Page 51 - An Introduction to Microelectromechanical Systems Engineering

30 Materials for MEMS

In the Seebeck effect, named after the scientist who made the discovery in 1822,
a temperature gradient across an element gives rise to a measurable electric field that
tends to oppose the charge flow (or electric current) resulting from the temperature
imbalance. The measured voltage is, to first order, proportional to the temperature
difference with the proportionality constant known as the Seebeck coefficient.
While, in theory, a single material is sufficient to measure temperature, in practice,
thermocouples employ a junction of two dissimilar materials. The measurable volt-
age at the leads, ∆V, is the sum of voltages across both legs of the thermocouple.
Therefore,

=
⋅
∆V =α 1 ⋅ (T cold − T hot )+α 2 ⋅ (T hot − T cold ) (α 2 −α 1 ) (T hot − T cold )
where α and α are the Seebeck coefficients of materials 1 and 2, and, T hot and T cold
1
2
are the temperatures of the hot and cold sides of the thermocouple, respectively (see
Figure 2.8). Alternately, one may use this effect to generate electrical power by main-
taining a temperature difference across a junction. Table 2.6 lists Seebeck coeffi-
cients for a number of materials.

Hot

Material 1 Material 2

Cold

∆V
Figure 2.8 The basic structure of a thermocouple using the Seebeck effect. The measured volt-
age is proportional to the difference in temperature. Thermocouples can be readily implemented
on silicon substrates using combinations of thin metal films or polysilicon.

Table 2.6 The Seebeck Coefficients Relative to Platinum
for Selected Metals and for n- and p-Type Polysilicon
µV/K µV/K
Bi –73.4 Ag 0007.4
Ni –14.8 Cu 0007.6
Pa 0–5.7 Zn 0007.6
Pt 000 Au 0007.8
Ta 003.3 W 0011.2
Al 004.2 Mo 0014.5
Sn 004.2 n-poly (30 Ω/ ) –100
Mg 004.4 n-poly (2600 Ω/ ) –450
Ir 006.5 p-poly (400 Ω/ ) 0270
Note: The sheet resistance is given for the 0.38-µm-thick polysilicon films.
Polysilicon is an attractive material for the fabrication of thermocouples and
thermopiles because of its large Seebeck coefficient.