Drift Currents Of Carriers

In an intrinsic semiconductor the electron and hole densities are equal, (n_e = n_h = n_i), but the two carriers respond differently to the field because their mobilities differ. The drift current contributed by each carrier type is (I \propto n,\mu), so with equal densities the currents are in the ratio of the mobilities. Mobility measures how fast a carrier drifts per unit applied field, and electrons typically move more readily than holes because hole transport requires successive valence electrons to shift into vacancies, an inherently slower process. That physical difference is exactly what makes the two contributions unequal here. The electron current is proportional to (\mu_e = 0.36) and the hole current to (\mu_h = 0.18). The fraction carried by electrons is (\mu_e/(\mu_e + \mu_h) = 0.36/(0.36 + 0.18) = 0.36/0.54 = 2/3). The one-half option wrongly assumes equal currents, forgetting that mobilities differ even when densities match. The one-third option inverts the ratio, giving the hole fraction instead. The three-quarters option uses a mobility ratio of 3:1 rather than the given 2:1. As a plausibility check, electrons have the higher mobility here, so they should carry the larger share of current; two-thirds is indeed greater than half, consistent with electrons drifting twice as readily as holes.