Two identical pure germanium crystals, A and B , are doped with arsenic and indium respectively. The doping is carefully adjusted such that the number density of majority charge carriers in crystal A is exactly equal to the number density of majority charge carriers in crystal B . Let _A and _B be the electrical conductivities of crystals A and B respectively at the same temperature. Which of the following relations

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Crystal A is doped with arsenic (a pentavalent impurity), making it an n-type semiconductor where electrons are the majority charge carriers. Crystal B is doped with indium (a trivalent impurity), making it a p-type semiconductor where holes are the majority charge carriers. The electrical conductivity of a semiconductor is given by = e(n_e _e + n_h _h) . For the n-type crystal A, the conductivity is mainly due to electrons: _A e n_e _e . For the p-type crystal B, the conductivity is mainly due to holes: _B e n_h _