ZhETF, Vol. 149,
No. 3,
p. 530 (March 2016)
(English translation  JETP,
Vol. 122, No. 3,
p. 456,
March 2016
available online at www.springer.com
)
Electron gas induced in SrTiO_{3}
Han Fu, Reich K.V., Shklovskii B.I.
Received: August 18, 2015
DOI: 10.7868/S004445101603007X
This minireview is dedicated to the 85th birthday of Prof. L. V. Keldysh, from whom we have learned so much. In this paper, we study the potential and electron density depth profiles in surface accumulation layers in crystals with a large and nonlinear dielectric response such as SrTiO_{3} (STO) in the cases of planar, spherical, and cylindrical geometries. The electron gas can be created by applying an induction D_{0} to the STO surface. We describe the lattice dielectric response of STO using the LandauGinzburg free energy expansion and employ the ThomasFermi (TF) approximation for the electron gas. For the planar geometry, we arrive at the electron density profile , where . We extend our results to overlapping electron gases in GTO/STO/GTO heterojunctions and electron gases created by spillout from NSTO (heavily ntype doped STO) layers into STO. Generalization of our approach to a spherical donor cluster creating a big TF atom with electrons in STO brings us to the problem of supercharged nuclei. It is known that for an atom with a nuclear charge Ze where Z > 170, electrons collapse onto the nucleus, resulting in a net charge Z_{n} < Z. Here, instead of relativistic physics, the collapse is caused by the nonlinear dielectric response. Electrons collapse into the charged spherical donor cluster with radius R when its total charge number Z exceeds the critical value , where a is the lattice constant. The net charge eZ_{n} grows with Z until Z exceeds . After this point, the charge number of the compact core Z_{n} remains , with the rest Z^{*} electrons forming a sparse TF atom with it. We extend our studies of collapse to the case of long cylindrical clusters as well.

