Two-Dimensional Electron-Hole Liquid in Single Si Quantum Wells with Large Electronic and Dielectric Confinement

We report a luminescence study of the electronic properties of the 2D electron-hole liquid in crystalline Si quantum wells with ${\mathrm{SiO}}_2$ dielectric barriers. The Fermi-Dirac condensation of $e\mathrm{\text{−}}h$ pairs into a metallic liquid is strongly enhanced by spatial localization. We present experimental evidence for the formation of liquid nanodroplets, with size increasing with $e\mathrm{\text{−}}h$ pair density. The quantum confined regime is observed for well width below 15 nm. The data are analyzed in a confinement model that takes account of the band-gap renormalization by 2D many-body effects and the increase of the Coulomb interactions due to the dielectric mismatch between the Si well and the ${\mathrm{SiO}}_2$ barriers.

Figure 1

PL of Si wells with $l_z$ varying between 4.7 and 190 nm. Monitored temperature is 15 K (except other indication) and $P_{\mathrm{ext}}\approx 7\mathrm{W}{\mathrm{cm}}^{-2}$. The dotted curves are fits of the data following the 3D model for $l_z>13\mathrm{nm}$ and the 2D model for $l_z\le 13\mathrm{nm}$. ${\mathrm{FE}}_{\mathrm{sub}}$ and ${\mathrm{BE}}_{\mathrm{sub}}$ denote substrate free exciton and bound exciton recombination lines, respectively. Inset: representation of the “quantum droplet” of radius $r_D$ (case of parabolic potential for carriers).

Figure 2

PL of (a) a 190 nm well at 15 K and (b) a 28 nm well at 1.8 K for different laser power: $a=0.5$, $b=2$, $c=4$, $d=8$, $e=2.6\times {10}^3$, and $f=4\times {10}^3$, in $\mathrm{W}{\mathrm{cm}}^{-2}$.

Figure 3

Comparison between experimental and theoretical positions of the 2D EHP peak vs $l_z$. Squares: $E_G(l_z)-1\hslash {\omega }_{\mathrm{TO}}$; triangles: experimental $E_{\max }(l_z)$; circles and solid line: theoretical $E_{\max }(l_z)$ with and without dielectric mismatch respectively.