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Formation and annihilation of nanocavities during keV ion irradiation of Ge

Nanocavities in Ge(111) created by 5 keV Xe ion irradiation are characterized by ex situ transmission electron microscopy and Rutherford backscattering spectrometry. Nanocavities nucleate near the surface and then undergo thermal migration. Nanocavities with average diameter of 10 nm and areal density of 5.1 x 10-3 nm-2 are observed at 773 K, while nanocavities with average diameter of 2.9 nm and areal density of 3.1 x 10-3 nm-2 are observed at 673 K. The estimated Xe gas pressure inside the nanocavities is 0.035 GPa at 773 K, much smaller than the estimated equilibrium pressure 0.38 GPa. This result suggests that the nanocavities grow beyond equilibrium size at 773 K. The nanocavities are annihilated at the surface to form surface pits by the interaction of displacement cascades of keV Xe ions with the nanocavities. These pits are characterized by in situ scanning tunneling microscopy. Pits are created on Ge(111) and Ge(001) at temperatures ~ 523-578 K by keV Xe ions even when less than a bilayer (monolayer) of surface material is removed.


I. Introduction
Ion sputtering of solids is used in many fields of science and technology: e.g., thin film microanalysis, preparation of clean surfaces for surface science experiments, sputter deposition, and dry etching in microelectronic device fabrications. Ion sputtering often introduces defects in the crystal lattice such as dislocations and cavities. 1 The application of nanometer-size cavities or nanocavities for gettering impurities in Si has been recently investigated. 2,3 Nanocavities are formed during inert gas ion irradiation due to low solubility of inert gases in solids; for example, nanocavities have been observed in Ni, 1,4 Zr and Zr alloys, 5,6 Nb, 6 Al, 1,7 mica, 8 amorphous Ge, [9][10][11] and Si. 2,3,[12][13][14][15] Nanocavities migrate inside the crystal during thermal annealing 6,16 and by the interaction of the nanocavities with high energy ions [17][18][19] or high energy electrons. 20 During high energy ion irradiation, nanocavities can migrate when nanocavities and displacement cascades overlap; Donnelly et al. observed discrete jumps in Au of nanocavities containing He under 400 keV Ar ion irradiation at 230 o C. 17,18 Donnelly et al. also observed the disappearance of many nanocavities and proposed that some nanocavities annihilate on the surface while most nanocavities are disintegrated by displacement cascades. 17,18 In present work, we consider the formation of nanocavities during keV Xe ion irradiation of Ge, and examine their formation as a function of temperature and their interactions with surfaces. We have previously reported the surface morphology of Ge(111) during keV Xe ion etching at temperatures from room temperature to 300 o C. 21 In this study of the surface morphology of Ge(111), we prepared the starting surfaces by annealing the Ge(111) samples at 620 o C to avoid formation of nanocavities, and we could determine the mechanisms of roughening and smoothening of Ge(111) surfaces during keV Xe ion etching. 21 Therefore, the present work on nanocavities as bulk defects in Ge is complementary to our previous study on the surface morphology of Ge (111) which is governed by the kinetics of surface or near-surface defects.

II. Experimental details
Our Ge samples are typically 1.5 × 1.5 cm 2 and are bonded with In to a Mo sample stage which is attached to a 3.5 inch diameter Mo sample block. The sample stage is thermally isolated from the sample block by alumina spacers to enhance the heating efficiency by an electron beam. Sample temperatures are measured by an infrared pyrometer operating with a wavelength band centered at ~ 5 µm. The uncertainty in the temperature measurements is ± 5 o C; the reproducibility is ± 2 o C.
The Xe ion beam is produced by an Omicron ISE 10 sputter ion gun, which generates ions with energies up to 5 keV. For the experiments on the formation of nanocavities, which are performed using transmission electron microscopy (TEM) and Rutherford backscattering spectrometry (RBS), the 5 keV Xe ion flux is 1.0 × 10 13 ions cm -2 s -1 . For the experiments on the annihilation of nanocavities, which are carried out by scanning tunneling microscopy (STM), the 5 keV Xe ion flux is 3.1 × 10 13 ions cm -2 s -1 .
The angle of incidence of keV Xe ions is 50 o from the surface normal in both cases.
The Ge(111) and Ge(001) surfaces for STM experiments are prepared by 5 keV Xe ion etching at 520 o C with an ion fluence of 5.6 × 10 16 ions cm -2 , corresponding to a removal of 120 bilayers of Ge(111) and a removal of 270 monolayers of Ge(001). 22 This high temperature ion etching of the Ge surfaces results in crystalline starting surfaces without prominent surface defects other than steps, see Fig. 1. Immediately after the high temperature ion etching, the sample is cooled to a lower temperature, and ion-etched or annealed at that lower temperature. Then the sample is cooled to room temperature, transferred to the STM and imaged. All the STM images in this report are filled state images with a typical bias of 1.8-2.0 V. The nucleation rate of nanocavities should strongly depend on the densities of Xe atoms and vacancies. Therefore, the nucleation rate of the nanocavities containing Xe in Ge(111) must be the highest near the surface where these densities are the highest.

A. Formation of nanocavities in crystalline Ge
Nanocavities nucleated near the surface apparently migrate deeper into the crystal, while some nanocavities may annihilate at the surface. During migration, nanocavities are likely to grow by absorbing nearby vacancies or coalescence with other nanocavities and thus the diffusion coefficient may not be constant.
To derive the diffusion coefficient of nanocavities, we first assume that nanocavities migrate by adatom diffusion on the interior surfaces. The diffusion coefficient of a nanocavity D n is where f n is the jump frequency of the nanocavity and d is the average jump distance. 23 The number of adatoms participating per unit jump of the nanocavity is (4πR 2 )n o , where R is the radius of the nanocavity and n o is the equilibrium density of adatoms on the interior surface of the nanocavity. Then, , where f m is the jump frequency of adatoms. Also, for a given distance traveled by the nanocavity, a total of 4πR 3 /3Ω atoms are transferred the same distance in the opposite direction, where Ω is the atomic volume. Therefore, where a is the atomic lattice constant. The surface diffusion coefficient of adatoms D m is defined 23 Therefore, from the above equations, the diffusion coefficient of the nanocavity D n is therefore, larger nanocavities migrate much more slowly than smaller nanocavities.
If we assume D n is constant, the diffusion distance l of a nanocavity is where t is the diffusion time of the nanocavity. The slope of the two straight guidelines drawn in Fig. 3(a) is -1/2 and Eq. (6) seems to be consistent with our observation for nanocavities found deep inside the crystal. From the guidelines, the diffusion distance or depth of nanocavities at 500 o C is approximately 100 times larger than that at 400 o C for a similar nanocavity diameter. This result implies that, from Eq. (6), the product of equilibrium density of adatoms and surface diffusion coefficient at 500 o C is larger than that at 400 o C by a factor of 10 4 .
Here, we estimate n o D m assuming the nanocavities migrate by adatom diffusion on the interior surface of nanocavities. In Fig. 3(a), extrapolation of the guideline for the  The average density of Xe atoms for the sample prepared at 500 o C is 3.3 × 10 21 cm -3 ; the total number of Xe atoms is (surface area) × (density of Xe atoms), where the surface area was measured by TEM, 1.1 × 10 4 nm 2 , and the atomic density of Xe atoms was measured by RBS, 1.6 × 10 15 cm -2 , and the total volume of the nanocavities is calculated using nanocavity diameters measured by TEM, see Fig. 3(a).
To estimate the Xe gas pressure inside the nanocavities formed at 500 o C, we use van der Waals gas approximation. The van der Waals equation of state is where P g is the gas pressure, N is the total number of Xe atoms inside the nanocavity, V is the volume of the nanocavity, and B is a virial coefficient. 25,26 The virial coefficient B for Xe gas at 500 o C is -0.13 cm 3 mol -1 , 26  Equilibrium of a nanocavity is reached when the pressure exerted on the cavity wall by the Xe gas equals the pressure caused by surface tension, i.e., the equilibrium pressure p is where γ is the surface energy. To estimate the average equilibrium pressure, we calculated <R>, which is defined as 4π<R> 3 /3 = (total nanocavity volume observed by TEM). The surface energy of Si(111) is 1.2 J/m 2 ; 27 using the ratio of the cohesive energy of Si to Ge, 1.2, we estimate γ ≈ 1 J/m 2 for Ge. With <R> = 5.2 nm, p = 0.38 GPa. The equilibrium pressure is therefore much larger than the estimated van der Waals Xe gas pressure 0.035 GPa, which suggests that nanocavities grow beyond their equilibrium size at 500 o C.
Two mechanisms are possible candidates for the growth of nanocavities beyond the equilibrium size: i) bias driven growth 1,28 and ii) growth due to the coalescence of nanocavities. 29 Here, bias driven growth suggests that, in the presence of biased sinks of point defects, bulk vacancies can be readily absorbed by nanocavities allowing the nanocavities to grow. TEM micrographs in Fig. 2 do not reveal bulk defects such as dislocations that can act as biased sinks of interstitials for bias driven growth. 1,28 Therefore, if bias causes the growth of nanocavities, possible sources for the bias are the Ge surface acting as biased interstitial sink and the nanocavities acting as biased vacancy sinks.

B. Annihilation of nanocavities on Ge
We discovered that the nanocavities formed at 520 o C can be annihilated at the surface by ion irradiation at lower temperatures, ~ 250-305 o C. Figure 5 shows

IV. Conclusion
We        density of the pits is obtained from STM images as in Fig. 6 and the areal density of the nanocavities is obtained from TEM images. The areal density of the nanocavities is calculated by integrating the average nanocavity density shown in Fig. 3(b) over a 10 nm depth.