**4. In situ TEM of elemental semiconductor nanowire growth**

Si and Ge nanowire growth has been extensively studied by in situ TEM [46, 68–78, 81, 82, 85–88]. Several aspects such as diameter dependance of growth kinetics [70], nucleation kinetics [87], surface faceting [69], surface migration of catalyst (Au) on nanowire (Si) surface [71], tapering [94], and kinking [75] have been investigated. Depending on the growth conditions such as temperature, catalyst particle and precursor pressures the growth proceeds either by the VLS mode [46, 68–72, 74–76, 78, 81, 82, 85–88] or the VSS mode [46, 72–74, 77, 78, 82, 88]. It is interesting to note that VLS growth has been observed to occur even below the eutectic temperature [72].

The nanowire catalyst interface is atomically flat, except when a ledge is growing. The layer-by-layer growth of nanowire atomic layers has been studied in situ during the VLS growth of elemental nanowires [74, 78]. A new (bi)layer starts only after the previous one is completely grown (at least for the nanowire diameters studied) [74, 78]. The time each layer takes to complete once it has nucleated can be called ledge-flow time (or layer completion time, also called step-flow time in some references). We will use the term incubation time for the difference between the ending of one layer and the start of the next layer. (This is not to be confused with the incubation time before the birth/nucleation of the nanowire itself). In VLS growth of elemental nanowires each layer grows instantaneously (ledge-flow time ~ 0) while there is a significant incubation/waiting time between successive layer-growth events [74, 78]. This observation can be explained by a very simple argument — the amount of material required to raise the chemical potential high enough to nucleate a layer is sufficient for forming one full layer as soon as it nucleates. So the layer grows rapidly once nucleated [74]. There is a considerable incubation time, which in turn determines the average nanowire growth rate.

Most theoretical models for nanowire growth kinetics assume instantaneous layer completion and the growth rate is calculated in a nucleation-limited regime [95–98]. This assumption seems to be valid for the VLS growth of elemental nanowires we discussed above. However, we will now discuss in this section about elemental nanowires and the next section about compound nanowires cases where this assumption of instantaneous layer-growth breaks down.

As mentioned before, the growth can proceed by the VSS route where the catalyst is a solid particle. In the VSS growth of elemental nanowires the layer completion is slow [73, 74, 78, 82]. The incubation time in the VSS case is shorter than in VLS [74, 78]. The solubility of the growth material in the solid catalyst is much lower than in a liquid catalyst, thus a small amount of excess species can increase the chemical potential sufficiently to nucleate a new layer — making the incubation time short [74, 78]. But the limited amount of material present could be insufficient for forming a complete bilayer, in turn making the ledge-flow process slow [74, 78]. The limited solubility of the nanowire species inside the solid catalyst offers the opportunity to grow compositionally abrupt axial heterostructure [74]. Another interesting aspect about VSS growth of elemental nanowires is that there can be two or more ledges growing simultaneously [73, 78, 82]. This also is in contrast to VLS growth of elemental nanowires were a second ledge starts only after the first is fully grown.
