Russian Physics Journal, Vol. 61, No. 2, June, 2018 (Russian Original No. 2, February, 2018)
PHYSICS OF SEMICONDUCTORS AND DIELECTRICS
QUASI-TWO-DIMENSIONAL ELECTRON–HOLE LIQUID IN
SHALLOW SiGe/Si QUANTUM WELLS
A. A. Vasilchenko,
G. F. Kopytov,
and V. S. Krivobok
An analytical expression is obtained for the energy of a quasi-two-dimensional electron-hole liquid (EHL) in
shallow quantum wells. It is shown that in the Si/Si
/Si structures with small x, the EHL contains light and
heavy holes. With increasing x, the transition of EHL to a state with heavy holes occurs, and the equilibrium
density of electron-hole pairs strongly decreases. The effect of an external electric field on the EHL properties
Keywords: electron-hole liquid, light and heavy holes, Schrödinger equation.
Relatively recently, the possibility of the formation of a quasi-two-dimensional EHL in SiGe/Si quantum wells
(QWs) has been demonstrated [1–6]. The spectrum of such an EHL is largely formed by the structure of the valence
band, the density of states in which is nonmonotonic due to the presence of different hole subbands . At the same
time, according to the existing ideas, the appearance of jumps in the density of states should lead to the appearance of
additional local minima in the dependence of the total energy of a two-component Fermi liquid on its concentration.
Depending on which minimum is the main, the properties of the EHL will also change. As far as the authors are aware,
there is no theoretical analysis of the effects of this type in the modern literature.
The available experimental results do indicate a modification of the EHL properties depending on the
germanium composition in the SiGe layer. In particular, an unusual structure in the emission spectrum of the EHL in
a SiGe/Si quantum well with small germanium composition (of several percent) was observed experimentally in .
The authors managed to explain the shape of the condensed phase line within the framework of the concepts on
a multicomponent Fermi liquid containing both heavy and light holes. We note that the observed fine structure of the
EHL emission spectra disappears with increasing germanium composition in the quantum well.
The aim of this paper is to find an analytical expression for the energy of a quasi-two-dimensional EHL with
allowance for two types of holes. The theoretical approach in this study is similar to the one we used in . To calculate
the EHL energy, the density functional method is used.
/Si structures, a QW for holes and a barrier for electrons are formed in the SiGe layer. For
small x, the values of the barrier height and well depth are small, and the effect of the barrier and well will not be
Kuban State Technological University, Krasnodar, Russia, e-mail: firstname.lastname@example.org;
University, Krasnodar, Russia, e-mail: email@example.com;
P. N. Lebedev Physical Institute, Moscow, Russia, e-mail:
National Research Nuclear University “MEPhI”, Moscow, Russia. Translated from Izvestiya
Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 3–7, February, 2018. Original article submitted July 24, 2017.
1064-8887/18/6102-0205 2018 Springer Science+Business Media, LLC