handbook of modern sensors

3.9 Seebeck and Peltier Effects 89
For example, voltage as function of a temperature gradient for a T-type thermocouple
with a high degree of accuracy can be approximated by a second-order equation
V AB = a 0 + a 1 T + a 2 T 2 =−0.0543 + 4.094 × 10 −2 T + 2.874 × 10 −5 T 2 ; (3.92)
then, a differential Seebeck coefficient for the T-type thermocouple is
α T = dV AB
dT = a 1 + 2a 2 T = 4.094 × 10 −2 + 5.74810 −5 T. (3.93)
It is seen that the coefficient is a linear function of temperature. Sometimes, it is
called the sensitivity of a thermocouple junction. A reference junction which is kept
at a cooler temperature traditionally is called a cold junction and the warmer is a hot
junction. The Seebeck coefficient does not depend on the nature of the junction: Metals
may be pressed together, welded, fused, and so forth. What counts is the temperature
of the junction and the actual metals. The Seebeck effect is a direct conversion of
thermal energy into electric energy.
Table A.11 in the Appendix gives the values of thermoelectric coefficients and
volume resistivities for some thermoelectric materials. It is seen that to achieve the
best sensitivity, the junction materials should be selected with the opposite signs for
α and those coefficients should be as large as practical.
In 1826, A. C. Becquerel suggested using Seebeck’s discovery for temperature
measurements. Nevertheless, the first practical thermocouple was constructed
by Henry LeChatelier almost 60 years later [31]. He had found that the junction
of platinum and platinum–rhodium alloy wires produce “the most useful voltage.”
Thermoelectric properties of many combinations have been well documented and for
many years have been used for measuring temperature. Table A.10 (Appendix) gives
the sensitivities of some practical thermocouples (at 25 ◦ C) and Fig. 3.36 shows the
Seebeck voltages for the standard types of thermocouple over a broad temperature
range. It should be emphasized that a thermoelectric sensitivity is not constant over
the temperature range and it is customary to reference thermocouples at 0 ◦ C. In addition
to the thermocouples, the Seebeck effect also is employed in thermopiles, which
are, in essence, multiple serially connected thermocouples. Currently, thermopiles are
most extensively used for the detection of thermal radiation (Section 14.6.2 of Chapter
14). The original thermopile was made of wires and was intended for increasing
the output voltage. It was invented by James Joule (1818–1889) [32].
Currently, the Seebeck effect is used in the fabrication of integral sensors where
pairs of materials are deposited on the surface of semiconductor wafers. An example
is a thermopile which is a sensor for the detection of thermal radiation. Quite sensitive
thermoelectric sensors can be fabricated of silicon, as silicon possess a strong Seebeck
coefficient. The Seebeck effect results from the temperature dependence of the Fermi
energy E F , and the total Seebeck coefficient for n-type silicon may be approximated
as a function of electrical resistivity for the range of interest (for use in sensors at
room temperature):
α a = mk ( ) ρ
q ln , (3.94)
ρ 0