Correlating Photoluminescence and Structural Properties of Uncapped and GaAs-Capped Epitaxial InGaAs Quantum Dots

The understanding of the correlation between structural and photoluminescence (PL) properties of self-assembled semiconductor quantum dots (QDs), particularly InGaAs QDs grown on (001) GaAs substrates, is crucial for both fundamental research and optoelectronic device applications. So far structural and PL properties have been probed from two different epitaxial layers, namely top-capped and buried layers respectively. Here, we report for the first time both structural and PL measurements from an uncapped layer of InGaAs QDs to correlate directly composition, strain and shape of QDs with the optical properties. Synchrotron X-ray scattering measurements show migration of In atom from the apex of QDs giving systematic reduction of height and enlargement of QDs base in the capping process. The optical transitions show systematic reduction in the energy of ground state and the first excited state transition lines with increase in capping but the energy of the second excited state line remain unchanged. We also found that the excitons are confined at the base region of these elliptically shaped QDs showing an interesting volume-dependent confinement energy scaling of 0.3 instead of 0.67 expected for spherical dots. The presented method will help us tuning the growth of QDs to achieve desired optical properties.

However, it is becoming increasingly clear that this assumption is not in fact valid as In-Ga intermixing during growth of these two layers on GaAs (001) substrate, the buried-layer just above the buffer layer and the top-layer just below capping layer can be quite different. The process of strain release 18 , segregation, faceting, intermixing, and strain-enhanced diffusion between layers of QDs near buffer and capped layers known to vary 19,20 strongly affecting the confinement length of charge carriers within QDs that determine the characteristics of emitted photons [15][16][17] . Here we show, for the first time, that both structural and optical properties can be measured from same layer of QDs as a function of capping layer thickness. The atomic force microscopy (AFM) images obtained from uncapped QD sample enabled us to reconfirm the results obtained from synchrotron X-ray scattering measurements.
Grazing incidence diffraction (GID) X-ray measurements 14,[21][22][23][24][25][26][27][28] are ideal non-destructive techniques to extract the structural information of the nanometer-thin layer of QDs averaged over a large area depending on the footprint of the X-ray beam over a sample. GID studies reveal the average values of the structural parameters; composition, interfacial strain, lateral and vertical confinement lengths which are solely responsible for excitonic energy levels within QDs. The availability of intense synchrotron sources delivering nanometer-sized beams would enable us, in the future, to obtain information regarding composition and strain profiles averaged of a few tens of dots or perhaps an individual QD using the methods described in this paper. Here we present the results of uncapped and capped InGaAs QDs samples and the details of data analysis and measurements are given in the method section. It should be mentioned here that the volume of QDs on GaAs substrate is quite small, as a result only GID peaks like the (200), (220), (400) etc can be measured 29 nondestructively. Measurement of other conventional diffraction peaks require much higher incidence angle and GaAs peaks overshadows the QD data as the X-ray beam penetrates deeper into the substrate. We optimized the sensitivity of QD signal by varying the incident angle and available energy of the X-ray beam for these measurements. The ratio of integrated intensity of the (200) and (400) profiles from GaAs to InAs in-plane reflection are measured here as a function of in-plane lattice parameters to extract indium profile within an average quantum dot.
The measurements of (400) and (200) in-plane crystal planes of the QDs samples around the GaAs bulk peaks were done by orienting the substrate at an angle 'θ' with incident X-ray beam and 1D Mythen detector is kept at a detector angle (Φ) with respect to direct beam so that it is twice the incident angle of photons to crystal planes (Φ = 2θ) and the scattering geometry is shown in Fig. 1a. These scans provide direct measure of in-plane lattice parameter (a II ) defined in terms of the indices (h, k, l) of the nearest Bragg reflection of the substrate as . Measured scattering intensity taken by 1D Mythen detector data for different 'θ' values from the obtained scans have been stitched by Matlab programs to generate typical two-dimensional GID images around 400 and 200 Bragg peaks where vertical and horizontal axes denotes exit angle of Mythen detector (α f ) and in-plane lattice parameter (a II ) respectively. A representative 2D scattered intensity data around (400) Bragg peak of the uncapped InGaAs QDs is shown in Fig. 1b. We could not detect the signature of a pure InAs diffraction peak as the deposition amount of InAs was kept very small (1.8 MLs) and it is known to intermix with GaAs to form InGaAs QDs. Scattered intensity in-between the two extreme a II values (0.565 nm for GaAs and 0.605 nm for InAs) exhibit intermixing and alloying of In and Ga within wetting layer (WL) and QDs. The results from AFM measurements presented here clearly show that the InGaAs QDs are ellipsoidal in shape with a preferred elongation in the direction perpendicular to the miscut stair-steps (refer Fig. 1c). We performed both radial and angular momentum scans in GID around in-plane 400 and 200 Bragg diffraction peaks of GaAs, by keeping incidence angle of the X-ray beam below or around the critical angle of GaAs to make the technique sensitive to QDs layer near the surface (refer method section for details). Representative plots of the I 400 and I 200 profiles have been shown for uncapped QDs (Fig. 1d) and capped QDs with 5 nm (Fig. 1e) and 30 nm (Fig. 1f) GaAs. It is to be noted here that in 400 and 200 Bragg peaks contribution of GaAs arises from both the substrate and the cap layer. Scattered intensity reduces towards higher in-plane lattice parameter and reaches background counts when a II = 0.597 nm for uncapped, a II = 0.593 nm for 5 nm capped and a II = 0.589 nm for 30 nm capped QDs. This systematic reduction in data range may be due to X-ray absorption in increasing GaAs cap thickness. The variation of Indium content as a function of in-plane lattice parameter a II has been calculated using equation (1) given in method section and the obtained profile reveals compositional variation for differently capped QDs. It has been found that the concentration x within an average − In Ga As x x 1 QD varies between 0.85 and 0.1 as shown in the plot shown in Fig. 1g for the uncapped sample. For both 5 nm and 30 nm GaAs capped QDs, Indium fraction values reach a maximum of 0.6 and 0.75 respectively as shown in Fig. 1h and i. We shall discuss below the correlation between in-plane lattice parameter a II and the height of an average QD above the substrate by systematic measurements of Yoneda wings and show that a II increases toward the tip of the QD as indicated by vertical lines in Fig. 1d,e and f. It is clear from these figures that for all three types of samples, Indium content is higher in the lower and middle region of QDs 19,30 . The in-plane strain profile within QDs with respect to the GaAs were computed using expressions ε = − a ax a x ( ())/ ( )

II GaAs
, as a function of a II where a GaAs and a(x) are the lattice parameter of GaAs and of InGaAs obtained from Vegard's law corresponding to Indium content x 31 . The calculated strain profiles shown in Fig. 1e and f for QDs with 5 nm and 30 nm GaAs cap layer approach 0% strain at the tip of QDs. The uncapped QDs (Fig. 1g) show in-plane compressive strain of −1% even near the tip region. For all three types of QDs maximum compressive in-plane strain was obtained at the highest Indium containing region, which is about 1 nm height from the substrate. For uncapped, 5 nm and 30 nm capped samples the maximum strain was found to be −5.5%, −4% and −5% respectively (Fig. 1g,h and i). However, out-of-plane lattice parameter and strain can be calculated from the experimentally obtained in-plane lattice parameters by assuming that Poisson's relation holds here. Fitting of angular scans data for three different types of QDs, namely uncapped and 5 nm and 30 nm capped, samples are shown in Fig. 2a,b and c respectively and fitting parameters are shown in Table 1. The results of the fitting show increase in base dimension of QDs with increasing capping thickness. The dimensions of the base major axes 'a' for uncapped, 5 nm and 30 nm capped samples came out to be 24 nm, 29 nm and 32 nm respectively. The eccentricity values also increase with increasing capping thickness making buried QDs more elongated (refer Table 1). In Fig. 2d, we have compared the fitting quality of circular and elliptical disc model and it is clear from the figure that elliptical disc model represent the experimental data much better (see equation (3), method section). The circular disc model could not represent the data with any diameter as shown in Fig. 2d.
The results presented in Fig. 3a,b and c for uncapped, 5 nm and 30 nm capped QDs clearly show that QD-base region has in-plane lattice parameter a II close to GaAs and with increase in average QD height, a II approach the value of InAs lattice parameter. For uncapped QDs, refer representative data in Fig. 3a, at the heights 0.5 nm, 1.4 nm, 2 nm, 2.2 nm, 3.3 nm, and 3.8 nm above GaAs substrate the a II values become 0.57 nm, 0.573 nm, 0.576 nm, 0.58 nm, 0.589 nm and 0.593 nm, respectively following equation (5) (refer method section). The data shown in Fig. 3b for 5 nm capped QDs shows a similar trend but the apex region terminates at the a II value of 0.591 nm at a height of 3.4 nm over GaAs substrate indicating migration of the In-atoms from the apex region of QDs with the growth of GaAs cap-layer. In Fig. 3c the data and fitted profiles for 30 nm cap-layer are shown and the results indicate further reduction in the heights of QDs to 3.1 nm with the maximum measurable in-plane lattice parameter a II of 0.588 nm.
We have carried out systematic AFM measurement of the uncapped QDs to reconfirm the elliptical shape obtained from the X-ray analysis. A three-dimensional extracted image of an uncapped QD measured in AFM is shown in Fig. 3d -the elliptical base of 44 ± 4 nm and 25 ± 2 nm in the two mutually perpendicular directions can be clearly seen. It is to be noted here that unlike X-ray measurements the AFM can probe only the portions of uncapped QDs outside wetting layer. The average height of QDs was found to be around 2.2 ± 0.4 nm and we shall discuss detailed comparison of the extracted dimensions below to show that the results of AFM measurements are consistent with the results of the analysis of X-ray data. The AFM data from the other two samples could not be collected due to the presence of capping layers having thickness larger than QD heights. In Fig. 3e we have shown cross-sectional views of uncapped QDs obtained from AFM data along the major and minor axes directions at several measured heights of 0.5 nm, 1 nm, 1.5 nm, 1.85 nm and 2.25 nm. At the 0.5 nm height we obtain major and minor axes as 40.1 ± 4 nm and 23.1 ± 2 nm giving the eccentricity of 0.82 ± 0.05. At the tip region with 2.25 nm height these values become 18.1 ± 2 nm and 11.4 ± 1 nm giving lower eccentricity of 0.77 ± 0.04. At the three intermediate heights of 1 nm, 1.5 nm and 1.85 nm, the representative QD have eccentricity of 0.81 ± 0.05, 0.81 ± 0.04 and 0.78 ± 0.04 with decreasing major axes dimensions of 36.3 ± 3 nm, 32.2 ± 3 nm and 24.6 ± 2 nm respectively. Reductions of eccentricity are also clearly observed from base to tip of uncapped QDs in AFM measurements and the obtained values are in reasonable agreement with GID values.
The dimensions of the major and minor axes at the height of 1 nm in GID data comes out to be 48 nm and 26.7 nm giving eccentricity of 0.83 and only at the height of 1.9 nm we get the values of major and minor axes as 37 nm and 21.7 nm with eccentricity of 0.81, refer results of the uncapped sample shown in Fig. 4a. As mentioned earlier the measured height (Fig. 3e) in AFM was found to be about 1.5 nm less than that obtained from X-ray measurements (Fig. 4a) as AFM cannot access portion of QDs buried under wetting layer. The maximum height the particular QD shown in Fig. 3d and average height (3.8 nm) of uncapped QDs obtained from X-ray data also show this difference. The height of QD obtained from X-ray scattering and AFM measurements can be used to  in the base of an average QD (refer discussion on PL below) or that of the wetting layer is around x = 0.25 and 1.8 monolayer of deposited InAs would have given us 2.0 nm of wetting layer if there was no QD formation. An average QD has volume of 3825 (=1006.6 * 3.8) nm 3 for uncapped QDs layer with an average x = 0.4 and that is equivalent to the volume of 6120 (=3825 * 0.4/0.25) nm 3 for x = 0.25. This reduces the thickness of the wetting layer of area 16667.7 nm 2 allocated to each QD to about 1.6 nm -close to the observed difference of QD heights between X-ray and AFM measurements.
We have carried out systematic cross-sectional transmission electron microscopy (X-TEM) measurements 32,33 to cross-check the dimensions of the QDs and the estimated thickness of the wetting layer. A representative image of an uncapped QD having height of about ~3.8 nm is shown in Fig. 3f. The obtained height values are found to be consistent with the X-ray and AFM results presented here. Base dimension of 20 nm can be related to the minor axes dimension of elliptical-shaped QD. To determine wetting layer thickness we took X-TEM data in between QDs and the thickness of the measured rough surface giving higher contrast was determined to be around 1.5 nm as indicated by yellow dotted lines in Fig. 3g. This value matches well with the estimated wetting layer thickness.
With increasing height of QD, lateral dimensions reduce significantly and major and minor axes dimensions become 16 nm and 10.6 nm with eccentricity of 0.75 at the apex region of QD -this is also consistent with measured AFM value. The strain profile obtained from X-ray measurements has been indicated by the color-bar in the Fig. 4. Similar trends have been observed in the GID data on GaAs capped QDs; obtained results are schematically demonstrated in Fig. 4b and c for 5 nm and 30 nm GaAs capped QDs respectively. Tip region of 5 nm capped QDs obtained from X-ray analysis (refer Fig. 4b) show the average maximum height of QDs to be 3.1 nm with major and minor axes dimensions of 18 nm and 10.5 nm respectively. The shape of the uncapped, 5 nm and 30 nm capped QDs shown in Fig. 3e show much larger lateral dimension as compared to height and these QDs can be approximated as elliptical lenses. We notice increase in lateral size and reduction in height of the QD lenses as the capping thickness increases. For 30 nm capping (refer Fig. 3c) major axis dimension (and eccentricity) becomes 64 nm (0.89) and 20 nm (0.8) at height of 1.1 nm and at the tip region with height 3 nm respectively. The shape changes upon capping have been studied 34,35 earlier but direct correlations between PL energy and structural parameters were not investigated.
The micro-PL measurements on uncapped and capped Although generally E GS peak is expected to be more intense than E 1 and E 2 , here we observe stronger E 1 and E 2 lines for all the QD samples. The high incident excitation intensity used here to get micro-PL data may lead to such intensity reversal due to state filling effects 37 . As expected the PL emission from the uncapped QD sample was much weaker due to non-radiative emission process 13 through surface states, compared to capped samples. We have used 10 points (red line) data smoothening for guide to eye and presented in Fig. 4d both measured and smoothed data -the PL peak positions for uncapped QDs are not affected by smoothing process. The presence of strong heavy-hole free exciton (HHFE) PL emission from InGaAs wetting layer around 1450 meV 38,39 and similar emission from GaAs around 1490 meV for all the QDs samples were confirmed. The width 38 of the emissions for all the samples were found to be around 20 meV (refer Table 2) and this value is around half of the width observed in solution processed QDs used for technological applications 2-7 . We observed, except for E 2 emission line, that uncapped sample produces sharper (refer FWHM values Table 2) PL lines.
The relationship between QDs structure and confined exciton energy levels are schematically shown in Fig. 5a; the obtained optical transition lines are directly associated with the allowed exciton transitions. The value of E GS arise from the contribution of (i) composition dependent bulk band gap energy, (ii) confinement size and shape dependent confinement energy and (iii) exciton binding energy. The lateral dimension of the QD elliptical lens becomes larger as the capping thickness increase. The excitonic confinement volume of the average QD elliptical lens can be written as, lens h 24 2 2 , where L is the lateral confinement dimension and h is the height. It is known that for spherical confinement, E confinement is proportional to confinement volume as γ − V confinement where γ is 0.67 due to the fact that Ẽ r 1/ confinement 2 for sphere of radius 'r' . As the shape of confinement deviate from perfect sphere the power factor (γ) reduce from 0.67 to 0.43 (for cuboid shape) and to 0.33 (for pyramidal shape) 34 . E confinement for lens shaped QD are calculated by using electron ground state energy and heavy-hole ground state energy 40 ; we found γ to be 0.3 from the plot of the confinement energy variation with respect to confinement volume (refer Fig. 5b). Confinement energy for lens shaped QDs found to be primarily controlled by the highest lateral confinement dimension, which is the major length of base region of QDs. We obtained the confinement volume of 2049 nm 3 and 4080 nm 3 for 30 nm capped and uncapped QDs respectively from GID measurements, which indicate the confinement energy as 121.6 meV and 96.4 meV (refer blue and green lines in Fig. 5b) for 30 nm capped and uncapped QDs respectively. The measured ground state PL emission energy (E GS ) can be used to calculate effective composition of    Indium composition to be x = 0.26. Similarly for uncapped QDs, ground state PL energy of 1297 meV gives the value of Indium composition x = 0.22. It should be noted here that GID measurements also show larger Indium composition in uncapped QDs as compared to 30 nm capped QDs. The Indium composition obtained from PL measurement was found to be lower than the values obtained in GID measurements. This results indicate that excitons are near the base of the elliptical shaped QDs having lower Indium concentration; the confinement area of the excitons, as discussed below, also matched with the dimension of the base of QDs. We have carried out systematic Gaussian fittings of all the PL emission lines for all four samples having 0 nm, 5 nm, 15 nm and 30 nm GaAs capping and the resultant parameters are shown in Table 2. For uncapped sample the energy spacing, which are essentially decided by the exciton confinement volume, between E 2 , E 1 and E GS are found to be 32 meV and 29 meV. The energy spacing increases with capping thickness and become 36 meV and 33 meV for 30 nm capped QDs (refer Table 2). The measured separation energy between first excited and ground state energy (E 1 − E GS = 3π 2 ħ 2 /2 mL 2 ) also reconfirmed the consistency of GID and PL measurements. For 33 meV separation observed in 30 nm capped QDs calculated value of L came out to be 60.3 nm -this is consistent with the obtained major axis of the elliptical base of QDs obtained in the GID measurements. The increase in capping thickness shift PL lines towards lower energy as compare to the uncapped sample; for example a shift of 7 meV and 3 meV for E GS and E 1 was observed for 5 nm capping ( Table 2) and for 30 nm capping these shifts were found to be 9 meV and 5 meV respectively ( Table 2). However no significant shift could be detected for the E 2 line with capping.
In conclusion, we have reported a direct method to correlate structural and optical properties of epitaxially grown quantum dots with and without capping. The composition profile of an average QD extracted from GID and PL measurements show that excitons are confined near the base of the QDs. We also found that GaAs capping reduces peak concentration of Indium in the QDs. It will be interesting to extend the presented techniques for the solution processes QDs, which are easy to produce and attractive for display application but we need to find a way to orient these QDs in preferred crystallographic directions for such GID measurements. We also plan to use this method to probe smaller numbers of dots in future to reduce the effect of statistical averaging and thereby improve our understanding of structure-property correlation in these emerging materials.

Methods
Sample preparation. A set of samples is grown with similar growth conditions but different GaAs capped layer thickness (0-30) nm over InAs QDs on GaAs (001) substrate. The samples were grown by Molecular Beam Epitaxy (MBE). After oxide desorption a 250 nm GaAs buffer layer was grown followed by 100 nm Si-doped GaAs layer to enhance the supply of more photo-excited carriers into the surface of QDs in order to obtain a stronger PL response. The substrate temperature was then lowered to 470 °C during eight minute growth interruption followed by an additional 10 nm of GaAs to separate the QDs from the doped GaAs layer. Then 1.8 monolayers (MLs) of InAs were deposited with a deposition rate of 0.027 µm/h at same temperature with constant As 4 beam equivalent pressure at . × − 5 8 10 6 Torr. Different thicknesses of GaAs capping layers were grown over the InAs QDs with growth rate of 0.8 µm/h. X-ray GID, AFM, PL and TEM characterization. X-ray measurements were carried out with high beam energy (25 keV) to ensure sufficient X-ray penetration depth to probe buried QDs at Beamline P08 of Petra III, Synchrotron in DESY, Germany. A beam-defining slit of dimension μ μ × m m 50 300 was used in vertical and horizontal direction respectively and a position sensitive linear Mythen detector was used to collect scattered intensity. The sample surfaces are imaged by Atomic Force Microscopy (AFM) operating in tapping mode with a nominal tip radius of 10 nm using a Nanoscope-IV multimode SPM. Optical responses of QDs have been examined by micro-PL measurements at low temperature (4 K) with a laser source of wavelength 780 nm. The average density of QDs in the X-ray beam foot-print was around 60 per μm 2 as found by AFM measurements. The representative AFM image shown in Figure 1c; exhibit distribution of the epitaxial QDs over the stair-steps of the GaAs substrate. Cross-sectional TEM specimen was prepared by a FEI Helios NanoLab focused ion beam (FIB) system. A field-emission JEOL 2100 F S/TEM equipped with high-angle annular dark-field (HAADF) detector and X-ray energy-dispersive spectrometer (EDS) systems operated at 200 kV, was used for collecting high resolution images. Synchrotron X-ray Scattering. The As 200 with f In , f Ga and f As as atomic scattering factor for In, Ga and As. The fractions x within QDs and WL as a function of measured a II values can be calculated by taking ratio of the integrated scattered intensity as,

In Ga As
In Ga As 400 200 2 I 400 and I 200 have been measured by taking integrated scattered intensity over the detector exit angle α f . Lateral dimensions of QDs have been calculated by several angular scan measurements; each scan has a particular (θ, Φ) position around the radial intensity profile of (400) GID peak. At each position only incidence in-plane angle 'θ' was varied by keeping the detector angle fixed. During these scans radial momentum q r = (4π/λ) sin (Φ/2) remains constant but angular momentum [q a = (4π/λ) sin (θ − Φ/2)] changes depending on the variation of θ. The QDs are generally have been modeled as stacked of iso-strain circular discs 3 but AFM measurement for the present samples clearly show elongated InGaAs QDs. Our analysis of the radial data presented here clearly shows that stack of iso-strain elliptical discs each having particular in-plane lattice parameters (a II ) Scientific REPORTS | (2018) 8:7514 | DOI:10.1038/s41598-018-25841-7 represent the data much better. The iso-strain length scale has been considered as, R(θ) = ab/(a − (a − b) cos (θ)), where 'a' and 'b' are the sets of major axes and minor axes respectively. The dimension of the set of (a, b) values were determined by fitting the measured angular scans data and it was noted that higher values of (a, b) are associated with base region of QDs and lower values of (a, b) are linked with apex of QDs. The scattering contribution from each such elliptical disc can be written as, Here f InGaAs is the effective scattering factor. For simplicity we assume f InGaAs is independent of r and only depend on Indium concentration value x. We have assumed 14 for the fitting of each of a II radial data that two different discs contribute in the measured intensity profiles. This is known approach 3 to take care of size distribution of the QDs and the fitted values of two major axes a of the fitted discs with relative contribution within bracket are shown in Table 1; for simplicity we have assumed a common eccentricity = − e b a 1 / 2 2 value for the two discs. It is apparent from Table 1 that contribution of the second discs having very small lateral sizes contribute only 28% to 7% in the intensity and in the subsequent discussion we shall only compare the larger discs obtained from the fitting.
The height from the GaAs substrate of any elliptical discs with fixed a II can be calculated by analyzing Yoneda wing in the scattered intensity profile as a function of exit angle around 400 Bragg diffraction peak. The height 'z' above GaAs substrate for a fixed a II could be calculated from the position of first Yoneda maximum α f max as