The magic size determined by valence fluctuation in germanium atom clusters
When the size of solids becomes smaller than the critical size of the nanometre scale, their bonding states and atom periodicity are influenced. As a result, the properties of materials are changed remarkably [1]. Such functional ultrafine particles are here named "atom clusters". The interatomic bondings, particularly in atom clusters, differ from those in bulk crystals because the size of the region affected by the long-range interaction force among the constitutive atoms is close to or larger than the cluster size. We call such a cluster size the "magic size". The behaviour of semiconducting materials in the size below the magic size, particularly relating to structural fluctuations, has been observed as follows. The relationship between the crystalline size and lattice constant of silicon measured by X-ray diffraction suggested that amorphization occurs with decreasing crystalline size [2]. In addition, the Raman spectra of silicon and germanium ultrafine particles changed to amorphous-like spectra with decreasing particle sizes [3-5]. These results show that the magic size is 2-10 nm in covalent materials, such as silicon and germanium. The purpose of this work was to determine the magic size of germanium on the basis of a fluctuation of the valence electronic states in germanium atom clusters by Auger valence-electron spectroscopy (AES). Germanium atom clusters were prepared by the vacuum vapour deposition method. Germanium was first evaporated on a film-substrate of amorphous carbon from a tungsten filament under a base pressure below 4.0 x 10 -8 Pa at room temperature. The germanium deposition here became an amorphous film. Therefore, in order to form atom clusters, these films were heated by electron bombardment at 573 K for 1.8 ks (the formation of atom clusters under this condition was ascertained by in situ observation under heating in a transmission electron microscope (TEM)). The cluster sizes were controlled by the germanium coverages. After the preparations, the Ge Auger valence spectra were measured in the first-derivative mode with the resolution of A E / E = 0.3% by summing up more than 30 scans and processing by numerical integrations. The electron gun was operated at the primary acceleration voltage of 3 kV and the primary specimen current of 0.2 ~tA. The size distributions of clusters in the same specimen as that measured by AES were estimated by TEM observation. The average diameters were calculated from histograms. In addition, the germanium atom dusters were formed on MgO single crystals under the same conditions to observe the profile images of the clusters. The microstructures were observed by the many-beam lattice image method. The TEM used was operated at 200 and 300 kV. It was confirmed that the specimen was not damaged by the primary electron beam from 200 to 300 kV. Fig. 1 shows the Ge (M2,3Mn5V) Auger valence spectra as a function of the cluster size, where V indicates the Ge 4s(N1) and 4p(N23) valence states. As the Auger lineshape fluctuates variously in clusters below about 7 nm in size, a typical one (i.e.