We define Seebeck coefficient as the potential difference developed to the temperature gradient applied. For metal the charge carriers are more and hence applying a temperature gradient should lead to diffusion of more charge carriers on the other side and hence potential difference should be more. Why it shows low value and how it is related to the change in Fermi level.
Shantanu Misra This is the conventional approach. But i just want to know, if the Seebeck coefficient is a measure of voltage difference developed to the temperature gradient applied. In case of metals, when the carrier concentration are large. Applying a temperature gradient should push more number of charge carriers towards cold side and hence large potential difference. But we do not observed this. Why? Is this because of scattering of charge carriers?
An increase in charge carrier concentration is accompanied by an increase in the Fermi energy. The electron energy becomes large compared to its change, which we create by means of a temperature gradient. Therefore, the effect of the temperature gradient decreases with increasing concentration of conduction electrons. Dependence is described by the Mott formula.
Thank you for your comment, it means that the as the Fermi level approaches the conduction band, the electrons can not be diffused to the other side due to its high energy compared to what we apply using temperature gradient?
What is the case when semi-metallic system shows an increase in the Seebeck coefficient with increase in temperature? Alexander N Titov
In the case of the presence of two types of charge carriers - electrons and holes, the temperature dependence of the position of the Fermi level is determined by the ratio of their effective masses. Therefore, with heating, the Fermi energy can either increase or decrease.
The formula S~m*/n2/3 shows that the Seebeck coefficient is inversely proportional to the free charge carrier which mean if we increase the free charge carrier the Seebeck coefficient will decrease
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