Suppression of alloy fluctuations in GaAs-AlGaAs core-shell nanowires

Compositional fluctuations in ternary and quaternary alloys are the prominent problem encountered in many III–V semiconductor materials systems.^1–9 Even miniscule deviations from the homogeneous alloy have significant impact on the electronic band structure,¹⁰ inducing changes in the band gap energy, and band bowing parameters.^11–13 Alloy fluctuations further pose a deleterious effect on the performance of electronic and optical devices by reducing carrier mobilities,¹⁴ broadening the excitonic photoluminescence (PL) linewidth,¹⁵ and promoting non-radiative indirect Auger recombination in light emitting devices, limiting their operation at high power.¹⁶ 

Though alloy fluctuations have been intensively investigated for the planar bulk-like semiconductors, so far little efforts were undertaken to probe and control their nature in non-planar nanostructures, such as free-standing nanowires (NWs). Only most recently, investigations on alloy disorder in semiconductor NWs have become available, fueled by the ever increasing sophistication of nanoscale metrology techniques. For example, in the prominent GaAs-based NW system, alloy fluctuations in the shell of individual GaAs-AlGaAs core-shell NWs have been identified as the cause for sharp line photoluminescence (PL) features just below the AlGaAs band edge.^17–21 In particular, Ga-rich clusters along the {110}-oriented sidewall facets of radially grown AlGaAs shell layers^20,22 are revealed by three-dimensional atom probe tomography (APT) to directly correlate with the emission energies of distinct quantum-dot (QD)-like centers.²⁰ Likewise, Ga-rich clusters along the adjacent {211} corner facets have also been reported as another source for localized excitonic transitions.¹⁸ As these clusters induce potential modulations throughout the core-shell NW, they are further considered to impact the performance of the various NW-based devices, including coaxial GaAs-AlGaAs NW lasers²³ or ultra-scaled transistors.²⁴ Clearly, there is a strong motivation to obtain control over the prominent alloy clustering in GaAs-AlGaAs core-shell NWs, in particular, by tuning the critical growth kinetics.

In this letter, we demonstrate tuning of the alloy compositional structure and suppression of alloy fluctuations in the AlGaAs shell of catalyst-free, molecular beam epitaxy (MBE)-grown GaAs-AlGaAs core-shell NWs by systematically controlling the shell growth temperature, T_shell. Using the correlated PL spectroscopy, scanning transmission electron microscopy (STEM), and atom probe tomography (APT), we show that the alloy fluctuations change their nature and are successively minimized towards a nearly homogeneous random alloy by reducing the growth temperature from 620 °C to below 400 °C.

The investigated GaAs-Al_xGa_1-xAs core-shell NWs (nominal x(Al) = 0.30) were grown in a solid-source MBE system on a Si (111) substrate via a catalyst-free process, as described in Refs. 17 and 20. The NWs consisted of ∼50-nm wide/∼6-μm long GaAs cores oriented along the vertical [111] direction (grown at T_core = 630 °C), and a ∼100-nm-thick AlGaAs shell deposited coaxially around the GaAs core on the major {110} sidewall surfaces. The AlGaAs shell layer was further terminated by a 5 nm-thick GaAs cap layer to inhibit oxidation under ambient conditions. A schematic cross-section of the nominal core-shell structure as well as a representative scanning electron micrograph of a single NW grown on Si (111) are shown in Figs. 1(a) and 1(b). In total, we grew five different samples with shell growth temperatures T_shell varying between 370 °C and 620 °C, under otherwise fixed shell growth conditions, i.e., As-BEP (beam equivalent pressure) = 3.5 × 10⁻⁵ mbar, Ga-flux = 0.073 nm/s, and Al-flux = 0.17 nm/s as calibrated based on the planar growth structures. We note that the size and morphology of all NWs are very similar to Fig. 1(b), independent of the shell growth temperature. In addition, we also grew reference samples for APT analysis on identically grown GaAs cores, but with shell layer structures of ∼10-nm-Al_0.30Ga_0.70As followed by a 5-nm-GaAs cap. Keeping the total diameter lower enables the APT at sufficiently low standing voltages to avoid fracture.

In a first set of experiments, we studied the impact of shell growth temperature on the alloy fluctuation mediated sharp-line luminescence using low-temperature (LT) micro-PL spectroscopy. For the PL experiments, individual NWs were dispersed onto a Si substrate and excited by a 532-nm continuous-wave diode laser at 10 K in a confocal PL microscope (excitation spot size ∼1 μm).^20,25,26 Typical PL spectra of single NWs from three different samples (T_shell = 370 °C, 490 °C, and 620 °C) are displayed in Fig. 1(c). Each spectrum exhibits a peak at around 1.51 eV, which is attributed to emission from the GaAs core.^17,20 In most NWs, the core emission exhibits a shoulder at lower energies, which stems from optical transitions in crystal defects, such as rotational twin defects and short wurtzite (WZ) segments embedded in the zincblende (ZB) NW.^19,26–28

In the high energy region of the spectrum, we identify sharp-line transitions of localized excitons consistent with the existence of alloy fluctuations in the AlGaAs shell as observed previously in samples grown at fixed T_shell ∼ 490 °C.^17,19,20 Importantly, in the present growth series, we recognize a dynamic change of (i) the energetic window, (ii) the intensity, and (iii) the spectral shape of the shell luminescence centers when tuning T_shell. First, the energetic window, i.e., the range of energy at which sharp line emission occurs, widens towards lower transition energies (<1.7 eV) with increasing T_shell. Simultaneously, with increasing T_shell, the overall intensity of the sharp-line luminescence increases significantly while the GaAs core luminescence intensity decreases. Regarding the shape of the spectrum, an intermediate T_shell of 490 °C yields a high density of discrete sharp-line luminescence features.^17,19,20 In contrast, a low T_shell of 370 °C produces very few sharp line features superimposed on a broad Gaussian peak (∼25 meV peak width) centered at 1.85 eV, the origin of which is discussed below. At high T_shell of 620 °C, the spectrum is dominated by a high density of sharp lines and additionally a few broader features at arbitrary transition energies within the ∼1.6–1.9 eV energetic window.

To provide a more quantitative, statistically relevant analysis, we performed PL spectroscopy on 8 NWs from each sample and plotted the arithmetic mean of the spectra in Fig. 2(a). This analysis includes additional shell growth temperatures, all in the range between T_shell = 370 °C and 620 °C. To adequately compare the core and shell luminescence, the spectra are plotted on a logarithmic scale, and each spectrum is normalized to the power of the excitation laser (fixed at 80 nW). The energetic window of the shell luminescence is delineated by arrows in Fig. 2(a) and plotted as a function of T_shell in Fig. 2(b). Clearly, the spectrum broadens monotonically towards lower transition energies with increasing T_shell. While the minimum transition energy of the shell luminescence is at ∼1.80 eV for T_shell = 370 °C, the spectrum monotonically decreases down to ∼1.60 eV for T_shell = 620 °C. On the other hand, the maximum transition energy increases only slightly from ∼1.89 eV (T_shell = 370 °C) to ∼1.94 eV (T_shell = 620 °C). The integrated intensity of the AlGaAs shell luminescence is further plotted versus T_shell (blue data) and compared with the luminescence from the GaAs NW core (red data) in Fig. 2(c). In this analysis, we subtracted the contribution of the Gaussian background centered at ∼1.85 eV from the spectra of samples grown at the two lowest T_shell, in order to reveal trends in the sharp line luminescence. Comparative data are also plotted without background correction. Most strikingly, we find that the PL intensity of the AlGaAs shell luminescence decreases by more than one order of magnitude from the highest to the lowest T_shell.

The reduced energy interval and luminescence intensity of the AlGaAs shell luminescence towards lower T_shell indicate that alloy fluctuations are continually reduced. Large energetic broadening observed at high T_shell, on the other hand, stems from the enhanced alloy fluctuations, which occur either as Ga-rich clusters with increased size and higher Ga concentration as discussed previously²⁰ or as unintentional quasi-superlattice structures as shown below. Likewise, the increase in the PL intensity can also be explained by the formation of steeper Ga concentration profiles in the clusters and quasi-superlattices. As a result, photo-excited carriers inside the 100-nm-thick AlGaAs shell tend to recombine preferentially in localized states of the Ga-rich clusters/superlattices, given their size and Ga concentration are large enough, rather than diffuse to the GaAs core via tunneling processes.^19,20 Hence, the PL intensity from the GaAs core tends to be lowered relative to the shell luminescence at an increased T_shell (see red data in Fig. 2(c)). We note that in GaAs-AlGaAs core-shell NWs with significant alloy fluctuations, carrier diffusion mediated luminescence (i.e., from shell to core) constitutes only a small contribution to the total core luminescence,¹⁹ while most core luminescence arises from carriers directly photo-excited in the GaAs core.

One of the remaining questions of the PL data concerns the evolution of the broad Gaussian-like emission peak at ∼1.85 eV observed in all NWs of T_shell = 370 °C and 420 °C (see Figs. 1(c) and 2(a)). There are at least two possible origins for this emission feature. A first explanation is that it originates from the near-bandgap transition of bulk Al_xGa_1-xAs rather than from the localized states. In general, the low-temperature bandgap of 1.85 eV corresponds to an Al-content of x(Al) = 0.22 (Ref. 29), which is, however, much lower than the nominal value of x(Al) ∼ 0.3 expected for the AlGaAs shell. Based on the associated Raman spectroscopy measurements of the GaAs- and AlAs-like TO and LO phonon modes^17,25 of NWs from all samples, we verified that the averaged Al-content in the AlGaAs shell is indeed x(Al) = 0.32 ± 0.02, irrespective of T_shell. Hence, the lower effective band gap might be due to an AlGaAs alloy in the NW shell that does not yet fully exhibit the ideal random binomial distribution of a completely homogeneous alloy, as further confirmed by the APT data below. Indeed, even very short-range/small-scale order in an otherwise random AlGaAs alloy can reduce the direct band gap by more than >100 meV as predicted by electronic structure calculations.¹³ The fact that the band gap lowering and Gaussian-like emission are not visible in the AlGaAs shells grown at higher T_shell may be due to the more strongly localized potentials associated with much larger cluster sizes and more significant compositional modulations. Another cause for the Gaussian-like emission feature might be the existence of an additional defect emission band arising from impurity and point defect complexes, which are expected in low-temperature (LT) grown AlGaAs alloys. The LT-grown GaAs contains significant concentrations of As antisites and interstitials as well as Ga vacancies,^30,31 which may form complexes with each other or with impurities (e.g., carbon or oxygen, as in LT-grown MBE-GaAs)^32,33 and, thereby, induce donor-acceptor pair transition bands below band gap.

To corroborate the dynamic change in the AlGaAs shell luminescence, we investigated the nature of the alloy composition of selected samples using STEM high-angle annular dark-field imaging (STEM-HAADF) and APT. Fig. 3 shows exemplary cross-sectional STEM-HAADF images of NWs with AlGaAs shells grown at T_shell = 620 °C (Figs. 3(a) and 3(b)) and T_shell = 370 °C (Figs. 3(c) and 3(d)), respectively. Note that a similar sample grown at T_shell = 490 °C has been investigated previously (therefore not shown), where small (2–10 nm wide) Ga-rich clusters were observed as the dominant source of alloy fluctuations.^17,20 The images clearly show the as-grown layer sequence of inner hexagonal GaAs core, followed by the ∼100-nm-thick AlGaAs shell and the ∼5-nm-thin GaAs cap layer. In addition, we observe dark-contrast stripes along the six ⟨112⟩-oriented corner facets, which represent the regions of high Al-content^{17,20,23–25} due to capillarity limited diffusion. Note that the Al-rich stripes are broader, exhibit less Al-enrichment (weaker HAADF contrast), and are more inhomogeneous for the high-T grown shell (T_shell = 620 °C) as compared to the shell grown at low T_shell of 370 °C. The observation of wider, less confined enrichment profiles at higher T_shell is in good agreement with the kinetically modified adatom diffusion lengths.³⁴ 

More importantly, we find that the alloy compositional structure in the bulk part of the AlGaAs shell deviates strongly between the two respective samples. While the AlGaAs shell grown at T_shell = 620 °C exhibits very pronounced contrast modulations, i.e., alloy fluctuations along the $110$ radial directions (Figs. 3(a) and 3(b)), they are largely suppressed for T_shell = 370 °C (Figs. 3(c) and 3(d)). The compositional modulations observed at high T_shell mimic unintentional quasi-superlattices, since they homogeneously extend across the entire ${110}$ planes. We have further quantified the degree of alloy fluctuations along the $110$ directions via energy dispersive x-ray spectroscopy (EDXS). The ratio of Al/Ga in the EDXS signal, which is a relative measure of the alloy composition, is plotted as a function of position along one of the $110$ directions (linescans) as indicated in Figs. 3(a) and 3(c). On average, the Al/Ga ratio appears to be similar for both samples in the shell region close to the NW core; this ratio is increased towards the shell surface in the sample grown at high T_shell (see Fig. 3(e)). This is most likely due to the specific sidewall facet probed here and, thus, not representative for the entire NW shell characteristics, since the linescan captures much darker contrast areas (i.e., quasi-superlattices with higher Al-content) within the outer shell regions as compared to other neighboring {110} facets. Instead, the more relevant measure for the local alloy fluctuations is the relative variation in Al/Ga ratio within small increments probed along the shell growth direction. Indeed, we find that the magnitude in local point-to-point variations of the Al/Ga ratio is significantly larger (∼4×) for the AlGaAs shell grown at T_shell = 620 °C as compared to T_shell = 370 °C (see Fig. 3(e)). Note that the linescans also extend to the GaAs core and cap layer, confirming that the fluctuations in the Al/Ga-EDXS signal reproduce the sample structure very well with negligible measurement noise.

Based on both data, we can describe the alloy distribution in the high-T grown AlGaAs shell as random Ga-rich and Al-rich AlGaAs layers with thickness fluctuations down to the single monolayer level. The resulting electronic band structure of the AlGaAs alloy therefore produces effective 2D-quantum well (QW)-like confinement of the carriers along the $110$ directions with limited carrier diffusion along these directions, while additional confinement may occur within the ${110}$ planes of the quasi-superlattices. This explains, on the one hand, the observed increase in PL intensity of the AlGaAs shell luminescence and concurrent decrease of GaAs core luminescence (Fig. 2(c)). On the other hand, the confinement along and perpendicular to the $⟨110⟩$ directions further suggests the occurrence of both broader (2D-like) lines and sharper line luminescence features, as observed in Fig. 1(c) for the sample grown at T_shell = 620 °C. Finally, we can conclude from the STEM-HAADF and EDXS analyses that the alloy fluctuations are strongly reduced at low shell growth temperature (T_shell = 370 °C), in good agreement with the significantly weaker sharp line luminescence seen in Figs. 1(c) and 2.

Finally, we confirm the suppression of alloy fluctuations towards the lower shell T_shell by analyzing the deviations from the random AlGaAs alloy using APT. To examine the degree of non-randomness, frequency distribution analysis (FDA) is performed in regions of interest (ROI) inside the AlGaAs shell that exclude the Al-rich stripes along the ⟨112⟩ facets. Fig. 4(a) schematically shows an example of a cuboid ROI selected for the generation of FDA. FDA histograms for the Ga concentration are shown in Fig. 4(b) for samples grown at different T_shell. We find an average Al concentration of x(Al) ∼ 0.30 in all histograms (T_shell = 420 °C and 560 °C are not shown in the figure), in good agreement with the data obtained by Raman spectroscopy. Only the sample grown with T_shell = 620 °C exhibits a slightly lower average Al concentration of x(Al) ∼ 0.26. For this particular sample, the extracted Al-concentration from the ROI is not necessarily representative for the average Al-concentration in the entire shell, because of the comparatively small ROI (5–12 nm width along the radial NW direction) in combination with the relatively wide alloy fluctuations along the radial directions (quasi-superlattice). For the lowest T_shell of 370 °C, the observed FDA histogram is very similar to that expected for an ideal binomial distribution (see corresponding curve). As the T_shell increases, the number of voxels corresponding to the average bulk composition decreases whereas those lower and higher voxels increase. In other words, the observed FDA histogram becomes flatter, indicating that the alloy distribution deviates from a random distribution to a larger extent at high T_shell. The degree of non-randomness can be quantitatively compared among different data sets by the Pearson coefficient. The Pearson coefficient, μ, is defined by μ = [χ²/(N_S + χ²)]^1/2, where N_S is the number of voxels sampled, and χ is count difference in between the observed distribution and the binomial distribution. The Pearson coefficient ranges from 0 to 1, where 0 corresponds to a random binomial distribution and 1 indicates a complete association of the solute atoms. As the Pearson coefficient depends on the size of voxels (i.e., the number of atoms in a voxel), the voxel size is kept the same for all data. Fig. 4(c) shows the Pearson coefficients obtained from several cuboid ROIs for each sample as a function of the different T_shell. Both the variation in Pearson coefficients of different ROIs and the average value (plotted by the solid data points in Fig. 3(c)) increase with T_shell. This result confirms that higher T_shell reduces the degree of randomness in the alloy by enhancing the formation of Ga-rich and Al-rich clusters and/or unintentional quasi-superlattices, while at lower T_shell a nearly homogeneous random alloy is formed with the Pearson coefficients approaching zero for near-ideal binomial alloy distribution.

The authors gratefully acknowledge the financial support from the German Science Foundation (DFG) via the excellence program Nanosystems Initiative Munich (NIM), the TUM International Graduate School for Science and Engineering (IGSSE), the TUM-IAS Focus Group “Semiconductor Nanowires,” and the IBM International PhD Fellowship Program. Atom-probe tomography was performed at the Northwestern University Center for Atom-Probe Tomography (NUCAPT). NUCAPT is a Shared Facility at the Materials Research Center of Northwestern University, supported by the National Science Foundation's MRSEC program (DMR-1121262). L.J.L. and N.J further acknowledge NSF DMR-1306854 for the support of this work.