An efficient and stable algorithm based on the Numerov method of solving the Schrödinger equation with complex potential boundaries (NCPB) in open multilayer heterojunction systems is presented. The NCPB solver provides the complex expressions of the system eigenvalues to obtain the quasi-bound state (QBS) energies and lifetimes. Examples of applications in investigating electron tunneling from an accumulation layer across a single AlGaAs barrier, resonant tunneling through double barriers and QBSs in a multilayer quantum cascade laser are discussed. These examples of applications show that the NCPB is a powerful tool with greatly improved efficiency for investigating, designing, and optimizing multilayer heterojunction devices.
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