handbook of modern sensors

90 3 Physical Principles of Sensing
Fig. 3.36. Output voltage from standard thermocouples as functions of a cold–hot temperature
gradient.
where ρ 0 ≈ 5 × 10 −6 m and m ≈ 2.5 are constants, k is the Boltzmann constant, and
q is the electronic charge. The doping concentrations used in practice lead to Seebeck
coefficients on the order of 0.3–0.6 mV/K. The absolute Seebeck coefficients of a
few selected metals and some typical values of silicon are shown in Table A.11. It
can be seen that the Seebeck coefficients for metals are much smaller than for silicon
and that the influence of aluminum terminals on chips is negligible compared to the
Seebeck coefficient for silicon.
In the early nineteenth century, a French watchmaker turned physicist, Jean
Charles Athanase Peltier (1785–1845), discovered that if electric current passes from
one substance to another (Fig. 3.37), then heat may be given or absorbed at the junction
[33]. Heat absorption or production is a function of the current direction:
dQ P =±pi dt, (3.95)
where i is the current and t is time. The coefficient p has a dimension of voltage and
represents thermoelectric properties of the material. It should be noted that heat does
not depend on the temperature at the other junction.
The Peltier effect concerns the reversible absorption of heat which usually takes
place when an electric current crosses a junction between two dissimilar metals. The