= Seebeck coefficient
{c}
{title2=$S$}
= Thermopower
{synonym}
The <Seebeck coefficient> $S(T)$ quantifies the thermoelectric voltage response per small <temperature> difference at zero <electric current>. Use $S=-dV/dT$ along a homogeneous material, with voltage understood through <electrochemical potential>. Its units are <volts> per <kelvin>, commonly $\mu\mathrm{V/K}$. The word <thermopower> is also used, despite this being a voltage response rather than <power>; some authors use that word for $|S|$, so check their convention. https://thermoelectrics.matsci.northwestern.edu/thermoelectrics/[Northwestern thermoelectrics research group: Seebeck coefficient and thermopower convention]{ref}.
For the A-minus-B terminal order in the <Seebeck effect> experiment,
$$
\frac{\partial V_{AB}}{\partial T_h}=S_A(T_h)-S_B(T_h),\qquad
\frac{\partial V_{AB}}{\partial T_c}=-\bigl[S_A(T_c)-S_B(T_c)\bigr].
$$
Thus a small <temperature> difference around $T_0$ gives $V_{AB}\approx[S_A(T_0)-S_B(T_0)]\Delta T$. The finite-interval ratio $V_{AB}/\Delta T$ is an average of the coefficient difference, not necessarily its value at either endpoint. Ordinary two-material measurements determine a relative <Seebeck coefficient>: to recover $S_A$ from the measured difference, add a separately known $S_B$. Neither the choice of a zero for voltage nor the use of a familiar reference material makes $S_B$ identically zero.
A concrete research example is Martin and colleagues' 2021 certification experiment. They measured small <temperature> differences and voltages on six <silicon>–germanium specimens at 13 base <temperatures> between $295$ and $900\,\mathrm K$. At each setting they acquired 40 voltage-and-<temperature>-difference pairs and used <linear regression> with a free intercept, so a constant voltage offset did not become part of the <slope>. Platinum voltage leads required a reference-material correction; their terminal order gave $S_{\rm measured}=S_{\rm Pt}-S_{\rm specimen}$, hence $S_{\rm specimen}=S_{\rm Pt}-S_{\rm measured}$. This is an actual measurement protocol, unlike the toy plot above. https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=932592[Martin et al., Development of a high-temperature (295–900 K) Seebeck coefficient Standard Reference Material (2021), certification measurements and Eq. (1)]{ref}.
Microscopically, a <temperature gradient> changes <charge carrier> transport until an opposing electrical response balances it at zero net <electric current>. In the usual simple <semiconductor> picture, <Electrons> and <electron holes> give opposite <Seebeck coefficient> signs, and their contributions are weighted by their <electrical conductivities>. The <Seebeck coefficient> is a transport property: <density of states> alone does not determine it, since carrier motion and scattering also matter. Its usefulness extends beyond <temperature> sensing to diagnosing which carriers transport <electric charge>. https://thermoelectrics.matsci.northwestern.edu/thermoelectrics/[Northwestern thermoelectrics research group: Seebeck coefficient, scattering contributions, and bipolar transport]{ref}.
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