Binding energies of positive and negative trions: From quantum wells to quantum dots

We compare binding energies for positive and negative trions in a series of narrow GaAs quantum wells and in “natural” quantum dots defined by quantum well thickness fluctuations. We assign photoluminescence features to oppositely charged trions through a combination of charging behavior, luminescence polarization, and spin fine structure. Negative trions are found to have a higher binding energy than positive trions. Our observations compare well with path integral Monte Carlo calculations for different well widths. This comparison provides a physical interpretation of the observed trends and sheds light on a longstanding disagreement between theory and experiment on the influence of lateral confinement on trion binding energies.

Figure 1

(a) Photoluminescence intensity (gray scale) for a single natural quantum dot in a $2.8\mathrm{nm}$ (nominal width) GaAs quantum well embedded in a $p$-type Schottky diode, as a function of emitted photon energy and applied bias. Neutral exciton $\left(X^{\circ }\right)$, positive trion $\left(X^{+}\right)$, and biexcitons $(X{X}^{\circ },X{X}^{+},X{X}^{-})$ are labeled. (b) Analogous spectrum for an $n$-type Schottky diode, which shows the negative trion $\left(X^{-}\right)$. (c) Photoluminescence circular polarization as a function of bias for the QD shown in (b).

Figure 2

(a) Photoluminescence intensity (gray scale) for a single natural quantum dot in a $4.2\mathrm{nm}$ (nominal width) $n$-type modulation-doped GaAs quantum well, as a function of emitted photon (PL) energy and laser excitation energy. (b) All three peaks from the same QD in a $6\mathrm{T}$ magnetic field (Voigt geometry). $X^{\circ }$ exhibits exchange fine structure.

Figure 3

(a) Ensemble photoluminescence spectra for GaAs quantum wells with four different widths. The top two pairs of spectra correspond to two well widths each, differing by one monolayer (see text). One single QD is shown for comparison. Solid and dotted lines correspond to different laser excitation energies, chosen separately for each well. Horizontal bars span exciton-trion splittings for each spectrum. (b) Photoluminescence circular polarization for the $4.2\mathrm{nm}$ ensemble spectra.

Figure 4

Binding energies obtained from PL spectra of quantum well ensembles (solid symbols) and individual natural quantum dots (open symbols). Symbol shapes for $X^{-}$ vs $X^{+}$, ensemble vs quantum dots, and $p$-type vs $n$-type samples are specified in the legend. Lines show PIMC calculations for $X^{-}$ and $X^{+}$ in quantum wells with interface fluctuations (diameter $D=30\mathrm{nm}$, solid lines) and perfectly smooth interfaces ($D=\infty$, dashed lines). The inset shows experimental results for the individual quantum dots that were averaged and converted to well width units to obtain the corresponding open symbols in the main graph.

Figure 5

PIMC calculations of the binding energy of negative and positive trions (symbols − and +, respectively) vs diameter of a 1 ML width fluctuation for a QW width $L=2.8\mathrm{nm}$ (solid lines) and $4.2\mathrm{nm}$ (dotted lines).