Different regimes of Förster-type energy transfer between an epitaxial quantum well and a proximal monolayer of semiconductor nanocrystals

We calculate the rate of nonradiative, Förster-type energy transfer (ET) from an excited epitaxial quantum well (QW) to a proximal monolayer of semiconductor nanocrystal quantum dots (QDs). Different electron-hole configurations in the QW are considered as a function of temperature and excited electron-hole density. A comparison of the theoretically determined ET rate and QW radiative recombination rate shows that, depending on the specific conditions, the ET rate is comparable to or even greater than the radiative recombination rate. Such efficient Förster ET is promising for the implementation of ET-pumped, nanocrystal QD-based light emitting devices.

Figure 1

(a) An example of a hybrid QW/QD structure that can be used for “noncontact” pumping of nanocrystals via nonradiative ET. The structure consists of an InGaN QW sandwiched between GaN barriers. A monolayer of $\mathrm{CdSe}∕\mathrm{ZnS}$ core/shell nanocrystals capped with organic molecules is assembled on the surface of the thin top barrier. The structure is driven electrically using metal contacts attached to the barrier layers. (b) Carrier relaxation and ET processes in the hybrid QW/QD structure. The QW-to-QD ET competes with recombination processes in the QW. High-energy excitations created in the nanocrystals through ET rapidly relax to the nanocrystal band edge, which prevents backtransfer. The relaxed excitations recombine, producing emission with the color determined by the QD size.

Figure 2

The Förster (solid line) and radiative (dashed line) transition rates calculated for QW excitons for $\xi =30\mathrm{\AA }$ and (a) $n_T={10}^{11}{\mathrm{cm}}^{-2}$ and $E_T=-0.005\mathrm{eV}$, (b) $n_T={10}^{11}{\mathrm{cm}}^{-2}$ and $E_T=-0.02\mathrm{eV}$, (c) $n_T={10}^{12}{\mathrm{cm}}^{-2}$ and $E_T=-0.005\mathrm{eV}$, (d) $n_T={10}^{12}{\mathrm{cm}}^{-2}$ and $E_T=-0.02\mathrm{eV}$. The dashed-dotted line is the efficiency of the Förster transfer.

Figure 3

The Förster (solid line) and radiative (dashed line) transition rates for QW classical free carriers, along with the ET efficiency (dashed-dotted line). (a) The calculations are shown for $n_{eh}={10}^{12}{\mathrm{cm}}^{-2}$ as a function of $T$ above the degeneracy temperature 34.7 K. (b) The calculations are shown for $T=300\mathrm{K}$ as a function of $n_{eh}$ below the degeneracy density $8.6\times {10}^{12}{\mathrm{cm}}^{-2}$. The straight-line segments indicate the asymptotic degenerate values in the limit $T\to 0$ for the Förster $\left(0.0749{\mathrm{ns}}^{-1}\right)$ and radiative $\left(0.0379{\mathrm{ns}}^{-1}\right)$ rates with efficiency 0.66 (a), and in the limit $n_{eh}\to \infty$ for the Förster $\left(0.175{\mathrm{ns}}^{-1}\right)$ and radiative $\left(0.0379{\mathrm{ns}}^{-1}\right)$ rates with efficiency 0.82 (b).

Figure 4

Experimental results: Förster (squares) and radiative recombination rates (crosses) as a function of excited carrier density (the solid and dashed lines are guides to the eye). The dash-dotted line is the ET efficiency $(\eta =57\%)$.