Problema

During ion irradiation of germanium, the long and medium-range order which characterise crystalline materials can be lost due to damage accumulation leading to amorphisation [27], [58], [118]. However, the short-range order is preserved as the equilibrium distances between atoms still remain [27], [58], [118]. In figure 2.14, the radial density of atoms is shown and reflects the probability of finding an atom at a given radius from another atom in germanium. In the figure, the radial density function (RDF) is shown for the crystal, the amorphous phase as well as the liquid phase of the material [124]. Figure 2.14 illustrates the fact that even in an amorphous phase, there is an equilibrium distance between neighbouring atoms (as there is a higher probability of the presence of an atom at approximately 2.5 angstrom). However, the ordering is much more pronounced in the crystal as the RDF illustrates both the short and long- range order that characterise the crystal. Indeed, in the crystal there are multiples distances with

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high probabilities of finding an atom whilst at the other distances the probabilities are close to zero. On the other hand, as shown by the RDF, in an amorphous material (or a liquid) the loss of long-range order is characterised by a more diffuse probability of finding a germanium atom at a given distance.

It is worth noting that in an amorphous material, the bond angles are not fixed and the distances between adjacent atoms are more variable compared with the crystalline phase [27]. This characteristic of the interatomic bond distance of the amorphous phase is illustrated by its wider peak at approximately 2.5 angstrom compared with the crystalline one at the same interatomic distance in the RDF. Furthermore, unlike the crystalline germanium material where the atoms are bonded in such a way that they form six membered rings, amorphous germanium has also seven and five folds membered rings [81]. Remarkably, it has been shown by MD simulations that when 25% interstitial-vacancies pairs are present in silicon, the RDF is indistinguishable from that of the amorphous phase. [27] Similarly when 25% interstitial-vacancies pairs are present in silicon the contrast of the structure in a microscope was shown to be analogous to that of an amorphous material as it results in the formation of 5 and 7 membered rings [89]. In the literature, it has thus been suggested that that during irradiation the formation of interstitial- vacancy pairs are responsible for amorphisation [27], [89], [125].

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Figure 2.14: Radial density function (RDF) of single crystal, amorphous and liquid

germanium. From [124].

Amorphisation is routinely observed to happen during ion irradiation [23], [27], [121], [126]. However, the fluence at which this process occurs as well as the manner in which the ion beam induces amorphisation of the crystal is still subject to debate [23], [25]–[27], [89], [117], [125]– [133].

Furthermore, the properties of an amorphous phase are more variable than those of a crystal [27]. For instance, whilst experimental results have shown that densities of both amorphous germanium [20], [121], [134] and amorphous silicon [27] are in most cases lower than their crystalline counterparts, these densities can vary widely depending on how the amorphous phase has been prepared [20], [27]. For instance, amorphous silicon made by physical vapor deposition can be more than 10% less dense than the crystalline structure [27], [135]. On the other hand, silicon rendered amorphous via ion irradiation is typically about 1 to 2% less dense than crystalline silicon [27].

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The density of amorphous germanium can vary extensively during ion irradiation and the germanium can even exhibit porosity. The magnitude of such porosity depends on the fluence, the angle of irradiation and the energy of the incoming ions [121], [134], [136]. Therefore, the density of germanium after irradiation does not have a fixed value but is known to sometimes be much lower than its crystalline phase [121], [134], [136]. Porous germanium has for instance been reported to be 30% less dense than the crystal after 1 MeV germanium ion irradiation in [134]. However, in the same work a change in the density of the ion-bombarded material was observed during irradiation as both the emergence and the thickness the porous layer depended on the fluence. Indeed, the thickness of the porous layer induced by the ion beam at RT was at least three times larger at a fluence of 3×1016 _ions.cm–2 _{compared with a fluence of 1×10}17

ions.cm–2 [134].

In another work, germanium has been reported to exhibit a foam-like structure after irradiation by a 30 or 60 keV ion beam (i.e. at the energy range used in the current work). As can be seen in figure 2.15, the porosity of the target material reaches a maximum for both energies when the fluence (ψ) is about 5×1016 _ions.cm–2 _{but the roughness of the surface is higher for the}

specimen irradiated at 60 keV [121].

Other authors have also reported such observations when germanium has been irradiated by ions such as gallium or gold [137]. In those studies, the porosity has been attributed to the accumulation of vacancies in the vicinity of the surface which migrate to form clusters and subsequently voids [121]. Interestingly, in a recent publication the swelling of germanium under silver ion irradiation was not observed even though the sponge-like structure was formed; thus the authors concluded that the morphology of germanium during ion bombardment is very sensitive to the irradiation conditions [136].

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Figure 2.15: Scanning electron microscopy (SEM) images showing the evolution of the

germanium surface during irradiation at RT by a 30 and a 60 keV bismuth ion beam at fluences ranging from 5×1013 cm–2 to 1×1017 cm–2 at normal incidence. From [121].