Relationship between the ground energy level and the well–width of one–dimensional Kronig–Penny model of GaAs/AlGaAs for electron, light hole and heavy hole using power series expansion

Abstract

Computational analysis of the dispersion equation of the simplest Kronig – Penney Model for a general one–dimensional periodic potential was analyzed using power series expansion. The resulting solution obtained when the first term of the expansion series was used, shows that the energy of a particle, Electron (E); Light Hole (LH) and Heavy Hole (HH) can never be zero as the well-width increases and that it has a minimum value at very large well-width. The result also shows that the use of different effective mass of E, LH, and HH in the potential well and the barrier provide the distinct differences between their eigen-values even though they all obey the similar power law.