Excitons in InGaAs quantum dots without electron wetting layer states

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. The application of quantum dots for quantum communication is limited by the wetting layer, which is inherent to the Stranski–Krastanov growth method. Here, the authors advance this method by decoupling the quantum dot and wetting layer states, which modifies their excitonic properties.


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 formation 52 (Fig. 1a, b). These islands become optically-active QDs upon capping with GaAs. A twodimensional InAs layer remains, the WL. This is the widely used SK self-assembly process.
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 Xray 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 conditions 54 . The overall thickness of the modified WL is similar to the WL of standard InGaAs QDs 55 . 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 tõ 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-coupled 41,56-58 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 rules 28,59 . 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 X 0 to a net charge of −3e, the exciton X 3− 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 occupied 31,35,[59][60][61] .
The PL from the AlAs-capped QD is strikingly different. Charging beyond X 3− to X 4− and X 5− takes place (Fig. 2c, Supplementary Note 5). The X 5− 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 X 4− and X 5− 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 transition 31,62 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 AlAscap 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 WLstates requires consideration of strain 63 and, possibly, a treatment beyond the envelope wavefunction approximation 64 . 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 X 3− -exciton as a function of the magnetic field parallel to the growth direction.
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 X 3− final state. Following X 3− recombination, there are two p-shell electrons yet just one s-shell electron. (Of the two s-shell electrons in the X 3− 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 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 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 ℏω 0 , the process is, therefore, a probe of the energy levels lying ℏω 0 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 X 2− to X 3−28,30 . For instance, in a QD without a d-shell, on applying a magnetic field, the X 3− PL shows a series of pronounced anti-crossings with Landau levels associated with the WL 28 : the WL is thereby probed without occupying it. We explore initially X 3− on standard InGaAs QDs. For the singly and doubly charged excitons, X 1− and X 2− , the emission splits into two lines by the Zeeman effect and blue-shifts via its diamagnetic response (see Supplementary Fig. 5). The X 3− has a much richer structure (Fig. 3a). At zero magnetic field, the X 3− 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 t s (triplet satellite) in Fig. 3a 28 . On increasing the magnetic field, the degeneracy (or near degeneracy) of the p-sub-shells is lifted. In the Fock-Darwin model 28,65,66 , the p − -sub-shell (angular momentum L z = +1) moves down in energy by À 1 2 hω c while the p + -sub-shell (angular momentum L z = −1) moves up in energy by þ 1 2 hω c (Fig. 3d). Here, ℏω c is the electron cyclotron energy. Once this splitting becomes large enough, the X 3− 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 X 3− singlet-PL-spectrum on a standard InGaAs QD shows several anti-crossings (Fig. 3a). We develop a model to describe the X 3− 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-WLcontinuum coupling as the continuum of WL-states facilitates rapid dephasing 28,43 .
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 (A 1 and A 2 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 X 3− singlet leaves behind two electrons in the lower p-sub-shell and one electron in the s-shell (state j ai). This final state can couple to state j bi 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 j ai and j bi 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 −ℏω c while the p + -sub-shell moves up with 1 2 hω 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 anticrossing. This is not surprising for a real QD where there is no exact rotational symmetry. To describe this, we introduce basis state j ci (with an electron in the p + -rather than the d − -shell) and a small coupling between states j bi and j ci to describe the symmetry breaking. This leads to the two characteristic anticrossings (A 1 , A 2 ) of the singlet emission pair with a line with a dispersion of approximately À 3 2 hω 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 X 3− PL extremely well. This strong agreement allows us to extract the key QD parameters from this experiment: the electron s-p splitting (ℏω 0 = 24.1 meV) and the electron effective mass (0.07m o ). We are also to conclude that the potential is subharmonic: the p-d splitting is smaller than the s-p splitting.
With this understanding of the X 3− , 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 X 3− 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. b QD-shells and their occupation for the different exciton complexes. The triply charged exciton X 3− 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 X 3− singlet (s) and triplet (t) as well as the highly charged exciton complexes X 4− and X 5− appear The X 3− from the AlAs-capped QD is revealing in a number of other respects. First, the X 3− singlet state shows one Zeeman-split line, not two as for the standard InGaAs QD. This is evidence that the j ai-j bi coupling is suppressed on account of the energies: state j bi lies at too high an energy to couple to state j ai (see Supplementary Note 3). A large ratio between j bi-j ai energy splitting and coupling strength leads to a very weak emission from the second line, strongly red-shifted for a positive j bi-j ai energy splitting. The absence of a second singlet emission line is evidence that the p-d splitting is larger than the s-p splitting, a superharmonic potential. This is consistent with the thin, AlAslayer in the STEM-characterization (Fig. 1g) which bolsters the lateral confinement; and also the ensemble-PL where the AlAscap blue-shifts the d-shell more than the p-shell (Fig. 1i). Second, the X 3− singlet and triplet X 3− -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 AlAscapped 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 X 3− exciton in the AlAs-capped QD has a very pronounced fine structure splitting: the splitting of the X 3− triplet into three lines is a prominent feature (Fig. 3b). This particular fine structure originates from the electron-hole exchange in the initial exciton state 60 , and its increase relative to standard InGaAs QDs is indicative of a stronger electron-hole confinement 67,68 .
We model X 3− 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 s-p splitting as ℏω 0 = 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 present 43 . Such a temperature broadening was observed for exciton complexes even with modest charge 43 , for instance, X 2− . For an AlAs-capped QD, we measure the PL-linewidth of all charged excitons (X 1− -X 5− ) as a function of temperature (Fig. 4a). Even for the highly charged excitons X 4− and X 5− , the temperatureinduced broadening is much weaker than that for charged excitons beyond X 1− in standard InGaAs QDs which show a strong, linear temperature dependence 43 . Instead, the linewidths are described well by a model which considers a localized exciton and dephasing via acoustic phonon scattering 69 . This too is evidence that the WL-states for electrons no longer exist.
Finally, we measure the linewidth of the singly charged exciton (X 1− ) with resonant excitation, detecting the resonance fluorescence 51 (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 QDs 51 . This shows that the AlAs-capped QDs retain the very low charge noise achieved for standard InGaAs QDs 51,70 . 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. Triply-charged exciton as a probe of the quantum dot (QD) and the wetting layer (WL) states. a X 3− 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 X 2− , not X 3− . c The optical decay process of the X 3− 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 state 28 . d X 3− assuming that angular momentum is a good quantum number: the p-shell has angular momentum L z = +1 and −1; the d-shell +2, 0 and −2. The X 3− ground state changes from a triplet to a singlet at a finite magnetic field. e The final state of the singlet X 3− . State j ai can couple to the d-shell of the QD via an Augerlike process (state j bi) and to a Landau level in the WL (state j di). When d − and p + come into resonance, state j bi couples to state j ci where one electron occupies the p + -sub-shell

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.