If we consider the conductivity equation for a semiconductor, σ=neqeμe + nhqhμh, what term(s) change most for extrinsic semiconductor when you change the temperature?

Question

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When analyzing conductivity in semiconductors, the total conductivity σ = nqeμe + pqhqμh depends on the charge, concentration, and mobility of carriers. Each answer choice should be evaluated in terms of how temperature affects it in an extrinsic (doped) semiconductor.

Option a: qe. Here q is the elementary charge, a constant. Temperature does not change the value of q, so this term remains fixed. Therefore, qe does not account for the temperature-induced changes in conductivity.

Option b: ne & nh. In extrinsic semiconductors, the carrier concentrations n (electrons) and p (holes) are set largely by dopant levels at low to moderate temperatures. As temperature rises, more dopants ionize and intrinsic generation increases, causing both electron and hole populations to change. Near room temperature and above, intrinsic excitation becomes significant, and n and p deviate from their fixed-dopant values, so the terms ne and nh are strongly affected by temperature.

Option c: μe & μh. Carrier mobilities μe and μh do depend on temperature, typically decreasing with increasing temperature due to enhanced phonon scattering. While mobility does vary with T, in an extrinsic material the dominant temperature-driven change in conductivity at many regimes arises from carrier concentrations shifting toward intrinsic levels, especially as temperature grows.

Option d: nh. This is specifically the hole concentration. In extrinsic material, nh can indeed change with temperature, but focusing on only holes ignores that electrons (ne) also change as temperature varies. Since both carrier populations are altered (n and p) with temperature, singling out only nh misses part of the overall effect.

Option e: ne. Similar to nh, ne can change with temperature, especially as dopants ionize and intrinsic generation ramps up. Like option d, considering only ne neglects the complementary carrier population and the broader impact on σ.

In summary, temperature affects several factors in the conductivity expression, but in an extrinsic semiconductor the most pronounced and fundamental changes with temperature arise in the carrier concentrations ne and nh due to dopant ionization dynamics and the onset of intrinsic carrier generation. Mobility changes with temperature are important as well, yet ne and nh capture the primary temperature-driven evolution of conductivity in the extrinsic regime.

If we consider the conductivity equation for a semiconductor, σ=neqeμe + nhqhμh, what term(s) change most for extrinsic semiconductor when you change the temperature?

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