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Luttinger–Kohn Model
A flavor of the k·p perturbation theory used for calculating the structure of multiple, degenerate electronic bands in bulk and quantum well semiconductors. The method is a generalization of the single band k ·p theory. In this model the influence of all other bands is taken into account by using Löwdin's perturbation method. Background All bands can be subdivided into two classes: * Class A: six valence bands (heavy hole, light hole, split off band and their spin counterparts) and two conduction bands. * Class B: all other bands. The method concentrates on the bands in ''Class A'', and takes into account ''Class B'' bands perturbatively. We can write the perturbed solution \phi^_ as a linear combination of the unperturbed eigenstates \phi^_: :\phi = \sum^_ a_ \phi^_ Assuming the unperturbed eigenstates are orthonormalized, the eigenequation are: :(E-H_)a_m = \sum^_H_a_ + \sum^_H_a_, where :H_ = \int \phi^_ H \phi^_d^3 \mathbf = E^_\delta_+H^_. From this expressi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K·p Perturbation Theory
In solid-state physics, the k·p perturbation theory is an approximated semi-empirical approach for calculating the band structure (particularly effective mass) and optical properties of crystalline solids. It is pronounced "k dot p", and is also called the "k·p method". This theory has been applied specifically in the framework of the Luttinger–Kohn model (after Joaquin Mazdak Luttinger and Walter Kohn), and of the Kane model (after Evan O. Kane). Background and derivation Bloch's theorem and wavevectors According to quantum mechanics (in the single-electron approximation), the quasi-free electrons in any solid are characterized by wavefunctions which are eigenstates of the following stationary Schrödinger equation: :\left(\frac+V\right)\psi = E\psi where p is the quantum-mechanical momentum operator, ''V'' is the potential, and ''m'' is the vacuum mass of the electron. (This equation neglects the spin–orbit effect; see below.) In a crystalline solid, ''V'' is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |