Nanohole etching in AlGaSb with Ga droplets
11 Diffusion-driven nanohole etching in AlGaSb withGa droplets
Joonas Hilska‡, Abhiroop Chellu‡, Teemu Hakkarainen*
Optoelectronics Research Centre, Physics Unit, Tampere University, Korkeakoulunkatu 5, 33720Tampere, Finland.KEYWORDS Nanostructures, Nanoholes, Droplet etching, Droplets, Gallium, AntimonidesABSTRACTWe demonstrate nanohole formation in AlGaSb by Ga droplet etching within a temperature rangefrom 270°C to 500°C, allowing a wide range of tunability of the nanohole density. By leveragingthe low vapor pressure of Sb, we can obtain high degree of control over droplet formation andnanohole etching steps and reveal the physics of adatom diffusion in these processes. Furthermore,by combining the experimental results and a geometric diffusion-based model, we can determinethe temperature and Sb-flux-dependencies of the critical monolayer coverage of Sb atoms requiredfor driving the droplet etching process to completion. These findings provide new insight into thedroplet formation and etching process present in the droplet-mediated synthesis of semiconductornanostructures and represent a significant step towards development of telecom-emitting quantumdots in the GaSb system.Semiconductor quantum dots (QD) embedded in a single-crystalline host matrix are importantbuilding blocks of emerging quantum technologies based on non-classical light sources, such assingle- or entangled-photon emitters [1,2]. Such quantum nanostructures can be fabricated byseveral techniques including Stranski-Krastanov growth [3,4], droplet epitaxy [5-7], growth insidepyramidal holes [8], vapor-liquid-solid growth in nanowires [9], and filling of nanoholes formedby local droplet etching (LDE) [10]. The LDE approach is particularly interesting due to itsadvantages which include narrow exciton linewidths [11], extremely small inhomogeneousbroadening [12], bright single-photon emission [13], and vanishing finestructure splitting [14].These properties have enabled the use of GaAs QDs grown by filling LDE nanoholes in non-classical light sources providing state-of-the-art performance in terms of photonindistinguishability and entanglement [13,15]. However, the operation of the light sources basedon LDE is restricted to the 680-780nm spectral range [11] due to the limited direct bandgap rangeof (Al)GaAs alloys. LDE of AlAs, GaAs, and AlGaAs is demonstrated with Al [10], Ga [16-19],and In [20-23] droplets, but surprisingly, there are no reports on LDE of nanoholes for other III-Vsemiconductor alloy systems, such as InP and GaSb-based materials which would provide suitablebandgaps for accessing the technologically important telecom wavelengths [24] and siliconphotonic integration [25].GaSb-based materials are particularly interesting candidates for quantum photonic applicationsdue to several beneficial properties: (i) the direct bandgap of GaSb is 0.73 eV [26] which is suitablein terms of QD emission at the telecom C-band; (ii) AlGa(As)Sb alloys provide very highrefractive index contrast [27] (exceeding that of AlGaAs), which is important for constructingphotonic devices; and (iii) the lattice mismatch between GaSb-based materials and dissimilarsubstrates can be relaxed right at the first interface by formation of a network 90°-dislocations[28,29] and exploitation of nucleation layers [30], which is particularly useful considering directgrowth of QD emitters on silicon waveguides for chip-level quantum photonic integration. Thistechnological potential, as well as the general aim for advancing the fundamental understandingof the important metal droplet-mediated processes in semiconductor materials, makes antimonidesan extremely interesting subject for studying LDE.In this letter, we present highly controllable etching of nanoholes in Al Ga Sb surfaces usingGa droplets. We show that LDE can be achieved at the temperature range from 270°C to 500°C,resulting in almost three orders of magnitude change in the nanohole density, and that a remarkablecontrol of the nanohole formation can be achieved by precise calibration of the amount of Sbprovided for the LDE process. The low vapor pressure of Sb allows controlling the group V fluxdeterministically with the needle valve of the cracker source unlike in the case of the arsenidesystem where low As-fluxes required for LDE are provided by flux switch-off transients andindirect As-fluxes [31]. This enables assessment of the critical amount of Sb required for thenanohole formation process at different temperatures.The samples were fabricated on n-GaSb(100) substrates using a molecular beam epitaxy (MBE)system equipped with effusion sources for the group III elements while Sb was provided by avalved cracker source. Following a thermal treatment and growth of a GaSb buffer layer, a 100nm thick Al Ga Sb layer was grown at 500°C using Ga and Al fluxes of J Ga =0.7 monolayers/s(ML/s) and J Al =0.3 ML/s, respectively. The samples were then set to target pyrometer temperaturesbetween 270-500°C for the Ga droplet deposition and LDE. The droplets were formed by Gadeposition with J Ga =0.7 ML/s. For both the Ga deposition and LDE, the Sb flux J Sb was set to apredetermined value ranging from 0 to 0.067 ML/s by carefully adjusting the Sb-valve opening. J Sb was calibrated to true atomic flux by depositing a bulk Sb film on GaSb at low temperature(<40°C) and calculating the equivalent J Sb based on the film thickness and deposition timeassuming unity sticking coefficient. All fluxes and deposited coverages are defined in ML/s andML, respectively, where the Sb coverage θ Sb =1 ML corresponds to the number of Sb atomsrequired for the formation of 1 ML of stoichiometric GaSb, and similarly for the Ga coverage θ Ga . The LDE begins with the formation of droplets on the AlGaSb surface by Ga deposition.Typically, this step is carried out in a small group V background [31]. In our case, the same valueof J Sb , set by the needle valve, was used for droplet formation and for the subsequent etching step.The droplet formation is preceded by saturation of the surface reconstruction with Ga atoms [5],thus the droplet formation begins after θ Ga exceeds a critical coverage θ c,Ga . The droplet growth isterminated by switching off the Ga flux. The sample is subsequently annealed in a small group Vflux, which in case of III-As materials is provided by the residual As-flux remaining in the MBEsystem after closing the As needle valve [31]. In case of Sb, we can control these small fluxesusing the needle valve because of the low vapor pressure of Sb and the lack of indirect Sb fluxes.This enables precise and repeatable control of the group V flux which plays an important role inLDE. The Sb atoms from the vapor phase are dissolved in the Ga droplet, which causes nucleationat the triple-phase line (TPL) where the vapor, liquid, and solid phases meet. During this kineticprocess, Sb atoms from the solid material below the droplet are dissolved in the liquid, whichenables further nucleation. As a result of the TPL nucleation, the droplet size decreases, and at thesame time it drills a hole in the semiconductor surface and creates a ring of solid material whichis formed by the Ga atoms from the droplet together with the Sb from the vapor phase and fromthe substrate. The second role of Sb is to form an Sb-terminated surface surrounding the droplets.This concentration gradient acts as a driving force for the diffusion of Ga atoms away from thedroplet and causes layer-by-layer growth of GaSb within the diffusion length of Ga around the droplet. These steps of the LDE process are presented in Fig. 4 (a) and discussed in detail in thetext. Figure 1.
Atomic force microscope (AFM) images showing the effect of Sb coverage θ Sb on thenanohole etching process at 500°C after deposition of 3.2 ML of Ga. In (a)-(d), the etching time iskept constant at 180 s and θ Sb is adjusted by setting the Sb-flux J Sb to 0 ML/s, 0.011 ML/s, 0.030ML/s, and 0.063 ML/s, respectively. In (e)-(g), J Sb =0.030 ML/s and θ Sb is adjusted by setting theetching time to 72 s, 180 s, and 360 s, respectively. The scale bars in (a)-(g) are 2 µm. The insetsin (a), (b), (e) show scanning electron microscopy (SEM) images and in (e)-(g) AFM close-ups oftypical droplets/nanoholes. The scale bars in the insets are 200 nm.Figure 1 presents the AlGaSb surface morphologies after droplet formation and LDE at 500°C.From Fig. 1(a)-(d), it is evident that the total amount of Sb atoms impinging the surface during theLDE process is a crucial parameter. With θ Sb =0 (Fig. 1(a)), we observe metallic Ga droplets whichhave just slightly reacted with the solid surface during the 180 s annealing time. With θ Sb =2.0 ML(Fig. 1(b)), the metallic droplets remain, but their height is reduced significantly. At θ Sb =5.4 ML(Fig. 1(c)) some of the holes are completely etched while some still contain a small liquid droplet.At this point the ring caused by the TPL nucleation is already clearly visible. Finally, at θ Sb =11.3ML, all holes are completely etched and there is no sign of liquid Ga. The final nanoholemorphologies are similar to what has been observed for (Al)GaAs etching with Ga and Al droplets[10,16-19]. Similar intermediate and final morphologies are observed also in Fig. 1(e)-(g), where θ Sb is adjusted by changing the annealing time with constant J Sb . There is clearly a critical valuefor θ Sb that is needed for consuming the liquid droplet and completing the LDE process. In case ofFig. 1, it is approximately 5.4 ML.Figure 2 presents the results of LDE at different temperatures, showing that nanoholes can besuccessfully formed by LDE throughout the temperature range from 270°C to 500°C with someimportant temperature dependencies in the morphology. The density increases with decreasingtemperature as expected from the thermally activated diffusion during droplet formation [5].Consequently, the deposited 3.2 ML of Ga is divided between a larger number of droplets, thuscausing a decrease of the hole size and depth as a result of a reduction in the droplet volume.Furthermore, the size of the disc formed by layer-by-layer growth around the droplet decreases asthe temperature is decreased. Just like the droplet formation, the diffusion of Ga atoms away fromthe droplet during LDE is a thermally activated diffusion process, but it should be noted that theenergetics of these two processes are different due to the differences in the surface chemistry. Figure 2.
AFM images of the AlGaSb surface after deposition of 3.2 ML of Ga for dropletformation and 180 s annealing with J Sb =0.060 ML/s at different temperatures. The scale bars are2 µm in (a)-(e), 600 nm in (f) and 200 nm in (g).The density of the nanoholes shown in Fig. 2 is plotted as a function of growth temperature inFig. 3, which shows nearly 3 orders of magnitude increase in the density when the temperature isdeceased from 500°C to 270°C, ranging from ultra-low densities in the 10 cm -2 range to 2×10 cm -2 . The measured density values exhibit linear behavior on semilogarithmic scale for the highertemperatures, while the density value of the two lowest growth temperatures deviate from thistrend. According to the phase diagram of GaSb surface by Bracker et al . [32], the surfacereconstruction of a GaSb surface is (1x3) in the high temperatures but changes to (2x5) when thetemperature is decreased, with the transition temperature depending on the Sb beam pressure. Asexplained in the Supporting Information (SI) , we find that θ c,Ga =1.15 ML for the growth at 500°C,while at 270°C, θ c,Ga =1.6 ML, which is consistent with the coverages required for saturating (1x3)and (2x5) reconstructions, respectively, with Ga adatoms [33]. With J Sb =0.060 ML/s which was used for the samples presented in Fig. 2 and Fig. 3, the critical transition temperature is expectedto be around 390°C [32]. Therefore, the density vs. temperature behavior with a transition regionat around 400°C can be explained by the change of surface reconstruction which influences theadatom diffusivity. It should also be noted that coarsening effects by Ostwald ripening, which istypical for the high-temperature LDE of AlGaAs [34], are not observed in Fig. 3. For temperaturesabove 400°C, we can model the droplet (and nanohole) density using the scaling law [35] (cid:1840)((cid:1846)) = (cid:1840) (cid:2868) (cid:1857) (cid:3006) (cid:3250)(cid:3117) (cid:3038) (cid:3251) (cid:3021)(cid:3415) (1)where N is a pre-exponential factor, E A1 is the activation energy, and k B is the Boltzmann constant. By fitting Eq. (1) to the experimental data in Fig. 3, we obtain N =2.1×10 cm -2 and E A1 =0.51 eV. This is well in agreement with the activation energy of 0.54 eV reported for the Gadroplets on AlGaAs [34]. Figure 3.
Droplet density as a function of growth temperature. The experimental data points arefrom Fig. 2. The vertical dashed line presents the temperature at which the surface reconstructionof GaSb is expected to change from (1x3) to (2x5) when J Sb =0.060 ML/s [32]. The solid line is a fit of Eq. (1) to the experimental data points in the (1x3) reconstruction regime. Just like the droplet formation (presented in Fig. 4(a) panel 1), the layer-by-layer growth aroundthe nanohole is also a thermally activated process driven by adatom diffusion. It happens duringLDE (Fig. 4(a) panel 2) as Sb atoms arriving on the AlGaSb surface from the vapor phase form anSb-rich surface which creates a concentration gradient that drives Ga diffusion away from thedroplet. The Ga atoms stack with the Sb atoms in a layer-by-layer manner within the diffusionlength and form the elliptical discs. However, the conditions during the layer-by-layer growtharound the nanohole are more Sb-rich than during the Ga droplet formation, which affects the Gadiffusivity. Consequently, the dimensions of the ellipses are significantly smaller than the distancebetween the droplets. Following the procedure from [36], the Ga diffusion length l during thelayer-by-layer growth can be obtained from the disc dimensions as (cid:1986)(cid:1844) = (cid:1844) (cid:2870) − (cid:1844) (cid:2869) = (cid:1864) = (cid:3493)(cid:1830) (cid:3008)(cid:3028) (cid:2028) = (cid:3495)(cid:1830) (cid:2868) (cid:1857) (cid:2879)(cid:3006) (cid:3250)(cid:3118) (cid:3038) (cid:3251) (cid:3021)⁄ (cid:3015) (cid:3268) (cid:3011) (cid:3268)(cid:3277) (2)where R and R are the radii of the ring structure and the disc, respectively, as illustrated in Fig.4(a), D Ga is the Ga diffusion constant and τ is the adatom lifetime on the surface. D Ga can beexpressed by the exponential diffusion equation where D is the diffusivity prefactor and E A2 is theactivation energy. The adatom lifetime τ is obtained from J Sb and the surface site density N s = cm -2 . The disc structures shown in Fig. 2 are elliptical, and thus the diffusivity shouldbe examined separately for the [ (cid:3364) ] and [ (cid:3364) (cid:3364)] crystal directions.The values of ∆(cid:1844) [(cid:2868)(cid:2869)(cid:3365)(cid:2869)] and ∆(cid:1844) [(cid:2868)(cid:2869)(cid:3365)(cid:2869)(cid:3365)] were obtained from several nanoholes for each temperatureby measuring values of (cid:1844) (cid:2870)[(cid:2868)(cid:2869)(cid:3365)(cid:2869)] − (cid:1844) (cid:2869)[(cid:2868)(cid:2869)(cid:3365)(cid:2869)] and (cid:1844) (cid:2870)[(cid:2868)(cid:2869)(cid:3365)(cid:2869)(cid:3365)] − (cid:1844) (cid:2869)[(cid:2868)(cid:2869)(cid:3365)(cid:2869)(cid:3365)] from cross-sectional AFM profiles(Fig. 4(b)). In case of the highest growth temperatures where the disk is very diffused, (cid:1844) (cid:2870)[(cid:2868)(cid:2869)(cid:3365)(cid:2869)] and (cid:1844) (cid:2870)[(cid:2868)(cid:2869)(cid:3365)(cid:2869)(cid:3365)] were estimated from the AFM maps (Fig. 4(d)) which provided more reliable data.0 By fitting Eq. (2) to the experimentally obtained values of ∆(cid:1844) [(cid:2868)(cid:2869)(cid:3365)(cid:2869)] and ∆(cid:1844) [(cid:2868)(cid:2869)(cid:3365)(cid:2869)(cid:3365)] (Fig. 4(d)), weobtain the parameters of the physical diffusion process of Ga atoms along the orthogonal [01(cid:3364)1] and [01(cid:3364)1(cid:3364)] directions. As a result, we get E A2 =1.05+/-0.010 eV and D =0.019×(1.2 +/-1 ) cm /s forthe [01(cid:3364)1] direction, and E A2 =0.98+/-0.011 eV and D =0.003×(1.21 +/-1 ) cm /s for the [01(cid:3364)1(cid:3364)] direction. These activation energies are smaller than the value of 1.31+/-0.15 eV reported for theGa LDE of GaAs [36] , as expected from the generally higher temperatures needed for LDE of(Al)GaAs, and the different bond dissociation energies of Ga-Sb (192 kJ/mol) and Ga-As (210kJ/mol) [37] . Figure 4. (a) An illustration of the phases of droplet formation and droplet etching. The criticaldimensions of the droplets and final hole morphologies are indicated. (b) Cross-sectional profilesof the holes and surrounding disc structures etched at different temperatures. The anisotropy of thelayer-by-layer growth process is accounted by analyzing Δ R=R -R in the orthogonal [ ] and [ ] directions, as shown in (c) and (d). (e) shows the experimental data of Δ R for [ ] and [01 (cid:3364) (cid:3364) ] directions and fits according to Eq. (2).1To our knowledge, no previously reported data is available for the adatom diffusivity on(Al)GaSb. However, rectangular mound defects consisting of spiral step edges on GaSb surfaceare elongated in the [ (cid:3364) ] direction [38] which is consistent with our results, revealing longerdiffusion length in the [ (cid:3364) ] direction than in the [ (cid:3364) (cid:3364)] direction.Now that the temperature dependencies of the diffusion processes are known for both dropletformation and etching, we can analyze in more detail the critical Sb coverage θ c,Sb needed forcompleting the LDE process. Assuming unity sticking coefficient and no diffusion for Sb, we canformulate θ c,Sb from the fact that during LDE, the number of Sb atoms n Sb arriving from vaporphase within the Ga diffusion length from the droplet, i.e. on the elliptical area defined by (cid:1844) (cid:2870)[(cid:2868)(cid:2869)(cid:3365)(cid:2869)] and (cid:1844) (cid:2870)[(cid:2868)(cid:2869)(cid:3365)(cid:2869)(cid:3365)] , should be equal to n Ga , the initial amount of Ga atoms in the droplet. When thiscondition is satisfied, the droplet is completely consumed either to nucleation at the TPL (directimpingement of Sb to the droplet) or to the layer-by-layer growth within the Ga diffusion length.This condition can be formulated as (cid:1866) (cid:3008)(cid:3028) = (cid:2869)(cid:2870) (cid:3087) (cid:3256)(cid:3276) (cid:2879)(cid:3087) (cid:3278) , (cid:3256)(cid:3276) (cid:3015) ( (cid:3021) ) × (cid:1840) (cid:3008)(cid:3028)(cid:3020)(cid:3029) = (cid:2869)(cid:2870) (cid:2024)(cid:1844) (cid:2870)[ (cid:3364) ] (cid:1844) (cid:2870)[ (cid:3365) ] (cid:2016) (cid:3030) , (cid:3020)(cid:3029) × (cid:1840) (cid:3008)(cid:3028)(cid:3020)(cid:3029) = (cid:1866) (cid:3020)(cid:3029) , (3)where N(T) is the droplet density from Eq. (1), and N GaSb is the atom density in GaSb. The factorsof ½ on both sides are due to the definition used for ML coverages of Ga and Sb. By replacing R with R + Δ R and solving for θ c,Sb we get (cid:2016) (cid:3030) , (cid:3020)(cid:3029) = (cid:3087) (cid:3256)(cid:3276) (cid:2879)(cid:3087) (cid:3278) , (cid:3256)(cid:3276) (cid:3015) ( (cid:3021) ) (cid:3095)(cid:3435)(cid:3057)(cid:3019) [ (cid:3364) ] (cid:2878)(cid:3019) (cid:3117)[ (cid:3364) ] (cid:3439)(cid:3435)(cid:3057)(cid:3019) [ (cid:3364)(cid:3364)(cid:3364)] (cid:2878)(cid:3019) (cid:3117)[ (cid:3364)(cid:3364)(cid:3364)] (cid:3439) . (4)Since the outer edge of the ring surrounding the etched nanohole is defined by the nucleation atthe TPL right in the beginning of the LDE process, the radius of the ring R can be replaced withthe initial droplet radius R D, as illustrated in Fig. 4(a). The droplet shape can be described as a2spherical cap with a volume (cid:1848) = (cid:2869)(cid:2870) (cid:2024)(cid:2018)(cid:1844) (cid:3005)(cid:2871) (cid:4672) (cid:2018) (cid:2870) (cid:3415) (cid:4673) , where (cid:2018) = (cid:3035)(cid:3019) (cid:3253) and h is the initial dropletheight. From the AFM profiles of droplets grown at 500°C, we estimate that κ =0.46+/-0.023 (seeFig. S1 in the SI), which can be assumed to be independent of V and T as long as R D >20 nm [39].The initial number of Ga atoms in the droplet can thus be expressed as (cid:1866) (cid:3008)(cid:3028) = (cid:3023)(cid:3096) (cid:3256)(cid:3276) (cid:3040) (cid:3256)(cid:3276) = (cid:2869)(cid:2870) (cid:2024)(cid:2018)(cid:1844) (cid:3005)(cid:2871) (cid:4672) (cid:2018) (cid:2870) (cid:3415) (cid:4673) (cid:3096) (cid:3256)(cid:3276) (cid:3040) (cid:3256)(cid:3276) = (cid:2869)(cid:2870) (cid:3087) (cid:3256)(cid:3276) (cid:2879)(cid:3087) (cid:3278) , (cid:3256)(cid:3276) (cid:3015) ( (cid:3021) ) × (cid:1840) (cid:3008)(cid:3028)(cid:3020)(cid:3029) , (5)where ρ Ga =5.9 g/cm and m Ga =69.7 u are the density and atomic mass of Ga, respectively. Bysolving Eq. (5) for R D , we get (cid:1844) (cid:3005) = (cid:4680) (cid:3087) (cid:3256)(cid:3276) (cid:2879)(cid:3087) (cid:3278) , (cid:3256)(cid:3276) (cid:3095)(cid:3089)(cid:4672)(cid:2869)(cid:2878)(cid:3089) (cid:3118) (cid:2871)(cid:3415) (cid:4673)(cid:3015) ( (cid:3021) ) (cid:3040) (cid:3256)(cid:3276) (cid:3096) (cid:3256)(cid:3276) × (cid:1840) (cid:3008)(cid:3028)(cid:3020)(cid:3029) (cid:4681) (cid:3117)(cid:3119) . (6) Now Eq. (4) can be rewritten as (cid:2016) (cid:3030) , (cid:3020)(cid:3029) = (cid:3087) (cid:3256)(cid:3276) (cid:2879)(cid:3087) (cid:3278) , (cid:3256)(cid:3276) (cid:3015) ( (cid:3021) ) (cid:3095)(cid:3435)(cid:3057)(cid:3019) [ (cid:3364) ] (cid:2878)(cid:3019) (cid:3253) (cid:3439)(cid:3435)(cid:3057)(cid:3019) [ (cid:3364)(cid:3364)(cid:3364)] (cid:2878)(cid:3019) (cid:3253) (cid:3439) , (7)which includes temperature-dependent expressions for N(T) and (cid:1986)(cid:1844) [ (cid:3364) ] , [ (cid:3365) ] from Eq. (1) andEq. 2 with the fitted pre-exponential factors and activation energies (Fig. 3 and Fig. 4),respectively.Figure 5 shows θ c,Sb plotted from Eq. (7) as a function of growth temperature for different valuesof J Sb . This diffusion-based model predicts that θ c,Sb decreases as temperature is increased andincreases when the J Sb is increased. Both effects are consequences of the change in the Gadiffusivity. J Sb reduces the adatom diffusivity (Eq. (2)) and the temperature increases it. Thediffusion length during LDE affects the size of the elliptical area which participates to the two3processes that consume the Ga droplet: formation of the ring structure by nucleation at the TPLand layer-by-layer growth driven by the Ga diffusion away from the droplet. The temperaturedependency of θ c,Sb is particularly interesting since one might expect that less Sb is required forconsuming the small droplets formed at low temperatures. However, the effect of the reduction ofthe thermally activated Ga diffusion during LDE is significantly stronger than that of the reductionof the droplet volume. The model is also consistent with the experimental findings presented inFig. 1(a)-(c), which show that, for J Sb =0.030 ML/s, θ c,Sb should be close to 5.4 ML since in Fig.1(b) we observe some completely etched holes and some holes which still contain a small liquiddroplet. Furthermore, the temperature-dependency predicted by the model is in agreement withour experimental findings. For J Sb =0.060 ML/s (Fig. 2), we find that with θ Sb =10.8 ML all holesare completely etched when T=500°C, while for T=353°C we find that 19% of the holes stillcontain some liquid Ga (See Fig. S5 and S6 in the SI), which confirms that more Sb is required forcompleting the etching process at a lower temperature.The understanding of θ c,Sb is important for controlling LDE in order to provide enough Sb forcompleting the nanohole etching process in the given set of growth conditions, but still avoidingunnecessarily long etching. Furthermore, by selecting appropriate Sb fluxes and etching times, itis possible to adjust the Ga diffusion during LDE while still ensuring completion of the LDEprocess.4 Figure 5.
Critical Sb coverage calculated for different Sb fluxes J Sb from Eq. (7) for (cid:2016) (cid:3008)(cid:3028) −(cid:2016) (cid:3030),(cid:3008)(cid:3028) =1.93 ML, which corresponds to deposition of 3.2 ML of Ga on a (1x3) reconstructed surface,while taking into account the Ga atoms consumed in planar growth due to reaction with the Sbatoms (as explained in the SI). The experimental data points from Fig. 1 (e)-(g) J Sb =0.030 ML/sare presented by the round symbols. The filled, half-filled, and empty symbols correspond to theSb coverage that results in incomplete etching with liquid droplets remaining, situation close tothe critical Sb coverage with liquid Ga remaining only in some of the droplets, and completelyetched holes with no liquid Ga present, respectively. These phases of the etching process arepresented in the 3D AFM profiles showing droplet and nanohole morphologies.In conclusion, we demonstrated highly controllable formation of nanoholes in Al Ga Sb byLDE with Ga droplets over a temperature range from 270°C to 500°C, which provides tunabilityof the nanohole density by almost three orders of magnitude. The low vapor pressure of Sb enables5precise control of the Sb flux, which provides high degree of repeatability and provides means foradjusting the diffusion processes in LDE. We have analyzed the diffusion of Ga adatoms in bothdroplet formation and LDE steps and presented a model for predicting the critical amount of Sbrequired for complete hole etching and consumption of the liquid Ga droplets. This work representsthe first demonstration of LDE in the GaSb-based materials which provide direct bandgapscovering the important wavelength range from telecom to mid-infrared.ASSOCIATED CONTENT
Supporting Information . Determination of the droplet shape; Critical Ga coverage for dropletformation; Assessment of the completion of the nanohole etching process.AUTHOR INFORMATION
Corresponding Author *[email protected]
Author Contributions
The manuscript was written through contributions of all authors. All authors have given approvalto the final version of the manuscript. ‡These authors contributed equally.
Funding Sources
Academy of Finland Project QuantSi (decision No. 323989)Academy of Finland Project NanoLight (decision No. 310985)ACKNOWLEDGMENT6The authors acknowledge financial support from the Academy of Finland Projects QuantSi(decision No. 323989) and NanoLight (decision No. 310985)REFERENCES1. Arakawa, Y.; Holmes, M. J. Progress in quantum-dot single photon sources for quantuminformation technologies: A broad spectrum overview.
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