The preparation of NWs in a controllable way is a challenging task that can be achieved using a large range of approaches and fabrication techniques [51–54]. Two general ap-proaches referred to as "bottom-up" and "top-down" are employed. In the former one, atoms are-self assembled to form increasing larger structures by control of the crystal-lization. In contrast, the top-down approach relies on the etching of narrow columns from planar structures by lithography [55].
These two approaches are combined with the conventional growth techniques. Besides MBE, the major fabrication technique in use is chemical vapor deposition (CVD) which is composed of several subclasses like the hydride vapor phase epitaxy (HVPE) and metal-organic CVD (MOCVD). In this case, instead of the physical deposition of ele-ments, chemical precursors decompose and react at the substrate surface to produce the desired substance. The sticking coefficients are much lower than in the case of physical deposition unless enhanced by a catalyst. Metal-organic-MBE (MOMBE) or chemical beam epitaxy (CBE) is a hybrid technique which combines the advantages of UHV like MBE with the versatility of MOCVD.
Although largely employed in the past, the top-down approach is less attractive as the desired length scale of devices shrinks. The major concern stems from the limitation
template-assisted growth [69, 70], and the selected area growth (SAG) [71, 72]. Next we will focus on two of these approaches: the catalyst-assisted and the catalyst-free ones.
2.3.1 Catalyst-assisted approach
The most common bottom-up method in the framework of the catalyst-assisted ap-proach is the vapor-liquid-solid (VLS) technique whose model was proposed by Wag-ner and Ellis in 1964 [60]. In this technique nanometer-sized metallic particles form a low-temperature eutectic alloy with the NW material and act as a preferential sink for arriving atoms (physical catalyst) or in the case of precursor molecules as a catalyst for the necessary chemical process leading to the reactant incorporation [Figure 2.9(a)]. In any case these particles act as a collector for the deposited material [73] once the chem-ical potential of the surrounding vapor is higher than the one of the particle [74]. By further atom incorporation, the chemical potential of the particle increases until super-saturation is reached. At this point, the NW material precipitates under the particle at the liquid-solid interface. Crystal growth proceeds thus unidirectionally by lifting of the particle. More recently it was evidenced that these particles could also be solid [75–77], growth occurring then through the vapor-solid-solid (VSS) mechanism.
Several models were developed to account for the NW morphology in dependence on the different experimental growth parameters. Givargizov studied the growth rate of Si whiskers grown by CVD using Au as a catalyst in dependence of their diameters and showed that the growth was strongly affected by the Gibbs-Thomson effect caus-ing faster growth of the wider whiskers and the cessation of growth for whiskers of diameter smaller than a critical value [78]. However, for growth by MBE, the opposite trend was ascertained by Schubertet al. [79], while Kodambakaet al. [80] observed no dependence. The apparent contradiction can be attributed to the very different growth conditions. As we will see next, the generally accepted growth mechanism implies the incorporation of atoms not only by direct impingement onto the NW tip but also by diffusion on the substrate and along the side-facets of the NW. In consequence, it is to expect that for growth techniques inducing different surface reaction and diffusivity, different dependences are obtained. From the observation of longer tilted thin whiskers nucleated at substrate steps, Givargizov concluded that the rate-limitation of whisker growth was the incorporation of the whisker material into the crystal lattice under the seed. Indeed, the nucleation barrier was expected to be strongly reduced at the step interface with the seed. In contrast, Bootsma and Gassen [62] earlier reported that the
Figure 2.9:Schematic of the processes involved (a) in the catalyst-assisted and (b) in the catalyst-free growth. (1) Adsorption on the NW tip. (2) Incorporation. (3) Diffusion through the parti-cle. (4) Precipitation. (5) Adsorption on the substrate. (6) Film growth. (7) Surface diffusion.
(8) Adsorption on the NW side facets. (9) Desorption from the different surfaces.
chemical decomposition at the liquid-solid interface should be the rate-controlling pro-cess [Figure 2.9(a)]. The nature of this limiting step has been investigated not only for theoretical but also for economical interest and it is obviously dependent on the NW synthesis technique since different physical/chemical surface reactions occur.
The catalyst-assisted approach offers the immediate advantage that the NW location and size are defined by the particle ones. Thus, by combination with lithography, it is possible to precisely position NWs of desired dimension as long as tapering effects do not modify their shape [81–83]. However, in counterpart, it has been reported that the catalyst may also incorporate into the NW material, thus degrading its physical properties [84–87]. Hence there are constant efforts to develop other approaches not relying on any external catalyst.
2.3.2 Catalyst-free approach
This technique is usually preferred in order to grow NWs of high material purity, since no foreign catalyst material is required. However, it raises the question why matter prefers to grow unidirectionally. Already in 1921, Volmer and Estermann tried to ex-plain the different growth rates on different crystal facets observed for the growth of Hg [88] and concluded that another mechanism than the simplest reflection or condensa-tion must occur, suggesting that the molecules diffuse on the surface of adsorpcondensa-tion. In the early 1950s Sears proposed a growth mechanism based on the presence of a built-in screw dislocation to account for the growth of Hg whiskers [89]. The screw dislocation introduces a regenerative step that would catalyse the formation of a new monolayer
flat top one. The debate is still open after the recent observation of screw dislocations in PbS NWs [91] and in GaN NWs [92, 93].
The diffusion model postulated by Sears is very important for NW growth in general.
It was further developed [94, 95] and also extended to the catalyst-assisted growth by Givargizov [78] who postulated that the active sink could also be a catalyst particle instead of a screw dislocation. According to this model the axial growth rateVis given by:
V= dl
dt = I+4Iλs
d tanh l
λs, (2.4)
withlthe whisker length,d the whisker diameter,t the time, I the impingement cur-rent at the whisker tip andλs the root mean square diffusion distance on the whisker surface.
The first term accounts for the growth by direct impingement of atoms at the tip while the second one is related to the surface diffusion on the surface of the substrate and on the side-facets of the NW. This model was experimentally verified for catalyst-free NW growth [25] as well as for the catalyst-assisted one [79, 96, 97] for different mate-rial systems and different growth techniques. Its sophistications take into account the adsorption - desorption processes on the NW tip surface, the effects of growth on the substrate surface and the growth parameters (supersaturation, temperature) [98] and explain the divergence observed for the NW length-diameter dependence [73, 78–80].
Last, an interesting simple model proposed in 1967 by Schwoebel [99] attracted much less attention although it is complementary. Starting from a surface covered by cir-cular concentrary steps, this model assumes different adatom mobilities on top and side-facets and different capture rates at steps for atoms approaching either from the upper or the lower terrace of the step as a consequence of the ES barrier. This analy-sis predicted that for certain capture ratios a "filamentary crystal" with atomically flat sidewalls could be formed.
Importantly, all these models always consider the diffusion and impingement of only a single species, even in the case of compound materials. In particular, for the III-V semiconductors the group III atoms are considered as the surface-diffusing, rate-limiting species assuming that the group V atoms are always in excess [96]. But as reported by several experimental results on NW growth by MBE [19, 23, 100] and as we will see in chapter 4, the axial growth rate of the NWs was evidenced to be group
V limited. Also, it is clear that these different species exhibit different adsorption / desorption / diffusion behaviors that are dependent on their ratio [22, 45, 48, 101–103]
(different sticking coefficient, different diffusion length, different residence time), so that the implementation of this consideration is still lacking in the present models.