Dynamics of mass transport during nanohole drilling by local droplet etching
© Heyn et al.; licensee Springer. 2015
Received: 12 December 2014
Accepted: 22 January 2015
Published: 13 February 2015
Local droplet etching (LDE) utilizes metal droplets during molecular beam epitaxy for the self-assembled drilling of nanoholes into III/V semiconductor surfaces. An essential process during LDE is the removal of the deposited droplet material from its initial position during post-growth annealing. This paper studies the droplet material removal experimentally and discusses the results in terms of a simple model. The first set of experiments demonstrates that the droplet material is removed by detachment of atoms and spreading over the substrate surface. Further experiments establish that droplet etching requires a small arsenic background pressure to inhibit re-attachment of the detached atoms. Surfaces processed under completely minimized As pressure show no hole formation but instead a conservation of the initial droplets. Under consideration of these results, a simple kinetic scaling model of the etching process is proposed that quantitatively reproduces experimental data on the hole depth as a function of the process temperature and deposited amount of droplet material. Furthermore, the depth dependence of the hole side-facet angle is analyzed.
KeywordsDroplet epitaxy Droplet etching Semiconductor nanostructures Nanoholes Self-assembly Mass transport Growth modelling
Nanostructuring fundamentally modifies the optoelectronic properties of semiconductor crystals establishing low-dimensional confinements for embedded charge carriers. In particular, self-assembled semiconductor nanostructures are of appreciable interest, since they allow research on well-defined quantum structures without the need for sophisticated lithography. In the field of epitaxial nanostructuring, mainly two self-assembly techniques are utilized: the strain-driven Stranski-Krastanov formation involving, for example InAs [1-3] or Ge  nanostrutures, as well as the droplet-epitaxy-based techniques [5-10], both based on molecular beam epitaxy (MBE) fabrication. In comparison to Stranski-Krastanov growth, droplet epitaxy is more flexible regarding the choice of materials. Moreover, the fabrication of unstrained nanostructures is possible.
A central point for droplet epitaxy is the agglomeration of the planarly deposited material into spatially well-separated droplets. The driving force for droplet formation in the Volmer-Weber growth mode  is the minimization of the surface energy of the deposited droplet material. In this sense, droplet-based techniques require as the central prerequisite a dewetting character of the solid-liquid interface.
Functionalized nanostructures arise when the holes are refilled with material in a subsequent epitaxy step. From the perspective of applications, local droplet etching introduces a novel degree of freedom for the self-assembled patterning of semiconductor surfaces using conventional molecular beam epitaxy technology. The process works with a number of different materials, such as Ga, Al, In, InGa, and AlGa droplets on GaAs, AlGaAs, and AlAs substrates [18,21,24,26]. By the filling of droplet-etched nanoholes with a material different from the substrate, the fabrication of novel types of nanostructures has been demonstrated, such as localized InAs quantum dots , strain-free GaAs hole quantum dots [27-30], vertically stacked quantum dot pairs , and ultra-short nanopillars for thermal and electron transport experiments [32-34].
Regarding the fabrication processes, the central parameters of droplet etching which differ from droplet epitaxy involve a low group V flux to avoid crystallization of the droplets, as well as higher temperatures allowing substantial substrate etching and material removal. As a result, during droplet epitaxy, the initial droplet shape is mostly conserved, whereas during droplet etching, the droplets are mostly removed together with an amount of substrate material. The present paper discusses experimental results on the dynamics during the surface mass transportation. Moreover, it introduces a simple model that illuminates the basic etching mechanisms and allows estimation of the process-parameter-dependent hole depth.
The morphology of nanoholes formed by local droplet etching are characterized using atomic force microscopy in tapping mode under ambient atmosphere. For the materials discussed here, we see no influence of oxidation. In contrast to that, earlier droplet-etching studies on AlAs surfaces exhibit fast and strong oxidation of the holes under air .
Results and discussion
In the present experiments, no indications for droplet motion were found. Spontaneous running of Ga droplets was observed on annealed GaAs surfaces in the regime of incongruent evaporation . In comparison to the experiments on GaAs, the present AlGaAs surfaces are thermally more stable with a critical temperature for incongruent evaporation which is assumed to be above the temperatures used here.
The essential processes for droplet etching, i.e., the etching of the substrate and the removal of the material from the initial droplet position, take place during the post-growth annealing step. A central process for etching is that material from the crystalline substrate is removed by diffusion of As into the liquid droplet material driven by the concentration gradient (Figure 2c) . As a consequence, the substrate becomes liquid at the interface to the droplet and the droplets quasi sink into the substrate.
As an important point, the solubility of As in the droplet material is limited to a maximum of about 10 −4 . As a consequence, etching would stop very fast without a mechanism removing As from the droplets. We identify the formation of the crystalline wall around the nanohole opening to be the essential process for As removal . That means, after removal from the substrate, the As atoms travel very fast through the liquid droplet  and crystallize the wall [38,41] with droplet material at the triple line at the border between the droplet surface and the substrate. This picture is supported by the observation of equal volumes of material stored inside a wall and of material removed from a hole . Since the wall is composed of Arsenides of the droplet material, etching with Ga droplets yields GaAs walls that act as quantum rings [21,26], whereas etching with Al droplets yields optically inactive AlAs walls . A model describing the etching process and wall crystallization is described in .
Nevertheless, the wall crystallization removes only a few percent of the initial droplet material at the beginning of the annealing step . Therefore, an additional process is necessary to uncover the etched holes below the droplets. While in a previous model with different focus  it has been suggested that droplet material might be removed by desorption, recent results indicate rather that the droplet material detaches from the initial droplet positions and uniformly spreads over the substrate . These experiments will be discussed in the following. A similar behavior with adatom detachment and spreading into ring structures was also observed during droplet epitaxy at T<400°C .
In a further experiment, we have measured the tunnel current density j over a 8-nm-thick AlAs barrier in a reference sample and over a 8-nm-thick AlAs barrier with additional Al-LDE step in a further sample. The inset in Figure 3b shows a scheme of the later sample. The LDE-holes in the second sample are filled with GaAs and act as quantum point-contacts. The current density data demonstrates that, surprisingly, the sample containing point-contact holes in the barrier has a higher resistance than the reference (Figure 3b). This result indicates that the current density j is dominated by electron tunneling through the barrier and that the tunnel barrier is thickened by the Al-LDE process . We conclude that also Al as a droplet material detaches from the droplet during annealing and spreads uniformly over the substrate surface.
The above results establish the interesting mechanism that the planarly deposited material evolves over localized droplets finally back into a planar distribution (Figure 2).
We introduce now a simple model of the droplet-etching process which assumes that the droplets are already nucleated and describes the dynamics during progressed droplet deposition (Figure 2b) and during annealing (Figure 2c). A model of droplet nucleation (Figure 2a) has been discussed previously . As a starting point, we assume an array of droplets of identical size. The droplets are characterized by their density N in units of droplets per lattice site and dimensionless average volume V≃θ/N in units of the number of atoms inside a single droplet, with the droplet material coverage θ in monolayers (ML). As a simplification under negligence of the Ostwald ripening , we assume a constant droplet density . In addition to the droplets, Ga adatoms with density n 1 per lattice site are located on the surface.
where F Ga is the Ga flux and σ As represents a reaction cross section. Considering the mass conservation indicated by the experiments shown in Figure 3, we assume that re-evaporation is negligibly small so that n 1 R R ≃0.
F Ga<F As: this is the usual GaAs growth regime with As overpressure. Here, neither droplets nor nanoholes are formed.
F Ga>F As: this is a growth regime used for the generation of Ga droplets. The excess Ga first increases the surface adatom density n 1 according to Equation 2 at N≃0, and droplets are nucleated by collisions between diffusing adatoms (Figure 2a). Later, the droplet volume increases due to the attachment of mobile adatoms according to Equation 1 (Figure 2b). Detachment of atoms from the droplets is negligible at this stage.
In the transition regime between regimes 1 and 2 at a relatively high F As, the value of d V/d t might become very small since most of the deposited Ga is directly incorporated into the substrate without forming droplets large enough for etching . This sets the upper limit in the As flux for the observation of droplet etching phenomena.
F Ga=0,F As≫0: this is an annealing regime under high As background flux as used for droplet crystallization in droplet epitaxy (Figure 5a). A model describing the mechanisms of droplet epitaxy in this regime is given in .
F Ga=0,F As>0: this is an annealing regime under small As background flux as used for droplet etching (Figure 5b). Ga atoms detached from the droplets react with arsenic with rate n 1 σ As F As>0 and form a planar GaAs layer (Figure 3a). As consequences, n 1≃0, re-attachment of adatoms becomes negligibly small n 1 V 1/3 R A ≃0, and thus, the droplets shrink d V/d t<0. This droplet material removal is essential to uncover the etched nanoholes.
F Ga=0,F As=0: this is an annealing regime under completely minimized As background flux (Figure 5c). Here, the balance n 1 R A =R D between attachment and detachment of atoms conserves the droplet volume d V/d t = 0.
with constant c h and E h =E E −E D +2E N /3. This simple scaling model allows the analytical calculation of the depth of droplet-etched nanoholes as a function of the most relevant process parameters temperature and droplet material coverage. More detailed numerical models which consider in addition the hole morphology including the wall are discussed in the complementary references [38,50], both relying on similar assumptions. In , the temperature-dependent hole morphology is modelled, whereas  models the influence of F As but without considering the temperature dependence.
The mechanisms behind the self-assembled etching of nanoholes into semiconductor surfaces through liquid metal droplets are studied. As a central finding, we observe that a small arsenic background flux is essential for etching. This As flux crystallizes atoms detaching from the droplets in the form of a uniform GaAs or AlAs layer. Otherwise, using a completely minimized As flux, the detached atoms will re-attach to the droplet and conserve it. On the other hand, an As flux being too high will also suppress nanohole etching . These results indicate a complex interplay between crystallization processes as well as adatom detachment from and re-attachment to the droplets and suggests the As pressure as an additional important process parameter for nanohole tuning.
A simple model is proposed that explains the mechanisms behind the surface mass transport during local droplet etching. Furthermore, the model allows an easy prediction of the nanohole structural properties, and in particular, a quantitative reproduction of experimental values of the nanohole depth as a function of the process parameters is demonstrated.
The authors thank Christian Strelow for PL measurements; Zhiming Wang for organizing the very inspiring EMN meeting 2013 in Chengdu, during which parts of the present study have been initially discussed; and the Deutsche Forschungsgemeinschaft for financial support via HA 2042/6-1, GrK 1286, and SPP 1386. DJ acknowledges support from a Marie Curie International Incoming Fellowship.
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