Dipole matrix elements of semiconductor intersubband quantum structures

A method for determining the dipole matrix element for an intersubband optical transition in multi-layered semiconductor quantum heterostructures is presented. The single-band effective-mass Schrödinger equation is solved by employing the argument principle method (APM) to extract the bound (B) and quasibound (QB) eigenenergies of the quantum heterostructure. The major types of optical transitions involving bound and QB states are defined and the corresponding dipole matrix elements are calculated for each type. The method presented incorporates the energy-dependent effective mass of electrons arising from conduction-band nonparabolicity. The performance and the accuracy of the method are evaluated for an asymmetric Fabry–Perot electron wave interference filter. The physical dimensions of the filter are varied to show their effect on the dipole matrix elements. Results with and without nonparabolic effects are presented and compared. Dipole matrix elements are also calculated for the filter with an applied electric field bias. In this case the eigenstate wavefunctions can be expanded as linear combinations of Airy and complementary Airy functions. In addition, results from the present method are compared to a Kronig–Penney and a multi-band model. The dipole matrix element values calculated by the present method are shown to be in excellent agreement with the values obtained from these models. Further, the present model is numerically efficient and easily implemented.