3.2. Substrate oxidation in the pre-amorphous regime

During MBE deposition by electron beam evaporation from a Pr oxide source, the growing film is in contact with vapor consisting of PrO molecules and O atoms. In practice, this means that the system is exposed to an oxidizing environment. Indeed, noticeable Si oxidation takes place unless the substrate temperature is so low that the Pr oxide film grows amorphous. When the temperature is high enough for epitaxial growth (e.g., 500ºC), some oxygen atoms arrive at the substrate and react there.

Stability of Pr2O3/Si(001) oxidation states

We have analyzed the stability of Pr₂O₃/Si(001) interface structures as a function of oxygen chemical potential µ(O). In the diagram, zero of the chemical potential is chosen at the equilibrium with SiO₂, while the equilibrium with O₂ vapor, ½µ(O₂) is far on the right-hand side (the LDA value of the oxygen energy in O₂ is 4.9 eV above that in SiO₂). The labels associate each structure with its characteristic feature: n(SiPr) means that there are n SiPr interfacial units per each 3×1 unit (for the atomic models of 0(SiPr) and 1(SiPr), see the previous Section), while n(SiOSi) means that there are n such units on the Si side.

Let us now go shortly through this diagram, starting from the oxygen poor (left hand side) and proceeding towards the oxygen rich (right hand side) limit. We focus on the interface structures with the lowest energies, indicated by thick solid lines. The interface labeled 4(SiPr) has four SiPr units in each 3×1 cell, that is, there is no oxygen between interfacial Si and Pr atoms. These interfacial SiPr sites are the first to be oxidized. The energy of oxygen incorporated into such a site depends on the local geometry (dimerized or undimerized Si atom) and on the total number of incorporated oxygen atoms and varies between -1.2 and -0.5 eV. S-Si bonds are oxidized next. Due to geometry constraints, O incorporated into a surface Si-Si bond has energy by about 0.6 eV higher than in SiO₂. This can be viewed as the onset of SiO_x formation (the energy of oxygen interstitial in bulk Si, that is, of an oxygen atom inserted into a Si-Si bond, is about 1.4 eV in this energy scale). Oxidation of subsurface Si-Si bonds leads to further stress accumulation, Si ejection, and eventually to formation of amorphized SiO₂ interfacial layer. Oxidized silicon has a strong tendency to mix with Pr oxide, as discussed in the next Section.

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