Excitons in InGaAs quantum dots without electron wetting layer states

Subjects

Abstract

The Stranski–Krastanov growth-mode facilitates the self-assembly of quantum dots (QDs) by using lattice-mismatched semiconductors, for instance, InAs and GaAs. These QDs are excellent photon emitters: the optical decay of QD-excitons creates high-quality single-photons, which can be used for quantum communication. One significant drawback of the Stranski–Krastanov mode is the wetting layer. It results in a continuum close in energy to the confined states of the QD. The wetting-layer-states lead to scattering and dephasing of QD-excitons. Here, we report a slight modification to the Stranski–Krastanov growth-protocol of InAs on GaAs, which results in a radical change of the QD-properties. We demonstrate that the new QDs have no wetting-layer-continuum for electrons. They can host highly charged excitons where up to six electrons occupy the same QD. In addition, single QDs grown with this protocol exhibit optical linewidths matching those of the very best QDs making them an attractive alternative to conventional InGaAs QDs.

Introduction

InGaAs quantum dots (QDs) grown in the Stranski–Krastanov (SK) mode are excellent photon emitters. Individual QDs provide a source of highly indistinguishable single-photons1,2,3,4,5,6 and a platform for spin–photon and spin–spin entanglement7,8,9. Their solid-state nature enables the integration of QDs in on-chip nanostructures such as photonic crystal cavities or waveguides10,11,12,13,14,15. In some respects, a QD can be considered as an artificial atom. However, this approximation is often too simplistic. Unlike a real atom in free space, an exciton (a bound electron–hole pair) in a QD can couple to further degrees of freedom in its solid state environment, for instance, phonons16,17,18,19,20 and nuclear spins21,22,23,24,25,26,27. One problematic source of unwanted coupling is the so-called wetting layer (WL)28,29,30,31. The WL is a two-dimensional layer lying between all QDs. It is an inherent feature of SK-growth.

On account of the confinement in the growth direction, there is an energy gap between the WL-continuum and QD-electron and QD-hole states. However, this gap protects the QD-electrons and -holes from coupling to the WL only to a certain extent. The gap vanishes for a QD containing several electrons due to the on-site Coulomb repulsion; the energy gap can be bridged by carrier–carrier and carrier–phonon scattering28,32. Furthermore, the gap is not complete: a low energy tail of the WL-continuum can extend to the QD-confined-states33,34. The result is that the WL has negative consequences for quantum applications: Multi-electron states of a QD hybridize with extended states of the WL28,30,35, severely limiting the prospects for using multi-electron states as qubits, for instance, the four-electron qubit proposed in ref. 36. A parasitic coupling between a QD and an off-resonant cavity37,38 can be caused by QD–WL Auger processes39,40. The low-energy tail of WL-states33,34 leads to damping of exciton Rabi oscillations29,41,42 and enhanced exciton–phonon scattering43. Finally, the WL limits applications of small QDs where the QD-WL energy gap is small44. Such QDs are useful for a hybrid system of QDs and Cs-atoms45,46.

We show here that the QD-properties can be radically altered when WL-states are absent. Electron WL-states are removed by a simple modification to the SK-growth: InGaAs QDs are overgrown with a monolayer of AlAs47,48,49,50. On the nanoscale, we propose that the absence of electron WL-states is related to the large bandgap of AlAs. Changes regarding the QD-properties are drastic: we observe highly charged excitons with narrow optical emission where up to six electrons occupy the conduction band shells of the QD—a novelty for QDs in the considered wavelength regime. The QD-potential is deepened and hybridization with any WL-continuum is absent. Furthermore, the QDs have close-to transform limited optical linewidths at low temperature, a very sensitive probe of the material quality51. Whenever the WL limits the QD-performance29,37,40,41,43, we propose that conventional SK QDs can be profitably replaced with their no-electron WL-counterparts.

Results

Sample growth and ensemble measurements

The QDs are grown by molecular beam epitaxy on a GaAs-substrate with (001)-orientation. The first monolayer of InAs deposited on GaAs (at 525 °C) adopts the GaAs lattice constant. After deposition of 1.5 monolayers, the strain mismatch between InAs and GaAs leads to island formation52 (Fig. 1a, b). These islands become optically-active QDs upon capping with GaAs. A two-dimensional InAs layer remains, the WL. This is the widely used SK self-assembly process.

Fig. 1
figure1

Growth and characterization of the quantum dots. af Schematic process of the quantum dot (QD) growth. a InAs is deposited on a GaAs-surface. b After deposition of ~1.5 monolayers of InAs, strain-driven QD-formation takes place. The QDs are capped with a monolayer of AlAs (c) and 2 nm GaAs (d). During these steps segregation of In atoms takes place (blue arrows) resulting in a wetting layer (WL) which is an alloy of GaAs, InAs, and AlAs. e The top part of the capped QD evaporates at 630 °C (flushing step). f The flushed QDs are overgrown with GaAs. g Scanning transmission electron microscopy image of a flushed QD. InAs appears bright, AlAs dark. h Chemical composition of the WL measured by spatially resolved energy dispersive X-ray (EDX) spectroscopy at a location without a QD (different location to g but nominally the same). i Ensemble photoluminescence (PL) at room temperature from a sample with unflushed, standard InGaAs QDs (red curve) and unflushed, AlAs-capped InGaAs QDs (black curve). The WL PL (highlighted by the red band) dominates the spectrum. The QD PL appears in the regime 1000–1300 nm. The QD-shells are labeled. j Ensemble-PL at 77 K from a sample with flushed, standard InGaAs QDs (red curve) and flushed, AlAs-capped InGaAs QDs (black curve). The flushing blue-shifts the QD-ensemble to ~900–980 nm

Here, the InAs islands are capped initially with a single monolayer of AlAs which has a higher bandgap than GaAs (Fig. 1c). Subsequently, a capping layer of 2.0 nm GaAs is grown (at 500 °C) (Fig. 1d). The additional AlAs monolayer is the only change of the standard SK protocol. For some samples, a “flushing step”53 is made following the growth of the GaAs-cap (increase of temperature to 630 °C) (Fig. 1e). With or without flushing, the heterostructure is completed with overgrowth of GaAs (Fig. 1f).

To determine the QD-structure post growth, we carried out scanning transmission electron microscopy (STEM). Figure 1g is a high-resolution high-angle annular dark-field STEM-image where the contrast is related to the atomic number. The QD is the ~3 nm high and ~30 nm wide bright feature close to the center of the image. The complete images with an atomic resolution demonstrate that the entire structure is defect-free (see Supplementary Note 1). The WL consists of InGaAs with a monolayer of AlAs contained within it. The AlAs capping layer can be clearly made out as a darker region surrounding the QD. Energy dispersive X-ray spectroscopy confirms the WL composition: indium atoms are found over a 2–3 nm thick region, yet the aluminum atoms are located within a 1 nm thick layer (Fig. 1h). These features point to highly mobile In atoms yet weakly mobile Al atoms under these growth conditions54. The overall thickness of the modified WL is similar to the WL of standard InGaAs QDs55. The In above the AlAs-layer is most likely due to In-segregation as illustrated in Fig. 1c–e. The STEM-image does not indicate a transition to a Volmer–Weber growth as found in ref. 48.

We probe the electronic states initially by photoluminescence (PL) experiments. Figure 1i shows ensemble PL from QDs grown with and without the AlAs-cap, in both cases without a flushing step. The spectra reveal the different shells (s, p, d) of the QDs. For the standard QDs, PL from the WL can be observed at ~925 nm, emission at lower wavelength is from bulk GaAs. In contrast, for the AlAs-capped QDs, the WL PL disappears. This is the first evidence for the absence of carrier confinement in the modified WL. We come to the same conclusion on flushed QDs for which the ensemble-PL is blue-shifted from 1000–1300 nm to ~900–980 nm (Fig. 1j). Without the AlAs-capping, there is strong emission from the WL at ~875 nm. For the AlAs-capped QDs, WL emission is not observed.

PL as a function of gate voltage

The ensemble-PL measurements do not distinguish between electron and hole confinement. We make this distinction by single-QD measurements. The particular concept is to probe the QD- and WL-electron-states by gradually lowering the energy of the states with respect to the Fermi energy of a tunnel-coupled41,56,57,58 Fermi sea. The QD is small enough to exhibit pronounced Coulomb blockade: electrons from the Fermi sea are added one-by-one and the QD-states are filled according to Hund’s rules28,59. A hole in the QD is provided by optical excitation with an above band laser (750 nm). We focus on flushed QDs, both without and with the AlAs capping layer.

For a standard InGaAs QD, PL as a function of gate voltage is shown in Fig. 2a. The plateaus correspond to different charge states of the QD-exciton (Fig. 2b): in the presence of a hole, electrons fill the QD-shells sequentially. The standard QD shows charging of the neutral exciton X0 to a net charge of −3e, the exciton X3− containing a total of four electrons and one hole. At higher gate voltage, the QD PL disappears. This is a sign that the WL becomes occupied31,35,59,60,61.

Fig. 2
figure2

Photoluminescence (PL) as electron states are sequentially filled. a PL counts versus gate voltage on a single, standard, flushed InGaAs quantum dot (QD). The plateaus correspond to Coulomb blockade59. b QD-shells and their occupation for the different exciton complexes. The triply charged exciton X3− has two low-lying states: a singlet (blue: s) or a triplet (green: t). c PL counts versus gate voltage on a single, AlAs-capped, flushed InGaAs QD. In the absence of wetting layer states for electrons, the X3− singlet (s) and triplet (t) as well as the highly charged exciton complexes X4− and X5− appear

The PL from the AlAs-capped QD is strikingly different. Charging beyond X3− to X4− and X5− takes place (Fig. 2c, Supplementary Note 5). The X5− contains a total of six electrons with fully occupied s- and p-shells. This is a novelty for QDs in this wavelength regime (960 nm). Further, even the X4− and X5− result in sharp emission lines and there is no rapid loss of intensity or rapid increase in linewidth at high gate voltages. This measurement points to, first, a deep confinement potential, sufficiently deep to accommodate six electrons despite the strong Coulomb repulsions, and second, the absence of WL-states for electrons.

At high positive bias, PL appears also at ~830 nm (see Supplementary Fig. 2), highly blue-shifted with respect to the QD PL, and close to the bandgap of GaAs. This PL line has a very strong Stark shift allowing us to identify it as a spatially indirect transition31,62 from an electron in the Fermi sea with a hole in the WL. From this line, we can, therefore, extract the properties of the WL in the valence band. We find that the AlAs-capped QDs have a valence band WL with ionization energy 19 meV with respect to the top of the GaAs valence band (see Supplementary Note 2). This ionization energy is reduced with respect to the WL of standard InGaAs QDs (ionization energy ~30 meV). The AlAs-cap eliminates any bound WL-states in the conduction band and pushes the bound WL-states in the valence band towards the GaAs valence band edge.

The full theoretical explanation for the absence of electron WL-states requires consideration of strain63 and, possibly, a treatment beyond the envelope wavefunction approximation64. This is left for future investigations.

Triply-charged excitons

For standard InGaAs QDs (Fig. 3a) and AlAs-capped QDs (Fig. 3b), we measure PL of the X3−-exciton as a function of the magnetic field parallel to the growth direction.

Fig. 3
figure3

Triply-charged exciton as a probe of the quantum dot (QD) and the wetting layer (WL) states. a X3− counts as a function of the magnetic field for a standard InGaAs QD (measurement and simulation). b As (a) but for an AlAs-capped QD. Note that the line appearing at ~5 T and wavelength ~961 nm arises from X2−, not X3−. c The optical decay process of the X3− singlet. Following photon emission, the p-shell is doubly occupied yet there is a vacancy in the s-shell. This turns on an Auger-like coupling to a state in which a high-lying level is singly occupied (QD-shell or WL-continuum) and the s-shell is doubly occupied. In this way, the PL-process is sensitive to the high-lying state even though it is not occupied in the initial state28. d X3− assuming that angular momentum is a good quantum number: the p-shell has angular momentum Lz = +1 and −1; the d-shell +2, 0 and −2. The X3− ground state changes from a triplet to a singlet at a finite magnetic field. e The final state of the singlet X3−. State \({\mid\! a \rangle}\) can couple to the d-shell of the QD via an Auger-like process (state \({\mid\! b \rangle}\)) and to a Landau level in the WL (state \({\mid\! d \rangle}\)). When d and p+ come into resonance, state \({\mid\! b \rangle}\) couples to state \({\mid\! c \rangle}\) where one electron occupies the p+-sub-shell

We present a method to probe the high-lying energy states, for instance, the QD-d-shell and WL-states, without occupying them. The method relies on an imbalance with respect to shell filling in the X3− final state. Following X3− recombination, there are two p-shell electrons yet just one s-shell electron. (Of the two s-shell electrons in the X3− initial state, one recombines with the hole to create a photon.) This imbalance enables Auger-like processes: one of the p-shell electrons falls into the s-shell thereby losing energy; the other p-shell electron is given exactly this energy and is promoted to a higher-lying state (Fig. 3c). This process will only occur if a high-lying state exists close to the right energy. If the s–p separation is ω0, the process is, therefore, a probe of the energy levels lying ω0 above the p-shell. Some spectroscopy is possible: the energy levels of a QD can be tuned with a magnetic field. These processes can result in large changes to the PL on charging from X2− to X3−28,30. For instance, in a QD without a d-shell, on applying a magnetic field, the X3− PL shows a series of pronounced anti-crossings with Landau levels associated with the WL28: the WL is thereby probed without occupying it.

We explore initially X3− on standard InGaAs QDs. For the singly and doubly charged excitons, X1− and X2−, the emission splits into two lines by the Zeeman effect and blue-shifts via its diamagnetic response (see Supplementary Fig. 5). The X3− has a much richer structure (Fig. 3a). At zero magnetic field, the X3− has a configuration with two electrons in the QD-s-shell and two electrons in the p-shell. According to Hund’s rules, the ground state electrons occupy different p-sub-shells with parallel spins (a spin-triplet) and two emission lines result, split by the large electron–electron exchange energy, denoted as t (triplet) and ts (triplet satellite) in Fig. 3a28. On increasing the magnetic field, the degeneracy (or near degeneracy) of the p-sub-shells is lifted. In the Fock–Darwin model28,65,66, the p-sub-shell (angular momentum Lz = +1) moves down in energy by \(- \frac{1}{2}\hbar \omega _c\) while the p+-sub-shell (angular momentum Lz = −1) moves up in energy by \(+ \frac{1}{2}\hbar \omega _c\) (Fig. 3d). Here, ωc is the electron cyclotron energy. Once this splitting becomes large enough, the X3− ground state turns from a triplet to a singlet where two electrons of opposite spin populate the lower p-sub-shell (Fig. 3d)28. The transition from triplet to singlet ground state occurs at ~1.3 T (Fig. 3a). The singlet (and not the triplet) ground state represents the probe of the higher lying electronic states.

The magnetic field dependence of the X3− singlet-PL-spectrum on a standard InGaAs QD shows several anti-crossings (Fig. 3a). We develop a model to describe the X3− final state including Coulomb interactions within a harmonic confinement and couplings to a WL-continuum (see Supplementary Note 3). In addition to the energies of the transitions, the linewidths are a powerful diagnostic. The spectrally narrow PL-lines arise from intra-QD-processes; the spectrally broad PL-lines from QD–WL-continuum coupling as the continuum of WL-states facilitates rapid dephasing28,43.

The singlet emission at ~1.3 T is spectrally broad, which signifies that the final state couples to the WL-continuum. There is an anti-crossing at ~3 T with a state with a linear magnetic field dispersion. This anti-crossing indicates a hybridization with the 0th WL-Landau-level (Fig. 3e). A second singlet emission line appears at higher energy, and there are two further anti-crossings at a high magnetic field (A1 and A2 in Fig. 3a). We exclude that these processes are caused by hybridization with the WL since the optical emission stays narrow in this regime. The first part of the explanation is an Auger-like process within the QD itself (Fig. 3e). The optical decay of the X3− singlet leaves behind two electrons in the lower p-sub-shell and one electron in the s-shell (state \({\mid\! a \rangle}\)). This final state can couple to state \({\mid\! b \rangle}\) via an Auger-like process where one p-electron fills the vacancy in the s-shell and the other goes up into the d-shell. This coherent coupling between the two basis states \({\mid\! a \rangle}\) and \({\mid\! b \rangle}\) leads to two eigenstates after optical decay and thus explains the second emission line at higher energy. The second part of the explanation involves the single particle states. With increasing magnetic field, the d-sub-shell of the QD moves down in energy with a dispersion of −ωc while the p+-sub-shell moves up with \(\frac{1}{2}\hbar \omega _c\). In the Fock–Darwin model, angular momentum is a good quantum number and d and p+ therefore cross. Experimentally, this is not the case: there is a small anti-crossing. This is not surprising for a real QD where there is no exact rotational symmetry. To describe this, we introduce basis state \({\mid\! c \rangle}\) (with an electron in the p+- rather than the d-shell) and a small coupling between states \({\mid\! b \rangle}\) and \({\mid\! c \rangle}\) to describe the symmetry breaking. This leads to the two characteristic anti-crossings (A1, A2) of the singlet emission pair with a line with a dispersion of approximately \(- \frac{3}{2}\hbar \omega _c\).

An analytic Hamiltonian describing all these processes is given in Supplementary Note 3. Using realistic parameters for the QD, the model (Fig. 3a) reproduces the X3− PL extremely well. This strong agreement allows us to extract the key QD parameters from this experiment: the electron sp splitting (ω0 = 24.1 meV) and the electron effective mass (0.07mo). We are also to conclude that the potential is subharmonic: the pd splitting is smaller than the sp splitting.

With this understanding of the X3−, we turn to the spectra from an AlAs-capped QD (Fig. 3b). As for the standard InGaAs QD, there is a transition from triplet to singlet X3− ground state, albeit at higher magnetic fields. In complete contrast to the standard InGaAs QD, the hybridization with a Landau level is not observed. This is powerful evidence that the electron WL-states no longer exist.

The X3− from the AlAs-capped QD is revealing in a number of other respects. First, the X3− singlet state shows one Zeeman-split line, not two as for the standard InGaAs QD. This is evidence that the \({\mid\! a \rangle}\)\({\mid\! b \rangle}\) coupling is suppressed on account of the energies: state \({\mid\! b \rangle}\) lies at too high an energy to couple to state \({\mid\! a \rangle}\) (see Supplementary Note 3). A large ratio between \({\mid\! b \rangle}\)\({\mid\! a \rangle}\) energy splitting and coupling strength leads to a very weak emission from the second line, strongly red-shifted for a positive \({\mid\! b \rangle}\)\({\mid\! a \rangle}\) energy splitting. The absence of a second singlet emission line is evidence that the pd splitting is larger than the sp splitting, a superharmonic potential. This is consistent with the thin, AlAs-layer in the STEM-characterization (Fig. 1g) which bolsters the lateral confinement; and also the ensemble-PL where the AlAs-cap blue-shifts the d-shell more than the p-shell (Fig. 1i). Second, the X3− singlet and triplet X3−-PL-lines appear simultaneously at low magnetic field (Fig. 3b) yet there is a rather abrupt transition for the standard InGaAs QD (Fig. 3a). This is an indication that relaxation to the exciton ground state is slower for the AlAs-capped QDs. This may also be related to the WL: electrons in the WL can mediate spin relaxation and without the WL, this process is turned off. Finally, the X3− exciton in the AlAs-capped QD has a very pronounced fine structure splitting: the splitting of the X3− triplet into three lines is a prominent feature (Fig. 3b). This particular fine structure originates from the electron–hole exchange in the initial exciton state60, and its increase relative to standard InGaAs QDs is indicative of a stronger electron–hole confinement67,68.

We model X3− in the AlAs-capped QD with the model developed for the standard InGaAs QD. The coupling to the Landau level is set to zero. A small perturbation is included to account for the anharmonicity of the confinement potential. The model describes the experimental results extremely well (Fig. 3b). The model determines the electron sp splitting as ω0 = 27.5 meV.

Temperature dependence

The temperature dependence of the exciton linewidths is a further probe of the coupling to continuum states. Linewidths of excitons in standard InGaAs QDs strongly increase with temperature as soon as hybridization with a WL is present43. Such a temperature broadening was observed for exciton complexes even with modest charge43, for instance, X2−. For an AlAs-capped QD, we measure the PL-linewidth of all charged excitons (X1−–X5−) as a function of temperature (Fig. 4a). Even for the highly charged excitons X4− and X5−, the temperature-induced broadening is much weaker than that for charged excitons beyond X1− in standard InGaAs QDs which show a strong, linear temperature dependence43. Instead, the linewidths are described well by a model which considers a localized exciton and dephasing via acoustic phonon scattering69. This too is evidence that the WL-states for electrons no longer exist.

Fig. 4
figure4

Linewidths of excitons in an AlAs-capped quantum dot. a Photoluminescence-linewidth (full width at half maximum) of the charged excitons as a function of temperature. The red lines represent a fit to a model that describes the interaction with acoustic phonons. b Linewidth of the singly charged exciton X1− in resonance fluorescence as a function of temperature. The inset shows an exemplary resonance fluorescence measurement at 4.2 K with a linewidth of 2.3 μeV. This measurement was carried out at low excitation power (coherent scattering regime). The saturation count rate obtained under resonant excitation is 60 kcounts/s

Finally, we measure the linewidth of the singly charged exciton (X1−) with resonant excitation, detecting the resonance fluorescence51 (Fig. 4b). The resonance fluorescence linewidth increases with temperature above ~10 K, indicative of acoustic phonon scattering (see Supplementary Note 4). At 4.2 K, the linewidth (2.3 μeV) is similar to the linewidth of the very best InGaAs QDs51. This shows that the AlAs-capped QDs retain the very low charge noise achieved for standard InGaAs QDs51,70. This is important: the AlAs-capped QDs have slow exciton dephasing and weak spectral fluctuations such that they are completely compatible with applications which place stringent requirements on the quality of the single-photons.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

M.C.L., I.S., and R.J.W. acknowledge financial support from SNF Project No. 200020_156637 and from NCCR QSIT. This project received funding from the European Union Horizon 2020 Research and Innovation Program under the Marie Skłodowska-Curie grant agreement No. 747866 (EPPIC). S.S., J.R., A.L., and A.D.W. gratefully acknowledge financial support from the grants DFH/UFA CDFA05-06, DFG TRR160, DFG project 383065199, LU2051/1-1, and BMBF Q.Link.X 16KIS0867.

Author information

S.S. and A.L. initiated the project. S.S., J.R., and A.L. carried out the QD-growth and ensemble-PL-measurements together with A.D.W. T.D., A.K., and B.E.K. carried out the STEM and EDX analysis. M.C.L. and I.S. carried out the single-QD-spectroscopy. M.C.L., I.S., A.L., and R.J.W. developed concepts and established the links between the various aspects of the project. M.C.L. and R.J.W. wrote the paper with input from all authors.

Correspondence to Matthias C. Löbl.

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