3.3. Mixing between Pr₂O₃ and SiO₂

3.4. Formation of the interfacial silicate

We computed total energies for numerous simplified models of interfacial silicates, differing in stoichiometry, atomic arrangement, and imposed lateral periodicity. Most of these structures are clearly unstable, that is, their energies fall well above the lowest energies of silicate-free film at any realistic value of oxygen chemical potential. However, some of the structures turned out to be stable for O chemical potential in the SiO_x range. This is in spite of the fact that the small cell sizes used (for practical reasons) in the calculation have most certainly lead to accumulation of lateral stress in the silicate layer.

Stability of Pr2O3/Si(001) interfacial silicate layers

Bold lines correspond to the structures discussed below. As in the previous energy diagram, the labels associate each structure with its characteristic feature: buck:SiO₂ and flat:SiO₂ refer to SiO₂ molecules dissolved in an ultrathin film under a buckled and a flat surface (see the structural models below), PrOSi indicates the presence of mostly Pr-O-Si bonds in an intercalating SiO₂ layer (see the structural model below) and PrOSiSi indicates that Si-Si bonds occur in a thicker intercalating SiO₂ layer (see the structural model below). The structures 0(SiPr) and 4(SiOSi) are the same as in the previous Section on substrate oxidation.

Substitutional SiO2 moiety in Pr2O3 bulk

The onset of silicate formation is the dissolution of a SiO₂ molecule in Pr₂O₃. Two O^-2 atoms from the Pr₂O₃ lattice are then substituted by the (SiO₄)^-4 moiety. The energy difference between the SiO₂ molecule being a member of the network of amorphous SiO₂ and the SiO₂ molecule incorporated into bulk Pr₂O₃ is about 1.2 eV. This means that dissolution of SiO₂ in Pr₂O₃ begins to be energetically favorable already at the chemical potential of oxygen about 0.6 eV above the equilibrium between Si, O and SiO₂ (i.e., 0.6 eV above the energy zero in the diagram above). This value which falls within the SiO_x region (in the energy diagram above, the limit of strained SiO_x is indicated on the upper abscissa axis; see also the energy diagram in the previous Section on substrate oxidation).

SiO2 at the interface

Calculations for a SiO₂ molecule dissolved in a Pr₂O₃/Si(001) film yield a similar result. Silicate formation begins at µ1 = 0.8 eV when the film is made of only three monolayers of the oxide. This is a higher energy than that obtained for the bulk; also in the energy diagram of interface silicates, this structure (labelled buck:SiO₂ there) has a high energy. A glance on the atomic structure suggests that the energy may be increased because the surface of this very thin film buckles due to the additional volume introduced by the molecule. This buckling is expected to lead to an increase in the surface energy of the film. We will now verify this hypothesis by making the film smoother.

SiO2 at the interface

The simplest way to remove the buckling is to deposit additional Pr₂O₃ to cover the depressions (compare both figures); the necessary amount of oxide is half a monolayer. This smoothing lowers the fomation energy noticeably indeed. The formation energy turns out to drop by the amount equal to ΔE_0.5 = E₄ - E_3.5 = E_3.5 - E₃, where E_x is the energy of the film with x atomic layers of Pr₂O₃. This is what one would expect if the reason for increased formation energy were an increase in surface roughness. It is also interesting to note that silicate formation begins now at µ₂ = 0.3 eV, that is, at energy even lower than that in bulk material; the dissolved molecule is more stable in the ultrathin film than in bulk (or in the middle of a thick film). The apparent reason for this is that realaxation of stresses is much easer close to the surface. The surface cannot support any stress in the normal direction, but in the stress field in the bulk has to decay in the crystal lattice. After cancelling out the energy loss due to surface buckling, we have taken the full adventage of stress relaxation at the surface. As a result, we obtain a structure which is stable already at µ(O) only 0.3 eV above amorphous SiO₂ (cf. the energy diagram above and the structure labelled flat:SiO₂). The price for this is, however, amorphization of the film.

Single-layer intercalate

Low energy of the interfacial silicate was computed for the case when a monolayer of Si oxide was intercalated above the first Pr₂O₃ layer. Most of the bonds of the intercalate are of silicate character, and many bonds between silicon atoms are not oxidized. Oxidation of these bonds is not favorable energetically; the resulting stress is too high. This structure is labeled PrOSi in the energy diagram above. Its energy is low enough to allow for the formation of the intercalate from oxidized Si arriving from strained SiO_x on the substrate side of the interface, but the stress induced by substrate oxidation must be somewhat higher than needed for insertion of SiO₂ in the form of flat:SiO₂. Nevertheless, due to the quasi-homogeneous distribution of silicon in the film, the surface of the film does not buckle. The intercalation process is thus an alternative way to keep the surface of the film smooth during silicate formation; this time, the surface layers of the film remain crystalline.

Double-layer intercalate

Also when additional two monolayers of Si suboxide are intercalated above the first Pr₂O₃ layer, there are Si-Si bonds in the silicate. This structure is labeled PrOSiSi in the energy diagram in the beginning of this Section; Above µ(O) = 0.5 eV, this structure is stable with respect to the loss of Si to the substrate and the loss of oxygen to the sites defining the chemical potential (also in this case this would be the SiO_x interfacial layer, but again the degree of oxidation-induced stress required for intercalate formation is higher than for previously discussed structures)

To summarize, we have seen how the concentration of Si in the interfacial silicate region may be stabilized in intercalate geometries, that is, when the Si atoms are inserted in layers between Pr₂O₃ planes. This process makes it possible to transfer the information on the substrate geometry into the film even if silicate is produced during early phase of growth. On the other hand, not all SiSi bonds in the intercalated silicate are oxidized. Oxidation of all these bonds may be difficult without simultaneous excessive oxidation of the substrate: the energy gain is comparable for both processes and the concentration of SiSi bonds is much higher in the silicon than in the silicate. In a separate Section we will argue that incompletely oxidized silicon is a source of positive fixed charge and (in another atomic configuration) it acts as a rechargeable trap.

The intercalated interfacial interface is not stable as a bulk material; for example, the formation energy of bulk Pr₂Si₂O₇ is negative even with respect to fully relaxed SiO₂. Nevertheless, a full mixing to an amorphous and relaxed silicate may be kinetically difficult during MBE deposition of Pr₂O₃ on a Si substrate. A partially ordered silicate existing in the kinetic growth path would explain the recovery of the substrate-determined orientation in the Pr₂O₃ film grown on top of the apparently amorphous interfacial layer. This recovery is clearly visible in TEM images and in XRD rocking curves.

SiO2 molecule on Pr2O3/Si(001) surface

But how does SiO₂ enter into the growing film? We found that SiO₂ moieties are stable on the surface of a single Pr₂O₃ monolayer if the oxygen potential is in the range of the oxygen energies in the surface Si-Si bonds (the labels on the lines in the energy diagram correspond to the labels on the structural models). These molecules can be overgrown with Pr₂O₃, leading to silicate formation from the very beginning. Comparison of energies and geometries of other structures computed by us indicates that the overgrowth process may be complicated: when the growth of a Pr₂O₃ plane is not yet complete and the surface is rough, or when the amount of SiO₂ is not high enough to build an intercalating plane without inducing a strong deformation to the capping Pr₂O₃ plane, then SiO₂ moieties tend to segregate to the surface. After the topmost Pr₂O₃ plane is closed or enough SiO₂ is collected, the silica units move under the surface in order to maximize the number of Pr-O-Si bonds.

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