Phases of damaged layer formation
The features of the measured ellipsometric signals (Figs. 2 and 4) as well as the evolution of the structure can be subdivided into 4 regions: (I) a baseline before switching on the ion beam, (II) damage accumulation, (III) rapid void formation, (IV) slow change of damage and voids, revealed by the increasing Ψ signal in Fig. 4.
The baseline of the ellipsometric angles was taken from region I and it was used to determine the dielectric function of the c-Ge substrate. From the numerous possible parameterizations of the dielectric function33, the dispersion of the c-Ge wafer was described using the Johs-Herzinger generalized critical point model51. Only the oscillator parameters of Ge transitions at 2.1, 2.3, and 3.4 eV were fitted in a c-Ge/GeO2 model. Subsequently, these parameters were fixed during the evaluation of the spectra measured during the ion implantation.
In regions II-IV a uniform two-layer model was used with components of c-Ge, Ge amorphized by implantation (i-a-Ge) and voids. Note that for the i-a-Ge component the parameters were taken from our previous work on Ge amorphized by Al ion implantation23. The effective dielectric function of each layer was calculated using the Bruggeman effective medium approximation (EMA52). The initial dielectric function of i-a-Ge23 was parameterized by the Tauc-Lorentz dispersion model, in which only the energy position of the single Lorentz oscillator was fitted. A deviation in the dielectric function of i-a-Ge makes sense, taking into account that amorphous semiconductors may have different optical properties depending on the preparation conditions.12,14,15,23,34,53,54
The thickness of the layers rapidly changes in region III, partly because of the increasing penetration depth of the implanted ions due to the void formation. The void fraction in the top layer accounts for the roughness52 as well. In the last phase of structure formation (Region IV) both the void fraction and the thickness of the bottom layer increases monotonically.
Figure 5 shows measured and fitted Ψ and Δ spectra for selected characteristic temporal points of the structure formation. The graphs reveal that the curves vary significantly in terms of time and spectral features. Note that the repeatability of the measurements of both Ψ and Δ is ≈ 0.2°, a small fraction of the width of the plotted lines.
Ion Beam-induced Amorphization And Track Size
The effective size of damaged zones formed from ion tracks initiated by individual bombarding ions can be estimated by numerical simulation compared with the dynamics of damage profiles measured by RBS and ellipsometry.55 In this case the numerical simulation assumes both a track size and a damage profile, the latter being measured by RBS. The evolution of damage was measured and calculated as a function of ion fluence, i.e., as snapshots of the process in time. In case of ellipsometry the analysis of the vanishing absorption features56 was enough to determine the dynamics of amorphization and the track size.55
A much simpler assumption is to take into account that the ions impinging at random positions of the surface satisfy the Poisson statistics, i.e. the probability that the next ion finds a non-damaged position is proportional to the area of the surface that has not yet been amorphized.56 Fig. 6(A) shows the fit considering Poisson statistics for the evolution of fa, i.e., the amorphous i-a-Ge fraction. The red line corresponds to the Poisson λ parameter value of λ ≈11 (computed in fluence units of 1⋅1012 cm− 2), and from λ a corresponding track diameter of 2.5 nm (track area of 5 nm2) can be estimated. In the calculation it was considered that λ = np, where n is the total number of possible individual events (total number of different independent positions for incoming ions within a window of 1 cm2, i.e., the inverse of the track size, (RT2π)−1, with RT being the track radius), and p is the probability to find undamaged region by an incoming ion, for which the center value of p = fa =½ was considered.
To ascertain more details about the progress of implantation-induced damage accumulation, we applied the direct-impact, defect-stimulated (D-I/D-S) amorphization model to reproduce the change in the amorphous fraction i-a-Ge vs. the applied ion fluence. Previously, this model has been successfully applied to describe the behavior of Ge46 and other semiconductor materials57 exposed to ion irradiation. In the D-I/D-S model, amorphous nuclei are directly produced in the core of a cascade (homogeneous amorphization) and irradiation-induced point defects and/or subsequently implanted ions stimulate further amorphization at the crystalline-amorphous interfaces (heterogeneous amorphization). If the probability for stimulated amorphization is taken as fa(1-fa) then the differential change in fa, due to an infinitezimal fluence, dD, can be written as:
df a / dD = σa(1-fa) + σs fa (1-fa) (1)
where σa is the direct-impact amorphization cross-section, and σs is the effective cross-section for stimulated amorphization57. The fit for fa can also be seen in Fig. 6A with corresponding values of σa = 0.6 nm2 and σs = 40 nm2, respectively. Note that, while the value of σa = 0.6 nm2 is comparable to an effective cross-section for defect formation, σeff ≈ 0.5-1 nm2 derived from SRIM vacancy profiles, the cross-section σs = 40 nm2 is much larger. That is, the overall damage formed in cascade processes initiated by one impinging ion is several times higher than predicted by SRIM. This result is consistent with molecular dynamics (MD) simulations performed for 5 keV Sb+ bombardment into Ge, showing that a large number of defects can be formed in hot collision cascades, and most of them is contained in larger defect clusters, which can be thermodynamically more stable than single point defects58. The probability to form such complex defect structure is much higher for heavy Sb+ ions than, e.g., for lighter B+ or Si+ projectiles50,58. For 5-keV Sb+ bombardment MD simulations show that the total number of atomic displacements (about 2000/ion) is about 20 times higher than predicted by SRIM (about 100/ion). This result is in agreement with our observations based on the D-I/D-S amorphization model. In general, the high damage cross-section for heterogeneous amorphization in Sb+-implanted Ge suggests its tendency for significant local atomic transport under these conditions that can be a prerequisite to initiate a spatial reorganization process and the formation of voids at higher ion fluences.
The different cross-sections for damage formation, obtained from Poisson statistics and the D-I/D-S model are due to the distinct basic assumptions applied. Note that the cross-section value given by the geometrical concept-based Poisson function falls between the values of σa and σs provided by the D-I/D-S model, which combines contributions to fa from both homogeneous and heterogeneous amorphization. In the D-I/D-S model the effect of the lower cross-section σa is compensated with the higher cross-section σs to reproduce the shape of the amorphous fraction curve, fa.
Our derived cross-sections for direct-impact, and heterogeneous amorphization differ from the values found for 3 MeV I+ ion irradiation, where σa = 9 nm2 and σs = 20 nm2 were reported46. The reason for the differences can be explained considering the dissimilar conditions for the lower energy Sb+ and the high energy I+ irradiation. The electronic energy deposition which is associated with temperature increase and local target melting is about 4 times higher for the I+ irradiation, as predicted by SRIM, and therefore the probability to directly form larger amorphous clusters via local melting and fast cooling can be increased compared to our Sb+ implantation. On the other hand, the higher local temperature may be accompanied by different in-situ defect formation, annealing, cluster formation and diffusion kinetics of defects for 3 MeV I+ compared to 200 keV Sb+. It is worth noting that in Ref. 46 the amorphous Ge fraction has been extracted from ex-situ RBS/C measurements while in this work these data were obtained from in-situ SE spectra.
The effective size of the ion tracks found in this work applying the D-I/D-S amorphization model for Ge is about four times the size of tracks of Xe ions implanted in SiC at an energy of 100 keV55, and 3–4 times the size of excitons in GaAs created by the implantation of As ions at an energy of 270 keV.56 However, the derived damage track size is much smaller than the exciton diameter of about 50 nm in Ge13. Differences in track sizes may be due to distinct materials properties, like displacement energy, collision cascade kinetics and relaxation, as well as thermal transport features, of the targets exposed to irradiation.
Mechanisms Of Damage And Void Formation
The temporal change of the ellipsometric model parameters is shown in Fig. 6B, using 2 layers on intact Ge substrate. Both layers contain c-Ge, i-a-Ge (fa) and void (fv) phases. It is important to emphasize that the ‘stripes’ of volume fractions in Fig. 6B are not vertically separated, in the optical model it is a uniform mixture of the indicated components within the layer, in fractions represented by the widths of the ‘stripes’. The volume fraction of void, fv, has previously been estimated by the expansion of the sample61 measured by Talystep or by the analysis of TEM images.44 The void parameter fv from the ellipsometry fit was measured real time during irradiation. The approximate accuracy of the determination of fv was a few percent, at a time resolution of 3 s. Effective thicknesses of i-a-Ge (da) and void (dv) are shown in Fig. 6C. Note, that both i-a-Ge and voids distribute in the modified depth continuously.
After starting the irradiation (temporal position of ≈ 60 s), the thickness of the surface layer increases to a value of ≈ 50 nm within less than 10 seconds. Note that the penetration depth of light in i-a-Ge in the used wavelength range is a couple of times 10 nm, which means that the saturation of da may be caused by the limited penetration of light.
Based on the paper written by Kaiser et al.44, the critical fluence of void formation for Sb implantation into Ge is between 3⋅1014 and 5⋅1014 cm− 2. These values were comparable to that found for Ge self-implantation (2⋅1015 cm− 2).45 In our experiment, the total fluence was 1⋅1016 cm− 2, which results in void formation at a fluence of 1⋅1015 cm− 2 measured at a high accuracy using the in-situ SE method (see Region III in Fig. 4 that can also be identified in Figs. 6B and 6C).
The proposed explanations of void formation in the literature range from sputtering and redeposition22,62 through thermal spikes63 to clustering of vacancies and diffusion of interstitials.40,64 It has also been shown by different authors that the void formation obeys mass conservation, and the sputtering effect can be ruled out,22,44,65 also proved by the use of a capping layer,66 by molecular dynamic simulations62 and by scanning tunneling microscopy (STM) measurements.63
Formation of columnar voids of 20–40 nm in diameter in Ge have been reported by many authors for different experimental (preparation) conditions.22,61,67 It was found by high-energy heavy ion bombardment that the voids are formed by the agglomeration of vacancies, and a critical defect production rate is necessary to initiate the formation of the sponge-like structure,65 It was found feasible already in the early investigation of Appleton et al. that the primary cause of void formation is the high mobility of defects.67 This was underlined by the fact that implantation of 280-keV Bi into Ge at liquid nitrogen (LN) temperature did not lead to void formation, whereas annealing and high-temperature ion implantation leads to the decrease of dopant retainment,67 also pointing out the gettering effect of voids.68
In case of self-implantation at the energy of 500 keV flattened vacancy agglomerates of 10.6 nm average size are formed at a fluence of 1⋅1015 cm− 2 at room temperature (RT).64 As shown in Fig. 6A, this is the temporal position in our measurement from which a pronounced growth of the damaged and porous layer starts. The study of Desnica-Fankovic et al.64 also shows that the size of these agglomerates grows to 17 nm at the fluence of 3⋅1015 cm− 2, and their shape becomes more spherical. At higher fluences, these nanoclusters agglomerate into larger voids of a broad size distribution, which completely dominates at the fluence of 3⋅1016 cm− 2. The thermal energy in the RT-implanted samples is large enough for the diffusion and restructuring of defects clustering the vacancies into voids and finally causing porosity – a feature that lacks in the case of implantation at LN temperature.64
The voids remain stable during annealing, which restricts shallow junction formation by the implantation of heavy elements.69 The void formation is the reason of finding unintentional O and C impurities by ion scattering measurement after removing the samples from vacuum.67 This structure can, however, be used for gettering as well.65,68 The structure created by the implantation of Sb into Ge can also be reproduced by other elements if the fluence and the temperature is high enough.40,66 Therefore, in device fabrication, lighter elements are used as dopants.69 B (with Ge pre-amorphization) and P (with self-amorphization) can be used as doping species with subsequent low-temperature annealing to achieve substitutional, electrically active positions of the dopants.
A detailed picture of the void formation mechanisms was shown by Nitta et al. for GaSb implanted by Sn+.59,60 Voids are formed by the migration of interstitials in the first stage of the implantation (Figs. 6D and 6E, as well as region II in 6B). The interstitials are not stable at RT.70 Those that survive the annihilation process can migrate to the bottom of walls. In this model the walls develop by the aggregated interstitials (region III in Fig. 6B), while the voids by the vacancies migrating to the bottom of existing voids (Fig. 6F). This model does not explain the driving force for the interstitials to aggregate at the bottom of the walls. A plausible background to this phenomenon might be the different depth profiles of interstitials under the voids and the walls between the voids (due to the different amounts of materials above a certain position in depth depending on the amount of void in the path of the penetrating ion), which results in a lateral gradient of interstitial concentration in the lattice.
In the final stage the voids burst to the surface at higher fluencies, as shown in Fig. 6G. These processes are confirmed by the present results which show that the volume fraction of voids is larger in the embedded layers, and the void fraction in the surface layer still increases at the end of the process (Fig. 6B). Note that the damage depth range at the initial stage is consistent with the SRIM ion range calculation shown in Fig. 3B. Note that Fig. 6A covers approximately 90 minutes of measurement with 3 s steps, i.e. almost 2000 individually fitted spectra. The noise at the edge of the stripes represents the approximate uncertainty of the measurement (a few nanometers and a few percent for the thicknesses and the volume fractions, respectively). The two homogeneous composite layers are a simplification of a depth profile that may in the future be better approximated by an analytical gradient profile, which however, due to the presence of voids, might be more complex that those used for simple unperturbed Gaussian damage profiles.24,26