Oxide Precipitation Via Coherent Seed-Oxide Phases

Abstract

Until now, oxide precipitation has been treated in theoretical models as homogeneous nucleation of incoherent SiO x precipitates. In view of the higher interface energy of an incoherent precipitate, one should also consider the possibility of having coherent precipitation. The key role of VO 2 complexes for nucleation of oxide precipitates has already been demonstrated on a broad experimental basis. Ab initio calculations have shown that the agglomeration of VO 2 is energetically favorable. In this contribution, the bulk modulus and molecular volume of nVO 2 clusters, named here seed-SiO 2 , are determined and an analytical nucleation model is developed. In a second step, a more advanced model is developed based on a monolayered agglomeration of VO 2 complexes on ͕100͖ planes, named here seed-SiO, and the heterogeneous nucleation of amorphous SiO 2 ͑a-SiO 2 ͒ at these plates. The advanced model is regarded as the more plausible nucleation path because the free energy is decreased stepwise.Until now, models for homogeneous nucleation of oxide precipitates have been based on nucleation of incoherent SiO x particles. These models provide feasible results only if the strain of the growing nuclei is relieved by the emission of interstitials or the absorption of vacancies ͑see, e.g., Ref. 1͒. These models are in agreement with the well-known precipitation enhancement by vacancy supersaturation and the amorphous or cristobalite structure of precipitates observed in various transmission electron microscopy investigations. A more-advanced model treats the incorporation of vacancies and oxygen into incoherent precipitates independently. 2 Another more-advanced model of incoherent nucleation also incorporates the segregation of interstitials to the precipitate nuclei. 3 It is assumed that part of the generated self-interstitials is incorporated into the growing oxide precipitate instead of being emitted into the host matrix. This would modify the composition of SiO x toward lower x with decreasing temperature. The disadvantage of interstitial-based models is that interstitial supersaturation in most practically applicable cases of crystal pulling or rapid thermal annealing ͑RTA͒ treatment is of negligible impact on nucleation. In view of the higher interface energy of incoherent precipitates, we are considering here the possibility of having coherent precipitation.Nucleation of oxide precipitates usually takes place below 1000°C. This is a temperature range where the majority of vacancies are bound to oxygen by forming VO 2 complexes. 2,4 In an earlier publication, we have demonstrated on a broad experimental basis the key role of these VO 2 complexes for nucleation of oxide precipitates. 5 We have shown that the agglomeration of VO 2 is energetically favorable and developed a model for an intermediate coherent seed-SiO 2 phase. Seed-SiO 2 is a SiO 2 polymorph which does not exist outside silicon. Its structure has been obtained from ab initio calculation of the coherent agglomeration of VO 2 complexes. The lattice structur...

An effective nucleation rate for oxide precipitation in Czochralski silicon and a simple framework for multi-step anneal calculations

“…We also find that the aspect ratio of the critical nuclei in our model never drops below two, consistent with the assumption of plate morphology and follows the suggestion by [11]. The number of oxygen atoms as computed by our model in the critical nuclei ranges between two and 12, which are in good agreement with the values reported by Kissinger and Dabrowski [33]. According to Kissinger and Dabrowski [33], the number of oxygen atoms in a strained precipitate can become half of the number in unstrained precipitates.…”

“…The number of oxygen atoms as computed by our model in the critical nuclei ranges between two and 12, which are in good agreement with the values reported by Kissinger and Dabrowski [33]. According to Kissinger and Dabrowski [33], the number of oxygen atoms in a strained precipitate can become half of the number in unstrained precipitates. The presence of only a few atoms in the critical nuclei of precipitates at temperatures below 750 1C makes it very difficult to detect their existence through experiments.…”

“…The thickness value chosen here is close to the one predicted by ab-initio calculations in [33]. We also accounted for residual strain in a way which is consistent with the expressions suggested in [33] and [6]. The notion that the surface and edge of the thin plates have different specific interfacial formation energies is also consistent with experimental evidence found in [7] and follows the suggestions of [33] and [12,25].…”

“…The thickness value chosen here is close to the one predicted by ab-initio calculations in [33]. We also accounted for residual strain in a way which is consistent with the expressions suggested in [33] and [6].…”

“…We also accounted for residual strain in a way which is consistent with the expressions suggested in [33] and [6]. The notion that the surface and edge of the thin plates have different specific interfacial formation energies is also consistent with experimental evidence found in [7] and follows the suggestions of [33] and [12,25]. The value of surface energy coefficient f s of 0.195 eV translates to about 0.5 Jm À 2 for interface energy per unit area.…”