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The electronic states of a core/shell quantum well (QW) system confined in a modified Pöschl–Teller (PT) plus Woods–Saxon (WS) potential in the presence of electric field are studied with the III-Nitride group owing to their wide bandgap for device applications. The bandgap energy in this regard is obtained by solving analytically the Schrödinger wave equation with the Pekeris-type approximation to the centrifugal term.

The approximate solutions of the Klein-Gordon equation with the shifted Tietz-Wei potential function are thoroughly studied for Klein-Gordon equation with both 2V and V potentials by usinga suitable approximation scheme for the centrifugal term in the framework of the supersymmetric approach. The non-relativistic limits in both cases are obtained, and the numerical results are computed. We have equally investigated the Fisher information on the shifted Tietz-Wei potential function in the case of the non-relativistic limit of the Klein-Gordon equation with potential V because this is only possible in the non-relativistic regime. The Fisher information is observed to be inversely proportional to both Ch and bh, where Ch is the optimization parameter and bh = β(1 − Ch), with β being the Morse constant.