Reformulating the instantons in a complex plane for tunneling or transmitting states, we calculate the pair-production rate of charged fermions in a spatially localized electric field, illustrated by the Sauter electric field E_0 (sech)^2 (z/L), and for a temporally localized electric field such as E_0 (sech)^2 (t/T). The integration of the quadratic part of WKB instantons over the frequency and transverse momentum leads to the pair-production rate obtained by the worldline instanton method including the prefactor of Phys. Rev. D 72, 105004 (2005) and 73, 065028 (2006). It is further shown that the WKB instanton plus the next-to-leading order contribution in spinor QED equals the WKB instanton in scalar QED, thus justifying why the WKB instanton in scalar QED can work for pair production of fermions. Finally we obtain the pair-production rate in a spatially localized electric field together with a constant magnetic field.
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