Why do thermoelectric generator designs often use long thin semiconductor legs?

Thermoelectric generator designs often utilize long, thin semiconductor legs to optimize the balance between two competing physical factors: thermal conduction and ohmic heating.1

The performance of these devices is heavily influenced by the geometry of the legs, specifically the ratio of their cross-sectional area to their length. This relationship functions as follows:1

• Thermal Conduction: The power lost through heat conduction between the source and the sink is directly proportional to the ratio of the leg's area to its length.
• Ohmic Heating: The power dissipated as heat due to electrical resistance within the legs is proportional to the inverse of that ratio (length divided by area).1

By designing legs that are relatively long and thin, engineers can effectively manage these trade-offs. Increasing the length relative to the area reduces thermal conduction losses, while the specific dimensions are chosen to minimize the power dissipated by electrical resistance, ultimately leading to an optimized design for power generation.1