Dipole matrix elements of semiconductor intersubband quantum structures

A method for determining the dipole matrix element for an intersubband opti cal transition in multi-layered semiconductor quantum heterostructures is p resented. The single-band effective-mass Schrodinger 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 typ es of optical transitions involving bound and QB states are defined and the corresponding dipole matrix elements are calculated for each type. The met hod presented incorporates the energy-dependent effective mass of electrons arising from conduction-band nonparabolicity. The performance and the accu racy of the method are evaluated for an asymmetric Fabry-Perot electron wav e interference filter. The physical dimensions of the filter are varied to show their effect on the dipole matrix elements. Results with and without n onparabolic 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 o f Airy and complementary Airy functions. In addition, results from the pres ent method are compared to a Kronig-Penney and a multi-band model. The dipo le matrix element values calculated by the present method are shown to be i n excellent agreement with the values obtained from these models. Further, the present model is numerically efficient and easily implemented. (C) 2000 Academic Press.