How does electrical resistivity affect the performance of a thermoelectric generator?

Electrical resistivity ($\rho$) significantly impacts the performance of a thermoelectric power generator by influencing internal power dissipation and overall efficiency.

In the semiconductor legs of the device, electrical current ($I$) generates heat due to electrical resistivity, a process known as ohmic heating. The power lost to this heating is calculated as $\rho I^2(L/a)$, where $L$ is the length and $a$ is the cross-sectional area of the leg. Because this ohmic heating dissipates a portion of the generated electrical power, high resistivity reduces the net power output available to the load resistance.1

To optimize performance, engineers must balance these losses against thermal conduction. While increasing the ratio of area to length reduces ohmic heating, it simultaneously increases thermal conduction power. Consequently, the effectiveness of a material is evaluated using a figure of merit, defined as the square of the Seebeck coefficient (${\alpha }^2$) divided by the product of electrical resistivity ($\rho$) and thermal conductivity ($\kappa$).1