Peltier coefficient measured by steady-state method and transient-state method

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Abstract

In the study of the physical effects of thermoelectric conversion, the Kelvin relationship is a bridge between the Seebeck coefficient and the Peltier coefficient, which brings the cooling and power generation performance of thermoelectric material into a unified evaluation system and dramatically simplifies the measurement process. However, some theoretical studies have shown that the Kelvin relationship is not satisfied under nonlinear conditions. Meanwhile, the measurement results of some experiments do not conform with this relationship. There have been few studies on accurately measuring the Peltier coefficient that is the basis of validating the Kelvin relation and studying the nonlinear thermoelectric effect. Based on this, a kind of Peltier coefficient measuring device with a cantilever beam structure is proposed in this work. We measure the difference between steady-state temperature and transient-state temperature on the sample surface and obtain the Peltier coefficients by the steady-state method and the transient-state method, respectively. By this measurement, we can obtain not only the Peltier coefficient of the material at low temperatures but also the interface resistance of the material. The Peltier coefficients measured by the steady-state method and the transient-state method are consistent with each other at various temperatures. Both of the variation trends with temperature are consistent with the temperature-dependent theoretical values calculated from the Kelvin relation. Our measured values are about 20% larger than the theoretical values.

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Authors and contacts

Corresponding author:Wang Jia-Fu,jasper@whut.edu.cn; Sun Zhi-Gang,sun_zg@whut.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant Nos. 12174297, 12204342) and the National Key Research and Development Program of China (Grant No. 2018YFE0111500).

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Cited By

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测量方法		研究对象	测量温度T/K	Peltier系数
测量方法		研究对象	测量温度T/K	测量值Π/mV	线性理论值αT/mV	相对误差P
直接法	外部热源补偿	Cu/Bi^[28]	291	16.1	16	0.6%
	测量热流	碲化铋热电模组^[29]	300	124.0±0.7	126	–1.6%
	测量热流	镍铝/镍铬^[23]	310	27.2±1.3	12.6	115.8%
	锁相热成像(LIT)	N型多晶硅^[24]	298	–72±10	–43^[25]	67.4%
		P型多晶硅^[24]	298	346±10	360^[30]	–3.9%
		含镍有机薄膜^[26]	298	–21.6	–23.5	–8.1%
间接法	测量电阻	金属薄膜界面^[31]	295	27.0	—	—
间接法	测量电压	(Bi, Sb)₂Te₃^[27]	300	31	55	–43.6%

DownLoad: CSV

测量温度 T/K	Joule热 Q_J/(10^–4W)	Fourier热 Q_F/(10^–3W)	Q_J/Q_F /%
100	0.357	1.33	2.69
140	0.510	2.24	2.28
180	0.756	3.27	2.31
220	1.07	4.59	2.34
260	1.48	6.00	2.47
300	1.88	7.33	2.56

DownLoad: CSV

测试温度T/K	不同测试电流I时的稳态温差∆T_std./K				Peltier系数Π_std./mV		界面电阻R_B/mΩ
测试温度T/K	–100 mA	+100 mA	–50 mA	+50 mA	±100 mA	±50 mA	±100 mA	±50 mA
100	0.47	–0.34	0.21	–0.19	–11.38	–11.23	16.49	13.78
140	0.92	–0.65	0.42	–0.36	–19.10	–19.02	28.71	27.24
180	1.56	–1.14	0.73	–0.62	–28.15	–28.10	38.83	39.78
220	2.39	–1.77	1.11	–0.96	–39.85	–39.66	49.89	51.37
260	3.35	–2.55	1.57	–1.38	–52.69	–52.63	58.79	56.42
300	4.17	–3.29	1.95	–1.77	–65.29	–65.22	61.03	46.41

DownLoad: CSV

测试温度T/K	不同测试电流I时的热源参数U_B/mV				Peltier系数Π_trans./mV		界面电阻R_B/mΩ
测试温度T/K	–100 mA	+100 mA	–50 mA	+50 mA	±100 mA	±50 mA	±100 mA	±50 mA
100	–12.41	–9.29	–11.36	–10.06	–10.85	–10.71	15.60	13.00
140	–20.32	–15.09	–18.87	–16.39	–17.71	–17.63	26.15	24.80
180	–30.82	–23.45	–28.98	–25.19	–27.14	–27.09	36.85	37.90
220	–42.99	–33.52	–40.5	–35.63	–38.26	–38.07	47.35	48.70
260	–59.00	–47.11	–55.85	–50.1	–53.06	–52.98	59.45	57.50
300	–70.06	–58.61	–66.49	–62.18	–64.34	–64.34	57.25	43.10

DownLoad: CSV

组别	稳态法Peltier系数Π_std./mV
组别	100 K	140 K	180 K	220 K	260 K	300 K
meas.0 (50 mA)	–11.38	–19.10	–28.15	–39.85	–52.69	–65.29
meas.0 (100 mA)	–11.23	–19.02	–28.10	–39.66	–52.63	–65.22
meas.1 (50 mA)	–11.06	–17.49	–27.89	–39.21	–55.62	–62.88
meas.1 (100 mA)	–11.15	–18.18	–26.51	–37.07	–56.12	–65.64
meas.2 (50 mA)	–11.09	–17.96	–26.98	–37.49	–53.61	–64.66
meas.2 (100 mA)	–10.69	–17.44	–28.07	–38.63	–54.89	–65.96
meas.3 (50 mA)	–10.88	–18.11	–27.60	–38.35	–54.90	–65.92
meas.3 (100 mA)	–10.93	–17.83	–27.88	–38.96	–52.15	–66.28
meas.4 (50 mA)	–10.93	–18.55	–27.27	–38.75	–54.13	–65.75
meas.4 (100 mA)	–10.99	–18.07	–28.45	–38.31	–54.30	–63.10
meas.5 (50 mA)	–11.00	–18.17	–26.65	–37.45	–54.26	–66.52
meas.5 (100 mA)	–11.00	–18.28	–27.99	–39.46	–55.16	–62.71
平均值/mV	–10.96	–18.00	–27.53	–38.42	–54.41	–65.01
标准差/mV	0.12	0.31	0.59	0.73	1.04	1.36
平均相对误差/%	1.23	2.20	2.00	1.95	1.80	1.69

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