Understanding Temperature Effects on Electrical Resistance

This question explores how ambient temperature influences the electrical resistance of two different types of materials: pure metallic conductors and intrinsic semiconductors. Understanding their distinct charge transport mechanisms is key to determining this relationship.

Metallic Conductors: Resistance vs. Temperature

In pure metallic conductors, the primary charge carriers are free electrons. Their concentration is very high and essentially constant regardless of temperature changes.

• Primary Conduction Mechanism: Electrical current flows when these free electrons move under an applied electric field.
• Role of Temperature: As the ambient temperature increases, the atoms within the metal lattice vibrate more vigorously. These vibrations are known as phonons.
• Scattering Effect: The increased lattice vibrations lead to more frequent collisions between the moving electrons and the lattice atoms (more frequent electron-phonon scattering).
• Impact on Resistance: Each collision impedes the flow of electrons, effectively increasing the material's opposition to current flow. Therefore, as temperature increases, the scattering increases, causing the electrical resistance of metallic conductors to rise. Mathematically, resistivity ($\rho$) can be linked to the mean free time between scattering events ($\tau$) as $\rho \propto 1/\tau$. Increased temperature reduces $\tau$, thus increasing $\rho$.

Intrinsic Semiconductors: Resistance vs. Temperature

Intrinsic semiconductors have a much lower concentration of charge carriers compared to metals. Conduction involves both electrons moving into the conduction band and holes left behind in the valence band.

• Primary Conduction Mechanism: At absolute zero, semiconductors act as insulators. As temperature rises, thermal energy allows some electrons to break free from their covalent bonds and jump into the conduction band, creating electron-hole pairs.
• Role of Temperature: Increasing temperature provides more thermal energy.
• Carrier Generation: This increased energy significantly boosts the number of electrons that can jump the band gap ($E_g$), dramatically increasing the concentration of both free electrons ($n$) and holes ($p$). The intrinsic carrier concentration ($n_i$) is approximately given by $n_i \propto T^{3/2} e^{-E_g / (2kT)}$, showing exponential growth with temperature ($T$).
• Impact on Resistance: While increased lattice vibrations (similar to metals) do cause some scattering and tend to increase resistance, this effect is overshadowed by the massive increase in the number of available charge carriers ($n$ and $p$). A higher density of charge carriers facilitates current flow, thereby significantly decreasing the electrical resistance. Conductivity ($\sigma$) is given by $\sigma = e(n\mu_n + p\mu_p)$, where $n$ and $p$ increase exponentially, leading to a decrease in resistivity $\rho = 1/\sigma$.

Comparative Analysis and Conclusion

Comparing the two:

• Metals: Resistance increases with temperature primarily due to increased scattering (reduced $\tau$).
• Intrinsic Semiconductors: Resistance decreases with temperature primarily due to a substantial increase in charge carrier concentration (increased $n$ and $p$).

Therefore, the correct statement is that resistance increases for metallic conductors due to more frequent electron-phonon scattering, while it decreases for intrinsic semiconductors due to a significant increase in available charge carriers.