Mathematical modelling and self-consistent calculation of the charge density of two-dimensional electrons system

I.M.Ivankiv, A.M.Yafyasov, V.B.Bogevolnov, B.S.Pavlov${}^*$, T.V.Rudakova


The mathematical model of the 2D-system of electrons in the subsurface
space of the homogeneous narrow-gap semiconductor was developed for
accumulation layers. The calculation of the 2D-systems
parameters was carried out by numerical self-consistent integration
of the Schr"odinger and Poisson equations by using the Fermi
and quasi-classical (WKB) descriptions of the eigenfunctions
of the continuous spectrum - the states of electrons
``in continuum".
It is shown that the quasi-classical
approximation is preferable in comparison with the Fermi one for
the description of the continuum for 2D-systems.
The parameters of the two-dimensional gas were computed in wide
range of temperatures (200---300,K) and potentials (0---0.2,V).
There exists possibility of experimental observation of quantum subbands
in accumulation layers in the subsurface space of the narrow-gap
semiconductor at room temperature.


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