الخلاصة:
Physical and chemical properties of atomic clusters of group-IV elements are receiving a lot of
research investigations due to their potential applications in several modern nanotechnological
devices. Particular research interest is shown in fundamental and applied aspects of nanosilicon
clusters whose properties lie between those of individual atoms and the properties of bulk materials.
Therefore, such properties would greatly be affected by the number of atoms, n, constituting these
clusters and the binding energy, Eb, between atoms. In this context, we study the variations of Eb as
a function of n for small sized clusters (2 ≤ n ≤ 20 at) of intrinsic nano-Si as well as monoatomic
doping effects with (i) transition metals: Ag, Au, Co, Cu, Fe, Mn, Ni, Ti, (ii) rare earth: Eu, Gd, La,
Lu, Tb, (iii) non metals: C, P & (iv) alkali metals: Na. To do so, we selected the most widely
reported computing methods: (a) Hartree-Fock (HF) and Post HF, (b) Density functional theory
(DFT) with Local Density Approximation (LDA), Generalized Gradient Approximation (GGA) and
functional hybrids. Finally, the results are quantified semi-empirically in order to deduce relations
between binding energy and cluster sizes for different doping elements. The obtained curves of Eb
versus nSi showed similar behaviors for all dopants and with various methods; these curves can be
divided into three regions: an initial sharp increase (2 ≤ n ≤ 5 at), followed by a transition region (5
≤ n ≤ 10 at) and ending by a saturation region (n>10 at). A close analysis of regions I and II, i.e., for
(2 ≤ n ≤ 10 at) led to the following observations: (i) similar variations (Eb increases with n), but not
sensitive to the choice of neither the dopant nor the method, (ii) the variation of Eb versus n takes an
exponential form whose quantification was found to be of the form: Eb = C + α exp (-nSi/β) with C,
α and β being characteristic constants which we deduced for each method and its variants
(iii)similar variationfordoped nano-Si clusterscalculatedbythe same method: the increase inatomic
radius, Rat, of thedopant atomcauses adecrease inEband (iv) the Eb for doped nano-Si clusters put
into evidence the great effect of the doping element. This effect may provide a useful way of
controlling the binding energy by choosing an impurity atom to dope Si clusters.Moreover, the
importance of the above deduced formulas lies not only in their applicability to all dopants and
methods but also in the possibility of predicting binding energies for known atom numbers in
clusters and vice versa
