermoelectric physical property with higher accuracy.

It is a block diagram explaining the thermoelectric property measuring apparatus in 1st Embodiment. It is a flowchart which shows the method of obtaining the Seebeck coefficient S by 1st Embodiment. It is a flowchart which shows the method of obtaining the Seebeck coefficient S by the 2nd Embodiment. It is a graph which shows the result of having measured the current value ΔI by changing the potential difference _ΔVA in each temperature difference ΔT. It is a graph which shows the result of having calculated L ₁₂ from the y-intercept of the graph of FIG. 4 and L ₁₁ from the slope for each temperature difference ΔT. It is the result of obtaining the Seebeck coefficient S from the values of L ₁₁ and L ₁₂ in FIG. 5, the horizontal axis of (a) is the temperature difference ΔT, and the horizontal axis of (b) is the average temperature. The data of the IVA graph is fitted by linear regression, where (a) is the case where ΔT is 2K and (b) is the case where ΔT is _0.4K .

(First Embodiment)
(Explanation of the thermoelectric property measuring device 1)
FIG. 1 is a block diagram illustrating a thermoelectric physical characteristic measuring device 1 according to the first embodiment of the present invention. The thermoelectric property measuring device 1 of the present embodiment is a device for obtaining a Seebeck coefficient S as a thermoelectric property, and includes a measuring unit 10 and a calculation unit 20 as shown in the figure.

The measuring unit 10 includes a sample mounting unit 11 on which an object to be measured having a Seebeck coefficient S (hereinafter referred to as a sample 12) is placed, and one end 12a and the other end 12b of the sample 12 placed on the sample mounting unit 11. It is provided with a first circuit C1 for connecting the above. In the first circuit C1, an ammeter 13 and a first switch S1 provided between one end 12a of the sample 12 and the ammeter 13 are arranged.

The wiring portion extending from the ammeter 13 to the first switch S1 side in the first circuit C1 is branched in two directions. A first terminal a is provided on one of the branches, a second terminal b is provided on the other of the branches, and a power supply 14 is arranged between the second terminal b and the ammeter 13. ..
The first switch S1 can switch between the first terminal a and the second terminal b on the ammeter 13 side. When the first switch S1 is connected to the first terminal a side, the first circuit C1 is connected from one end 12a of the sample 12 to the other end 12b through the ammeter 13 without passing through the power supply 14. When the first switch S1 is connected to the second terminal b side, the first circuit C1 is connected from one end 12a of the sample 12 to the other end 12b through the power supply 14 and the ammeter 13.

Further, the measuring unit 10 includes a second circuit C2 for connecting one end 12a and the other end 12b of the sample 12, and the second circuit C2 is between the voltmeter 15 and the other end 12b of the sample and the voltmeter 15. The second switch S2 provided in the above is arranged.
Further, the measuring unit 10 also includes a temperature difference generating unit 16 that adds a temperature difference between one end 12a and the other end 12b of the sample 12.

As will be described in detail later, the arithmetic unit 20 will describe the one end 12a and the other end 12b measured by the ammeter 13 when the potential difference _ΔVA is applied between the one end 12a and the other end 12b of the sample 12 by the power supply 14. One end measured by the ammeter 13 when the first current value _ΔIV flowing between the two and the temperature difference ΔT is applied between one end 12a and the other end 12b of the sample 12 by the temperature difference generating unit 16. Using the second current value _ΔIT flowing between the 12a and the other end 12b, an operation for obtaining the Seebeck coefficient S or the like is performed.

(Calculation method of Seebeck coefficient S)
Generally, the Seebeck coefficient S is calculated by giving a temperature difference ΔT to both ends of the sample 12, measuring the electromotive force Δv generated at both ends of the sample 12, and using the following equation (1).

S = Δv / ΔT ... (1)

However, in the present embodiment, the calculation of the Seebeck coefficient S using the above equation (1) is not performed. Hereinafter, how to obtain the Seebeck coefficient S according to the present embodiment will be described.

FIG. 2 is a flowchart showing how to obtain the Seebeck coefficient S according to the first embodiment.
[1] First, the sample 12 is placed on the sample placing portion 11 (step S1).
In the present embodiment, the sample 12 to be measured with the Seebeck coefficient S is rectangular, and the length l between one end 12a and the other end 12b and the cross-sectional area A in the direction orthogonal to the length direction are constant. be. However, not limited to this, the Seebeck coefficient S can be calculated even if the cross-sectional areas A are different in the length direction.

[2] Obtain the electrical conductivity L ₁₁ (step S2)
The electric conductivity L ₁₁ is a physical quantity indicating how easy it is for an electric current to flow when a potential difference is applied to an object (easiness of electric conduction in a substance). The electric conductivity L ₁₁ is obtained from the following equation (2) by giving a potential difference _ΔVA to both ends of the sample 12, measuring the current value _ΔIV flowing through the sample 12, and using these values. At this time, the temperature difference may not be given to both ends of the sample 12 (ΔT = 0).

L ₁₁ = (l / _A ) ( _ΔIV / ΔVA) ... (2)

Here, when measuring the electric conductivity L ₁₁ , the influence of the contact resistance r may or may not be included depending on the measuring method. In the present embodiment, the contact resistance r is a resistance generated at the contact portion when the sample 12 and the wiring constituting the first circuit C1 and the second circuit C2 are brought into contact with each other.
In order to calculate the Seebeck coefficient S with higher accuracy, it is necessary to obtain the electric conductivity L ₁₁ excluding the influence of the contact resistance r.

[2-1] The electrical conductivity L ₁₁ ⁽²⁾ including the influence of the contact resistance r is obtained by the two-terminal method (step S2-1).
The electric conductivity L ₁₁ ⁽²⁾ including the influence of the contact resistance r by the two-terminal method is obtained as follows.
First, the first switch S1 is connected to the second terminal b, and the second switch S2 is turned off. The power supply 14 is turned on so that _ΔVA is applied to the first circuit C1. In this state, the current value _ΔIV ⁽²⁾ flowing through the ammeter 13 is measured.
Information on the length l of the sample 12 and the cross-sectional area A of the sample 12 is input to the calculation unit 20. Using these values and the current value _ΔIV ⁽²⁾ measured as described above, the calculation unit 20 calculates the electric conductivity L ₁₁ ⁽²⁾ using the following equation (2-1). ..

L ₁₁ ⁽²⁾ = (l / A) ( _ΔIV ⁽²⁾ / _ΔVA ) ... (2-1)

[2-2] The electrical conductivity L ₁₁ ⁽⁴⁾ excluding the influence of the contact resistance r is obtained by the 4-terminal method (step S2-2).
The electric conductivity L ₁₁ ⁽⁴⁾ excluding the influence of the contact resistance r by the four-terminal method is obtained as follows.
First, the first switch S1 is connected to the second terminal b, and the second switch S2 is turned on. The power supply 14 is turned on so that _ΔVA is applied to the first circuit C1. In this state, the voltage ΔV _V is measured by the voltmeter 15, and the current value _ΔIV ⁽⁴⁾ is measured by the ammeter 13.

Similar to the electric conductivity L ₁₁ ⁽²⁾ , the arithmetic unit 20 uses the voltage ΔV _V and the current value _ΔIV ⁽⁴⁾ measured as described above to generate electricity according to the following equation (2-2). Calculate the conductivity L ₁₁ ⁽⁴⁾ .

L ₁₁ ⁽⁴⁾ = (l / A) (ΔIV ⁽⁴⁾ / _{ΔV V )} ... (2-2)

The order of steps S2-1 and step S2-2 may be reversed.

[3] Obtaining the contact resistance r (step S4)
Next, the arithmetic unit 20 uses the following equation (3) to obtain the electric conductivity L ₁₁ ⁽²⁾ by the two-terminal measurement method and the electric conductivity L ₁₁ ⁽⁴⁾ obtained by the four-terminal measurement method. From, the contact resistance r is calculated.

r = R ⁽²⁾ -R ⁽⁴⁾ = (1 / L ₁₁ ⁽²⁾ -1 / L ₁₁ ⁽⁴⁾ ) (l / A) ... (3)

[4] Obtain the thermoelectric coefficient (thermoelectric response coefficient, thermoelectric response function, thermoelectric constant) L ₁₂ (step S4).
Next, the calculation unit 20 obtains the thermoelectric coefficient L ₁₂ . The thermoelectric coefficient L ₁₂ is a physical quantity indicating how easily a current flows when a temperature difference is applied to an object. The thermoelectric coefficient L ₁₂ does not give a potential difference to both ends of the sample 12 ( _ΔVA = 0), gives a temperature difference ΔT to both ends of the sample 12 using the temperature difference generating unit 16, and determines the current value _ΔIT flowing through the sample 12. It is measured and obtained from the following equation (4).

L ₁₂ = (l / A) ( _ΔIT / ΔT) ... (4)

Here, too, when measuring the thermoelectric coefficient L12, the influence of the contact resistance r may or may not be included depending _on the measuring method. In order to calculate the Seebeck coefficient S with higher accuracy, it is necessary to obtain the thermoelectric coefficient L ₁₂ which does not include the influence of the contact resistance r.

[4-1] The thermoelectric coefficient L ₁₂ ⁽²⁾ including the influence of the contact resistance r is obtained by the two-terminal method (step S4-1).
The thermoelectric coefficient L ₁₂ ⁽²⁾ by the two-terminal method is obtained as follows.
A temperature difference ΔT is added to both ends of the sample 12.
Then, the first switch S1 is connected to the first terminal a, and the second switch S2 is turned off. In this state, _ΔIT ⁽²⁾ flowing through the ammeter 13 is measured.

Next, the calculation unit 20 calculates the thermoelectric coefficient L ₁₂ ⁽²⁾ using the following equation (4-1).

L ₁₂ ⁽²⁾ = (l / A) ( _ΔIT ⁽²⁾ / ΔT) ... (4-1)

[4-2] Calculation of thermoelectric coefficient L ₁₂ ⁽⁴⁾ not including the influence of contact resistance (step S4-2)
Using the contact resistance r obtained as described above, the thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected by the following equation (4-2) to obtain the thermoelectric coefficient L ₁₂ ⁽⁴⁾ not including the influence of the contact resistance r.

L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾ ... (4-2)

[5] Calculation of Seebeck coefficient S (step S5)
Next, using the electric conductivity L ₁₁ ⁽⁴⁾ obtained as described above and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ , the arithmetic unit 20 obtains the Seebeck coefficient S from the following equation (5).

S = L ₁₂ ⁽⁴⁾ / L ₁₁ ⁽⁴⁾ ... (5)

Further, the arithmetic unit 20 also obtains the electric conductivity L ₁₁ ⁽⁴⁾ and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ obtained as described above by the following equation (6) for the power factor PF which is the generated power per unit temperature. It can be obtained by using.

PF = (L ₁₂ ⁽⁴⁾ ) ² / L ₁₁ ⁽⁴⁾ ... (6)

In addition, this measurement is

J = L ₁₁ x E + L ₁₂ (-dT / dx) ... (7)

Is possible as long as is satisfied. J is the current density, E is the electric field, and l is the length of the sample 12. In order for equation (7) to hold, it is important not to make dT / dl too large. This is because when dT / dl is large, non-linearity appears in the JE curve. Further, when the situation in which the equation (7) does not hold, it is possible to confirm whether or not there is a problem in the measurement by confirming the linearity of the JE curve. In addition, dT / dx indicates the temperature gradient in the length direction of the sample 12.

(Second Embodiment)
In the first embodiment, the Seebeck coefficient S was obtained in consideration of the influence of the contact resistance r. However, since the contact resistance r has a slight influence as described above, the contact resistance r can be ignored. FIG. 3 is a flowchart showing how to obtain the Seebeck coefficient S according to the second embodiment.
The thermoelectric property measuring device of the second embodiment has only the configuration of the first circuit C1 of the first embodiment, and performs only two-point measurement. Since each part is the same as that of the first embodiment, the same reference numerals are given and the description thereof will be omitted.

[1] First, the sample 12 is placed on the sample placing portion 11 (step S21).
[2] Obtain the electrical conductivity L ₁₁ (step S22).
The first switch S1 is connected to the second terminal b. The power supply 14 is turned on so that ΔV is applied to the first circuit C1. In this state, the current value _ΔIV flowing through the ammeter 13 is measured. The calculation unit 20 calculates the electric conductivity L ₁₁ by the following equation (2) using this current value _ΔIV .

L ₁₁ = (l / A) ( _ΔIV / ΔV) ... (2)

[3] Obtain the thermoelectric coefficient L ₁₂ (step S23).
Next, the thermoelectric coefficient L ₁₂ is obtained. The thermoelectric coefficient L ₁₂ does not give a potential difference to both ends of the sample 12 (ΔV = 0), gives a temperature difference ΔT to both ends of the sample 12 using the temperature difference generating unit 16, and measures the current value _ΔIT flowing through the sample 12. do. The calculation unit 20 calculates the thermoelectric coefficient L ₁₂ by the following equation (4) using this current value _ΔIT .

L ₁₂ = (l / A) ( _ΔIT / ΔT) ... (4)

[4] Calculation of Seebeck coefficient S (step S24)
Next, using the electric conductivity L ₁₁ obtained as described above and the thermoelectric coefficient L ₁₂ , the arithmetic unit 20 obtains the Seebeck coefficient S from the following equation.

S = L ₁₂ / L ₁₁ ... (5)

Substituting the equations (2) and (4) into the equation (5) gives the following.

S = ( _ΔIT · ΔV) / ( _ΔIV · ΔT) ... (5-2)

Therefore, the calculation unit 20 can directly obtain the Seebeck coefficient S from the current value _ΔIV and the current value _ΔIT without calculating the electric conductivity L ₁₁ and the thermoelectric coefficient L ₁₂ .
Further, the arithmetic unit 20 can also obtain the power factor PF by the following equation (6) by using the electric conductivity L ₁₁ and the thermoelectric coefficient L ₁₂ obtained as described above as in the first embodiment.

PF = (L ₁₂ ) ² / L ₁₁ ... (6)

(Effect of embodiment)
[1] As described above, conventionally, the Seebeck coefficient S is obtained by the equation (1) S = Δv / ΔT using the electromotive force Δv measured by the voltmeter.
However, according to the present embodiment, as described above, the Seebeck coefficient S is of the formula (5) S = L ₁₂ / L ₁₁ or the formula (5-2) S = ( _ΔIT · ΔV) / ( _ΔIV · ΔT). It is expressed as.
Here, for example, in the case of Keysight's B2911A and precision source / measure unit, which will be described later, the minimum measurement resolution as an ammeter is 10 fA, and the minimum measurement resolution as a voltmeter is 100 nV.
Therefore, if noise countermeasures are properly taken, the system of Seebeck coefficient S calculated using the current value measured by the equation (5-2) is the voltage value measured by the conventional equation (1). The accuracy of the current measurement is guaranteed to be ¹⁰⁷ times higher than that of the Seebeck coefficient S obtained in.
Therefore, according to the present embodiment, the Seebeck coefficient is obtained with high accuracy as compared with the case where Δv measured by the voltmeter is used as the value directly used when the Seebeck coefficient S is obtained as in the equation (1). Can be done.

In the first embodiment, when L ₁₁ ⁽⁴⁾ is obtained, the following equation,
L ₁₁ ⁽⁴⁾ = (l / A) (ΔIV ⁽⁴⁾ / _{ΔV V )} ... (2-2)
As shown in, _ΔVV , which is a measured value of the voltmeter 15, is used. However, in L ₁₁ ⁽⁴⁾ , the following equation for obtaining the contact resistance r,
r = R ⁽²⁾ -R ⁽⁴⁾ = (1 / L ₁₁ ⁽²⁾ -1 / L ₁₁ ⁽⁴⁾ ) (l / A)
It is used to substitute for.
The contact resistance r is the following formula,
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾ ... (4-2)
The contact resistance r is very small as compared with the resistance value R ⁽⁴⁾ of the sample 12 obtained by the 4-terminal method, although it is used to improve the accuracy of obtaining L ₁₂ ⁽⁴⁾ . The influence of the contact resistance r in 4-2) is not large in the first place.
In the present embodiment, the influence of the contact resistance r is taken into consideration in order to obtain the Seebeck coefficient S with higher accuracy, and ΔV _V is a measured value of the voltmeter 15 used when obtaining the contact resistance r having a small influence. Even if some errors are included in the above equation, the influence on the measurement of the Seebeck coefficient S is very small as compared with the above equation (1).
Therefore, the Seebeck coefficient S can be obtained with higher accuracy than when the above equation (1) is used.

Further, since the resolution of the Seebeck coefficient is improved by improving the measurement accuracy of the Seebeck coefficient S, it is possible to measure the distribution of the Seebeck coefficient in the plane in one material, for example.

[2] According to the present embodiment, the thermoelectric coefficient L ₁₂ can also be obtained without using the measured value by the voltmeter. Therefore, according to the present embodiment, the thermoelectric coefficient L ₁₂ can also be obtained with high accuracy.

[3] Further, it is possible to improve the accuracy of not only the Seebeck coefficient S but also the power factor PF of the thermoelectric material.

Hereinafter, an example in which the thermoelectric property is actually measured using the thermoelectric property measuring device 1 of the second embodiment will be described. As the thermoelectric property measuring device 1 of the example, B2911A manufactured by Keysight Co., Ltd. and a precision source / measure unit were used as the ammeter 13 and the power supply unit 14. This unit can switch between 2-terminal measurement and 4-terminal measurement with one unit. The performance of this unit is shown below.
Minimum power resolution: 10fA / 100nV
Minimum measurement resolution: 10fA / 100nV
Maximum output: 210V, 3A DC / 10.5A pulse Further, the temperature difference generating unit 16 can perform heating control (Th) by a temperature controller and constant temperature control (Tc) at room temperature by water cooling. As the thermoelectric material as a sample for measuring the thermoelectric characteristics, Mg ₂ Si having a size of 2 × 2 × 11.6 mm was used.

The thermoelectric property measurement using the thermoelectric property measuring device 1 was performed as follows.
The sample 12 is placed on the sample mounting portion 11, the first switch S1 is connected to the second terminal b, the power supply 14 is turned on, and the temperature difference generating portion 16 is applied to the first circuit C1 while applying the potential difference _VA . Was used to give a temperature difference ΔT to both ends of the sample 12.
In the example, the current value ΔI was measured by changing the potential difference _ΔVA while keeping the temperature difference ΔT constant. The constant temperature difference ΔT is in eight stages of 2,3,4,5,6,7,8,9K. The measurement results are shown in FIG.

As shown in the figure, the slope of the ΔI− _ΔVA straight line is substantially constant regardless of the temperature difference ΔT, but as the temperature difference ΔT increases, the ΔI− _ΔVA straight line translates downward in the figure, that is, y. The intercept (ΔI section, ΔI when _ΔVA = 0) is smaller.

As described above, L ₁₁ and L ₁₂ are expressed by the formula (2) L ₁₁ = (l / A) ( _ΔIV / ΔV) and the formula (4) L ₁₂ = (l / A) ( _ΔIT / ΔT). Therefore, L ₁₁ was calculated from the slope of the graph of FIG. 4 and L ₁₂ was calculated from the y-intercept at each temperature difference ΔT. The results are shown in FIG. In the examples, _ΔIV and _ΔIT in the formulas (2) and (4) are measured at the same time and are represented by ΔI.

FIG. 6 shows the result of obtaining the Seebeck coefficient S from the values of L ₁₁ and L ₁₂ in FIG. The horizontal axis of FIG. 6A is the temperature difference ΔT, and the horizontal axis of FIG. 6B is the average temperature. Similar results are obtained in (a) and (b).
In the embodiment, the low temperature portion of the sample 12 is clamped to a room temperature of 18.7 ° C., and the heater side is heated and controlled to generate a temperature difference ΔT. The average temperature is (18.7 + 20.7) /2+273.15=292.85K when, for example, ΔT = 2 ° C.

As shown in FIG. 6, in the vicinity of the average temperature of about 293 to 296 K, the Seebeck coefficient S of the example was about −350 to 325 μV / K.

It should be noted that the accuracy can be further improved by performing linear regression processing on the measured data.
FIG. 7 shows the data of the IVA graph fitted by linear regression. FIG. _7A is a case where ΔT is 2K, and FIG. 7B is a case where ΔT is 0.4K.
As shown in the figure, there are variations such as noise in the data points, and in L12 represented by the equation ( ₄ ) L12 = (l / A) ( _ΔIT / ΔT), the temperature difference ΔT becomes smaller. Since the change in _ΔIT near the y-intercept is also small, it becomes difficult to calculate L ₁₂ with high accuracy.
In such a case, the accuracy of the y-intercept and the slope can be improved by performing the linear regression processing. Generally, the error (ERR) has a relationship of ERR∝1 / √ (number of measurements). For example, when 2500 points are measured, since there are points, it is possible to obtain 50 times the accuracy as compared with the case where one y-intercept is measured.

The conventional Seebeck coefficient evaluation device also performs averaging processing, but the voltage obtained for a certain temperature difference is one, and the accuracy is improved by repeating this measurement a plurality of times. Therefore, it is common to perform the measurement less than 2500 measurement points.
In the example, 2500 points of current density measurement under each electric field were performed while changing the applied electric field for a certain temperature difference. In the embodiment, the measurement of 2500 points is performed once, but the accuracy can be further improved by performing the measurement of 2500 points a plurality of times. In addition, since the number of measurement points is a problem in setting the instrument, the accuracy can be improved by utilizing a measuring instrument that can obtain a larger number of points or a plurality of measuring instruments.
By the way, the standard error obtained in the linear regression processing is the accuracy of this measurement, and the standard error is as follows. In the example, the measurement is performed 2500 times.

As described above, according to this embodiment, the standard error of the slope a of the IV straight line is on the order of ^10-5 , and the standard error of the I-intercept (V = 0) b is on the order of ^10-8 , 0.4K. Even if the temperature difference is as small as that, the standard error is extremely small, and the slope a and the I section b can be obtained with high accuracy.

1 Thermoelectric property measuring device 10 Measuring unit 11 Sample mounting unit 12 Sample 12a One end 12b Other end 13 Ammeter 14 Power supply 15 Voltmeter 16 Temperature difference generator 20 Calculation unit C1 1st circuit C2 2nd circuit a terminal b terminal r Contact resistance

Claims (4)

A power supply that applies a potential difference between one end and the other end of the object to be measured,
A temperature difference generating portion that adds a temperature difference between the one end and the other end,
An ammeter that measures the value of the current flowing between one end and the other end ,
A voltmeter that measures the voltage between the one end and the other end of the object to be measured,
With a calculation unit,
The arithmetic unit
When the length from one end to the other end of the measurement object is l and the cross-sectional area orthogonal to the length direction is A,
Using the current _ΔIV ⁽²⁾ measured by the ammeter when the potential difference ΔVA was applied _between the one end and the other end by the power source, the electric conductivity L ₁₁ ⁽ 2) was calculated from the following equation. ⁾ _
L ₁₁ ⁽²⁾ = (l / A) (ΔIV ₍ ²⁾ / _ΔVA )
The voltage ΔV _V measured by the voltmeter when the potential difference ΔVA is applied _between the one end and the other end by the power supply and the current ΔIV _V ⁽⁴⁾ measured by the ammeter are used. Then, the electric conductivity L ₁₁ ⁽⁴⁾ was obtained from the following equation.
L ₁₁ ⁽⁴⁾ = (l / A) (ΔIV ₍ ⁴⁾ / ΔV _V )
Using the electric conductivity L ₁₁ ⁽²⁾ and the electric conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r was obtained from the following equation.
r = R ⁽²⁾ -R ⁽⁴⁾ = (1 / L ₁₁ ⁽²⁾ -1 / L ₁₁ ⁽⁴⁾ ) (l / A)
A current value measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generating portion without giving a potential difference between the one end and the other end. Using ΔIT ⁽²⁾ , obtain the _{thermoelectric} coefficient L ₁₂ ⁽²⁾ from the following equation.
L ₁₂ ⁽²⁾ = (l / A) (ΔIT ₍ ²⁾ / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected by using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation.
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Using the electric conductivity L ₁₁ ⁽⁴⁾ and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ , the Seebeck coefficient S is obtained from the following equation.
S = L ₁₂ ⁽⁴⁾ / L ₁₁ ⁽⁴⁾
Thermoelectric property measuring device. A power supply that applies a potential difference between one end and the other end of the object to be measured,
A temperature difference generating portion that adds a temperature difference between the one end and the other end,
An ammeter that measures the value of the current flowing between one end and the other end,
A voltmeter that measures the voltage between the one end and the other end of the object to be measured,
With a calculation unit,
The arithmetic unit
When the length from one end to the other end of the measurement object is l and the cross-sectional area orthogonal to the length direction is A,
Using the current _ΔIV ^{(2) measured by the ammeter when the potential difference ΔVA was applied between the one end and the other end by the power source, the electric conductivity L 11 (2)} _{was calculated} ^from the following equation. ⁾
L ₁₁ ⁽²⁾ = (l / A) ( _ΔIV ⁽²⁾ / _ΔVA )
The voltage ΔV _V measured by the voltmeter when the potential difference _ΔVA is applied between the one end and the other end by the power supply and the current ΔIV _V ⁽⁴⁾ measured by the ammeter are used. Then, the electric conductivity L ₁₁ ⁽⁴⁾ was obtained from the following equation.
L ₁₁ ⁽⁴⁾ = (l / A) (ΔIV ⁽⁴⁾ / _{ΔV V )}
Using the electric conductivity L ₁₁ ⁽²⁾ and the electric conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r was obtained from the following equation.
r = R ⁽²⁾ -R ⁽⁴⁾ = (1 / L ₁₁ ⁽²⁾ -1 / L ₁₁ ⁽⁴⁾ ) (l / A)
The current measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generating portion without giving a potential difference between the one end and the other end. Using the value _ΔIT ⁽² ), obtain the thermoelectric coefficient L ₁₂ ⁽²⁾ from the following equation.
L ₁₂ ⁽²⁾ = (l / A) ( _ΔIT ⁽²⁾ / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected by using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation.
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Thermoelectric property measuring device. A power supply that applies a potential difference between one end and the other end of the object to be measured,
A temperature difference generating portion that adds a temperature difference between the one end and the other end,
An ammeter that measures the value of the current flowing between one end and the other end,
A voltmeter that measures the voltage between the one end and the other end of the object to be measured,
In a thermoelectric property measuring device equipped with
When the length from one end to the other end of the measurement object is l and the cross-sectional area orthogonal to the length direction is A,
Using the current _ΔIV ^{(2) measured by the ammeter when the potential difference ΔVA was applied between the one end and the other end by the power source, the electric conductivity L 11 (2)} _{was calculated} ^from the following equation. ⁾
L ₁₁ ⁽²⁾ = (l / A) ( _ΔIV ⁽²⁾ / _ΔVA )
The voltage ΔV _V measured by the voltmeter when the potential difference _ΔVA is applied between the one end and the other end by the power supply and the current ΔIV _V ⁽⁴⁾ measured by the ammeter are used. Then, the electric conductivity L ₁₁ ⁽⁴⁾ was obtained from the following equation.
L ₁₁ ⁽⁴⁾ = (l / A) (ΔIV ⁽⁴⁾ / _{ΔV V )}
Using the electric conductivity L ₁₁ ⁽²⁾ and the electric conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r was obtained from the following equation.
r = R ⁽²⁾ -R ⁽⁴⁾ = (1 / L ₁₁ ⁽²⁾ -1 / L ₁₁ ⁽⁴⁾ ) (l / A)
The current measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generating portion without giving a potential difference between the one end and the other end. Using the value _ΔIT ⁽² ), obtain the thermoelectric coefficient L ₁₂ ⁽²⁾ from the following equation.
L ₁₂ ⁽²⁾ = (l / A) ( _ΔIT ⁽²⁾ / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected by using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation.
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Using the electric conductivity L ₁₁ ⁽⁴⁾ and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ , the Seebeck coefficient S is obtained from the following equation.
S = L ₁₂ ⁽⁴⁾ / L ₁₁ ⁽⁴⁾
Thermoelectric property measurement method. A power supply that applies a potential difference between one end and the other end of the object to be measured,
A temperature difference generating portion that adds a temperature difference between the one end and the other end,
An ammeter that measures the value of the current flowing between one end and the other end,
A voltmeter that measures the voltage between the one end and the other end of the object to be measured,
In a thermoelectric property measuring device equipped with
When the length from one end to the other end of the measurement object is l and the cross-sectional area orthogonal to the length direction is A,
Using the current _ΔIV ^{(2) measured by the ammeter when the potential difference ΔVA was applied between the one end and the other end by the power source, the electric conductivity L 11 (2)} _{was calculated} ^from the following equation. ⁾
L ₁₁ ⁽²⁾ = (l / A) ( _ΔIV ⁽²⁾ / _ΔVA )
The voltage ΔV _V measured by the voltmeter when the potential difference _ΔVA is applied between the one end and the other end by the power supply and the current ΔIV _V ⁽⁴⁾ measured by the ammeter are used. Then, the electric conductivity L ₁₁ ⁽⁴⁾ was obtained from the following equation.
L ₁₁ ⁽⁴⁾ = (l / A) (ΔIV ⁽⁴⁾ / _{ΔV V )}
Using the electric conductivity L ₁₁ ⁽²⁾ and the electric conductivity L ₁₁ ⁽⁴⁾ , the contact resistance r was obtained from the following equation.
r = R ⁽²⁾ -R ⁽⁴⁾ = (1 / L ₁₁ ⁽²⁾ -1 / L ₁₁ ⁽⁴⁾ ) (l / A)
The current measured by the ammeter when the temperature difference ΔT is applied between the one end and the other end by the temperature difference generating portion without giving a potential difference between the one end and the other end. Using the value _ΔIT ⁽² ), obtain the thermoelectric coefficient L ₁₂ ⁽²⁾ from the following equation.
L ₁₂ ⁽²⁾ = (l / A) ( _ΔIT ⁽²⁾ / ΔT)
The thermoelectric coefficient L ₁₂ ⁽²⁾ is corrected by using the contact resistance r, and the thermoelectric coefficient L ₁₂ ⁽⁴⁾ is obtained from the following equation.
L ₁₂ ⁽⁴⁾ = {(R ⁽⁴⁾ + r) / R ⁽⁴⁾ } L ₁₂ ⁽²⁾
Thermoelectric property measurement method.

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