Excitation transfer in stacked quantum dot chains

The 1-stack QDC sample emits in the 1–1.4 eV range similar to conventional SK QDs, but with a much richer optical feature. Figures 1(a)–(f) show spatial- and energy-resolved spectral maps of the same 20 × 20 μm² area of the sample at 80 K. The PL maps, integrated over increasing energies from 1.005 eV in figure 1(a) to 1.275 eV in figure 1(f), show spatially non-uniform emissions with a cross-hatch pattern resembling the surface undulation of the underlying InGaAs/GaAs template. Figure 1(a) shows that at 1 eV, the lower energetic end of the spectra, emissions emerge from bright patches which look like stripes along the $[1\bar{1}0]$ direction. The stripes become clearer and better resolved as the energy increases to 1.045 eV in figure 1(b). The dottiness of the lines making up the stripes is simply a reflection of the variation in local QD density, in good agreement with the morphology of uncapped samples (see the supplementary data, available at stacks.iop.org/SST/30/055005/mmedia). When the energy increases to 1.105 eV in figure 1(c), emissions from the existing $[1\bar{1}0]$ direction begin to fade while those from the orthogonal, [110] direction emerge. The emissions from the [110] and $[1\bar{1}0]$ stripes overlap and yield the characteristic CHP luminescence observed in figure 1(c). As the energy continues to increase to 1.195 eV in figure 1(d), the $[1\bar{1}0]$ emission peters out, whereas the [110] emission intensifies. And as the energy keeps on increasing to 1.245 eV in figure 1(e) and 1.275 eV in figure 1(f), the [110] and $[1\bar{1}0]$ emissions are extinguished, replaced by bright patches emerging in the previously dark areas—i.e., the bright/dark regions in figures 1(a) and (f) are reversed. (The reversal is easily recognized in the first video in the supplementary data).

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The QDs can be categorized, in evolution sequence [27] and with corresponding labels shown in figure 1(d), into four distinct groups: 1. at the intersection of the orthogonal [110] and $[1\bar{1}0]$ dislocations, 2. on the $[1\bar{1}0]$ dislocation lines, 3. on the [110] dislocation lines, and 4. on the remaining areas. The four QD ensembles emit slightly differently. Figure 1(g) shows point spectra at pixels 1–4 in figure 1(d), corresponding to the four QD ensembles above. Emissions from pixels 1–3 comprise two principal peaks: a broad peak centered at around 1.15 eV and a narrow peak at 1.27 eV. In contrast, emission from pixel 4 comprises only one narrow peak, also centered at 1.27 eV.

The broad peaks result from QD chains along the $[1\bar{1}0]$ and [110] directions as unequivocally proven by microscopy and spectroscopy. The micro-PL maps in figures 1(a)–(f) provide the microscopic proof, whereas the macro-PL spectra in figure 1(h) provide the spectroscopic confirmation. It has long been known that the underlying InGaAs/GaAs CHPs are asymmetric: the $[1\bar{1}0]$ stripes nucleate earlier, have greater density, and result in surface steps which are taller than the [110] stripes [28]. The asymmetry is transferred to the overgrown layers, resulting in QDs along the $[1\bar{1}0]$ direction forming slightly earlier and are thus taller and emit at a lower energy than those along the orthogonal [110] direction [22, 27, 29]. The microscopic images in figures 1(c)–(d) provide a clear visual evidence of QD luminescence decorating the $[1\bar{1}0]$ and [110] stripes, at slightly different energies. This small energy difference however cannot be resolved in the corresponding point spectra: figure 1(g) shows that pixel 2, taken along the $[1\bar{1}0]$ direction, emits at a slightly lower peak energy than pixel 3, taken along the orthogonal [110] direction. Though these two peaks are spatially resolved in microscopy, they are spectrally unresolved as a result of micro-PL setup's fast integration time. The macro-PL setup, in contrast, has a much longer integration time and can provide complementary spectra with greater signal-to-noise ratios. Figure 1(h) shows excitation power-dependent macro-PL spectra of the same sample (but on a different area) at 20 K. The lowest two energetic peaks—1.04 eV for the $[1\bar{1}0]aligned$ QDs and 1.10 eV for the [110]-aligned QDs hi-lighted by the black arrows—can now be clearly resolved at high excitation powers.

The narrow 1.27 eV peak is asymmetric: the left and right sides of the 1.27 eV peak in figure 1(g) tail off slightly differently—a characteristic of two unresolved Gaussian peaks with different FWHM. The closely-spaced emissions arise from the superposition or spectral overlap of the small free-standing QDs and the underlying InGaAs CHP template. The PL map in figure 1(f) shows that the areas that give off this luminescence are those between the cross hatches which happen to be the nucleation sites for free-standing QDs, too.

The four small peaks between 1.3 and 1.47 eV (observed only in the macro-PL setup as indicated by the grey arrows in figure 1(h)) are most likely associated with multiple wetting layers, some of which were previously identified [22]. For conventional InAs/GaAs SK QDs, a single WL exists and emits at around 1.44 eV. This is true even if bimodal size distributions are present [21], as long as the growth front is flat. For InAs QDs on InGaAs CHPs, the growth front is not flat. In fact, the surface steps in the $[1\bar{1}0]$ and [110] directions are different [28]. The WL underneath the QD chains along the $[1\bar{1}0]$ and [110] directions can thus be expected to be different—for example, they could form one-dimensional wetting wires [30]—but similar structures investigated so far reported just a single WL energy [22].

The multiple WL peaks above are only observed close to the carbon-impurity, 1.49 eV peak and the bulk GaAs, 1.52 eV peak. Measurements taken at different areas where the 1.49 and 1.52 eV peaks are absent do not reveal the multiple WL peaks. This indicates the possibility that bulk C centers render ineffectual the carrier capture by QDs from the GaAs matrix and the WLs, and explain the elusiveness of the multiple WL luminescence. It is a normal practice for those carrying out PL measurements to shine the exciting laser on a spot that yields the best signal and in so doing move away from areas with large local concentrations of C, and hence miss the WL peaks.

It is worth pointing out that the multimodal size distribution of the 1-stack layer which gives rise to multiple emission peaks has not been optimized for broadband applications. If desired, one can increase the inhomogeneity of the spectrum by, for instance, growing the QDs at a higher rate or subjecting them to rapid thermal annealing [31]. In addition, one can also increase the luminous efficacy of real devices by soft-annealing under hydrogen so that most defects are neutralized and do not adversely affect long-term reliability [22].

In reflection-based PL set-ups, the 1-stack QDC layer enjoys an unobstructed output window but the 3- and 5-stack QDC layers may not. This depends on electronic coupling. If the stacked layers are coupled, they behave as a single ensemble and should enjoy an unobstructed output window as is the case for the 1-stack sample. But if the stacked layers are uncoupled, luminescence from all the layers should be detectable, unless some are obstructed—reabsorbed, scattered, or reflected—in which case the emissions are dominated by the overlying structures due to geometrical advantage. Such behaviour in stacks of randomly distributed QDs cannot be proven through spectroscopy alone. But if the random distribution is reduced, as is the case for QDCs, and with PL mapping capability, it is possible to draw such a conclusion as shown below.

Figures 2(a)–(d) show the PL maps of the 3-stack QDC sample at increasing integrated energy from 1.075 eV in figure 2(a) to 1.235 eV in figure 2(d). Similarly, figures 2(e)–(h) show the PL maps of the 5-stack QDC sample from 1.075 eV in figure 2(e) to 1.235 eV in figure 2(h) (see animated videos in the supplementary data for the complete ranges). The maps show luminescence which is CHP-like for the 3-stack sample, but stripes-like for the 5-stack sample. Since adjacent stacks are separated by a 10 nm GaAs spacer which is sufficiently thin to allow coupling in conventional SK QD stacks [11], a question emerges as to why CHP-like luminescence similar to the 1-stack sample described above is not observed in the 5-stack case, or is not more clearly observed in the 3-stack case because the bottom-most QDC layer for the three samples is identically grown, has the biggest dot size and the lowest GS energies, and should thus provide the same optical features (CHP-like) as observed in the previous section. The maps shown in figure 2 instead more closely match the AFM morphologies of the top-most QDC layer where the number density of QDs along the [110] direction is significantly reduced (see the supplementary data), implying that the emission is dominated by the top-most layer. The bottom-most QDC layer buried along the [110] direction is almost undetectable; it can be barely distinguished by the collinearity of bright or dark spots, as indicated by broken lines in figure 2.

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One possible explanation for the much reduced [110] emission is carrier tunnelling from the bottom to the top QDC layer as has been observed in the QD bi-layer reported by Heitz et al [11]. However, this mechanism cannot explain the missing CHP-like emissions because carriers always tunnel towards the lower energetic state, i.e., the bottom-most QDC layer (1.1 eV active), not the top-most QDC layer (1.2 eV). If inter-stack tunnelling were present, the CHP-like emissions would have been enhanced, not suppressed.

Another possible explanation is that the top QDC layer has the highest quantum efficiency, thus dominating the weaker emission from the low quantum efficiency bottom stacks. The QDC stack is strained throughout as it is sandwiched between the top GaAs capping layer and the bottom partially-relaxed InGaAs CHP layer which in turn rests on a GaAs buffer. Since the top stack is in contact with the dislocations-free GaAs cap layer, whereas the bottom stack is in close proximity to the dislocations-prone CHP layer, the top stack would have a greater optical quality. Unless the strain profile surrounding each QD layer is carefully compensated [32], increasing the number of QD layers would in general result in accumulated strain that ultimately degrades the optical quality of the whole QD stack [33].

After many trials to uncover the bottom layer emissions—mostly by varying the optical path from normal to edge—it was found that the elusive emissions are not entirely missing, only significantly diminished since they are partially retrieved simply by increasing the excitation power density. This approach is however against a normal PL practice of using minimum excitation to study the true ground-state energies of QDs [9] and also to avoid sample heating.

Figures 3(a) and (b) show the macro-PL spectra of the 3- and 5-stack QDC samples, respectively. The spectra are measured from a low excitation power density I₀ of 0.11 W cm⁻² to 50I₀. For the 3-stack sample, increasing excitation results in intensity saturation of the 1.2 eV peak emissions from the top-most layer. Such saturation in conventional SK QDs would coincide with the appearance of one or more higher energy peaks as a result of state filling, and this is true for both single-layered and stacked QDs [12]. The spectra in figure 3(a) are however the opposite: as the 1.2 eV peak saturates, a lower energy peak emerges at around 1.1 eV, and at 40I₀ excitation, another peak at an even lower energy of around 1.05 eV can be seen to be emerging. The sequential appearance of the 1.1 and 1.05 eV peaks upon saturation of the 1.2 eV peak is evident in the excitation-dependent PL intensity plots at the three energies shown in figure 3(c). The two additional peaks—1.1 and 1.05 eV—coincide with those of the 1-stack layer described earlier, strongly indicating that they arise from the bottom-most QDC layer.

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The partial recovery of the bottom-most QDC emissions could be a direct or an indirect result of increased excitation, or a combination of both. The direct result is simply due to the greater availability of photons reaching the bottom-most stack. The indirect result is due to excitation transfer of carriers from the top- (high energy) to the bottom (low energy) layer, which is energetically favorable but ineffective at low-level excitations. The inefficiency is a result of suppressed tunnelling. At 10 nm (∼36 ML), the GaAs spacer is sufficiently thin that tunnelling readily occur among stacks of conventional SK QDs [11]. But this is not the case for stacks of QDCs here. The tunnelling between stacks of QDCs must have been suppressed by the presence of the underlying misfit dislocations—the sole differentiating factor between the QDC and QD stacks. Often associated with dislocations are strain fields known to cause local inhomogeneities in various physical properties [34]. The strain fields can be so strong that they affect surface atom motion and guide the nucleation of nanoscale QDs [35, 36] or the running direction of micron scale droplets [37]. Their effects on coupling are thus not surprising. External strains applied via piezoelectric crystal, for example, have been shown to affect fundamental QD excitonic properties [38], particularly to tune the excitonic binding energies [39]. Internal strains caused by interfacial misfit dislocations should likewise affect excitonic GS wavefunctions as a result of electric field induced by piezoelectric effects and/or strain gradients. Electric fields, built-in or externally applied, increase the effective distance between carriers confined in vertically-stacked quantum structures, and thus decrease coupling. The decrease is offset at high-level optical excitation. As the GS becomes saturated from the increased excitation, the first excited state (ES) would normally emerge in uncoupled nanostructures. For the multi-stack QDC structures, however, the ES wavefunctions extend further in space (are less localized) than those of the GS, penetrating further into the GaAs spacer and subsequently falling into the lower GS of the bottom stack. The extra carriers that would normally give rise to the higher-energy ES peaks thus avail themselves of the lower-energy GS of another stack which explains the successive emergence of the lower-energy PL peaks and the absence of state-filling effects in figure 3(a). Excitation transfer between an ES of one nanostructure and a GS of another in resonant has been reported in many systems [11, 12].

For the 5-stack sample, increasing excitation also results in intensity saturation of the 1.19 eV peak of the top-most QD layer and the appearance of the 1.09 eV peak as shown in the spectra in figure 3(b) and the excitation-dependent PL intensity plots of the two peaks in figure 3(d). The saturation of the 1.19 eV peak and the emergence of the 1.09 eV peak seen in figure 3(d) are, however, more gradual than those of their equivalence in the 3-stack sample—the 1.2 and 1.1 eV peaks—in figure 3(c). This possibly results from the greater saturated intensity due simply to the 5-stack sample's greater QD areal density—approximately by 5/3 times. The state-filling effects are also absent; the high energy peaks between 1.3 and 1.47 eV are WLs as described while discussing the 1-stack sample earlier. These WL peaks cannot be observed in figure 3(a) since this is a low C-impurity area evidenced by the 3-stack sample's lowest 1.47 eV peak among the three samples.