International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Zhukov V.P.   Федорук М.П.  

One-parameter 6-kp model for hetero nano structures

Reporter: Zhukov V.P.

6-kp model is widely used to describe semiconductor structures. Initially this model was suggested for the materials with constant effective masses. But the contact of materials with strongly different masses is a common for the semiconductor structures. This demands the generalization of 6-kp model on this case. In previous papers the heterotransition is assumed sharp and the condition of wave function continuity and linear connections between the derivatives are used. This approach has the following disadvantages. 1. uncertainty of the connection coefficients, 2. It is impossible to use this approach in the case of smooth (diffusive) heterotransition, 3. there are difficulties in the case of heterostrucrures of complicated form and the case of a contact of more then 2. There are also nonphysical solutions (interface mode) for a certain boundary conditions.
In presented paper a very simple generalization of 6-kp model in the case of no constant masses which is free of the mentioned disadvantages is suggested. Our approach consist of a definite view of the terms with mixed derivative. We add the only one addition parameter in the model. For a certain value of this parameter nonphysical mode can take place. But for the main materials (Ge, Si, Ga, As, AlAs, InAs, GaAs, GaSb, InP, InN, GaN, AlN, InN, GaP, AlP) nonphysical mode are absent for the same value of this parameter.
Note, that when the calculation methods are used, the small scale of a problem is limited by finite-difference step. Because of this nonphysical mode sometimes is not appear in calculations. But for the geterostructures of nano scales the presence of interface mode is principle.
In presented paper the finite-difference analog of Schrodinger operator of 6-kp model using shifted grids is suggested. It is Hermitic, compact and divergent. To search a ground and first exited states the iteration splitting method is suggested.
The work is supported by Integration Project SB RAS № 43.