Mathematical analysis of the two‐band Schrödinger model

Abstract

International audienc

Existence of solution of a non-linear multiband kp model with transparent boundary conditions

“…Here, G(q) is a given function whose support is contained in a compact interval of  + . The details of the derivation of equations ( 9)- (10) are given in appendix A. The function G(q) represents the statistical weight of the Schrödinger problem…”

“…We remark that in our model the full Schrödinger solution is replaced by a set of envelope functions. In this framework, the electron density is expressed by equations ( 9)- (10). The presence of a term proportional to the product ψ ψ ε ε q c q v , , ensures the existence of the correct a priori estimate for the Poisson equation.…”

“…For the sake of completeness, we derive the expression of the particle density used in the present work. The non-standard definition of the particle density provided by equations ( 9)- (10), is consequence of the energy conservation equation. This can be seen by writing the MEF problem in the time-dependent formulation (i.e.…”

“…The derivation of multi-band models for the simulation of charge transport in semiconductor is today an active area of research [10][11][12][13][14][15]23]. The main interest is to predict the current-voltage performances of heterostructure devices characterized by quantum mechanical and by non-linear effects, induced for example by the electrostatic and the contact potential [16].…”

Mathematical Analysis of a Nonparabolic Two-Band Schrödinger-Poisson Problem

“…The study of multiband models is a very active area of research (Ben Abdallah and Kefi, 2008;Barletti and Frosai, 2010;Barletti, Frosali, and Demeio, 2007;Barletto and Mahats, 2010;Mahats, 2005;Ben Abdallah, Jourdana, and Pietra, 2012;Pinaud, 2004;Barletti and Ben Abdallah, 2011;Morandi and Schuerrer, 2011;Morandi, Hervieux, and Manfredi, 2010;Morandi and Demeio, 2008). A considerable effort has been made in order to develop mathematical models that reproduce the steady states and the out-of-equilibrium dynamics in heterostructure devices (Ben Abdallah and Mehats 2004).…”