Implementación de la aplicación móvil

In this chapter, I have calculated the properties of possible oxygen species in a — quartz. Table 4.1 contains the summary of the results on incorporation energies, vertical electron affinities, relaxation upon charging, diffusion barriers and possibility of isotope exchange during diffusion processes. Figure 4.14 illustrates graphically the energetics of the species during charging and possible dissociation processes. Some initial conclusions for silicon oxidation can be drawn on the basis of these results: First, molecular species are energetically more favorable than atomic species, in line with earlier views on oxidation. For example, the incorporation energy of two inter­ stitial atomic oxygens is 4.1 eV, whereas incorporation energy of oxygen molecule is 2.1 eV, which means that dissociation of interstitial oxygen molecule into two atomic species requires 2.0 eV of energy and that atomic oxygens react exothermi- cally to form molecules. In context of silicon oxidation, interstitial atomic oxygen, once incorporated, may never encounter another oxygen to react with (given the low

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Species Lowest incorporation energy (eV) Diffusion barrier c axis (eV) Oxygen exchange w. network Vertical capture of an electron Vertical electron affinity (eV) Relaxation upon charging (eV) 0& 2.07 0.09 no 0 2i + e~ — > Û2i 0.7 1.4 O^i -0.6 0.6 no C>2i + e - ^ 0| r -0.2 1.6 o l r -1.9 0.4 no — No affinity — 0? 2.03 1.3 yes 0? + e - ^ O f -0.5 3.2 0.- -0.7 0.2 yes 0 7 + e- ^ O t -0.3 2.4 o t -2.9 0.3 yes - No affinity — Oli 5.46 _ —

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4 Properties of the oxygen species in a — quartz

oxygen solubility in silica, see sec. 1.5). As a consequence it can be expected, for instance, that plasma oxidation happens mainly due to diffusion of atomic species (possibly in negative charge state).

Secondly, charged species are energetically more favorable than the neutral species (with assumption th at electrons are available at the bottom of the conduction band of silicon or above). The incorporation energy decreases with the increasing negative charge state (compare the incorporation energies in Table 4.1). Polarisation of silica is only partially included in supercell calculations and the part missing will favor charged species even more. Charging may happen if there is an efficient way of transferring an electron from bulk silicon to the species incorporated in silica; for instance, if the species stays within an electron tunneling distance from Si for sufficient time. The electron affinities give the energy gain after species in its lowest energy configuration captures an electron from the bottom of Si conduction band without relaxation. During diffiision the species will sample a number of other higher energy configurations for which the electron capture may be more or less likely and therefore, electron affinities quoted in Table 4.1 should be regarded only as rough estimates. Although it is energetically preferable to have negative charge localised on oxidising species rather than in the form of conduction electrons in in some cases it may require inelastic tunneling [84, 85] to transfer the electron, as indicated by negative vertical electron affinities.

Thirdly, the diffusion of atomic species will lead inevitably to oxygen exchange (isotope exchange) with the S i0 2 network, whereas diffusion of molecular species

cannot easily lead to oxygen exchange with non-defective S i0 2 network.

Fourthly, upon capture of an electron the molecular species can either relax in molec­ ular form or dissociate into two atomic species in appropriate charge states. The former process always releases more energy and so is more likely from the thermal equilibrium point of view. It does not eliminate, however, the possibility of dis­ sociation. Isotope exchange experiments during dry oxidation [8] show significant exchange only close to both interfaces. This isotope exchange can be due to creation and motion of atomic species, in particular, near the S i / S i0 2 interface where elec­

tron transfer from S i may encourage the dissociation. If so, there may be no need for so called reactive layer [24] near the Si joxide boundary. The change of trans­ port mechanism postulated by the reactive-layer model (see chapter 1) would arise

naturally due to charging which would result in populations of atomic and molec> ular species in different charge states close to the interface, effectively affecting the structure of the grown oxide and the kinetics of the process.

5 Oxygen species in amorphous

S 1 O 2

In chapter 4, I have calculated the properties of oxygen species in A — quartz^ In this chapter, I will concentrate on the properties of the same species in a amorphous model of Si02, with the emphasis on the differences with a — quartz. To my best knowledge, this is the first work attempting to calculate the statistical properties of defects in an amorphous sample at this level of theory. Generally, in the amorphous host material, defect properties will have characteristic distributions. Sampling over all sites would allow to determine these distributions for a given amorphous sample. The properties of amorphous samples vary depending on the preparation procedures and conditions, and hence the defect property distributions will be different for different samples.^ Here, I am concerned mainly with the qualitative trends in the energetics of oxygen species which are, in context of silicon oxidation, the potential oxidising species. I will sample a subset of all sites in my model of amorphous Si02

(amorphous_5). I choose five bigger interstices for calculation of molecular species and seven Si — O — Si sites for the atomic species to sample the possible values of Si — O — Si angle. The relaxation of neutral molecular oxygen lead to three distinct local minima and therefore only these are considered in further calculations of charged species. Appendix 9.2 gives a more detailed description of the sites. In chapters 6 and 7 ,1 will extend the number of sites for neutral interstitial molecules

^The distributions could be also different depending whether the defects were created during the synthesis of the material or afterwards by other processes. In the former case, the presence of defects during synthesis may affect some of the initial properties of the material through its topology. In the latter, the concentration of defects may influence the longer-range properties like strain fields and, in turn, the distribution of defect energies.

and atoms in a — S i0 2 to explore the important differences found with respect to

a — quartz. The results of this chapter for 0°^ and 0°, which are subset of results obtained in chapters 6 and 7, are still valuable on their own, as they are obtained for a consistent set of sites with the charged species. The sites for different charge states are linked by the preferred relaxation of the species after electron capture. This relaxation results sometimes in a stable configuration at a different site than the initial one. In this way, the results obtained here reflect charging processes which start with the neutral molecular oxygen distributed in the bigger voids of a — Si02 and the atomic oxygen distributed randomly over the sites. Additionally, the comparison of results for a subset of all sites (this chapter) and all the sites (chapters 6 and 7) shows an agreement for the mean values within a tenth of an eV. For each species, I report the mean values and the spread of results. These values are approximations to the statistical mean and spread of the distribution describing the given property. Because of the statistical calculations involved, I generally quote all values in tables up to second decimal place, whereas the overall accuracy of the calculations in the case of charged species can be lower. Otherwise, I round the results to flrst decimal place, where appropriate, for the ease of discussion.

5.1

Neutral interstitial molecular oxygen in

o — Si02

The neutral interstitial molecular oxygen is stable in the voids of SiÜ2 network, as in

the case of a —quartz. The lowest energy conflgurations are in the middle of the voids and there is a preferred direction of the molecule with respect to the surrounding network. The calculations indicate that there is relatively small number of stable sites for two of the molecules in the smaller voids of the five sites initial sites relaxed to other interstices leaving only three distinct sites. Table 5.1 summarises the properties of the three interstitial molecules.

It is striking that incorporation energy of is 1.7 eV less on average (for the three bigger voids) in the amorphous sample than in a — quartz. This is a very signif­ icant result; many other works assume that a — quartz is a good mimic of silica

5 Oxygen species in amorphous Si02

o i 0 2i 4- e

Site Einc (eV) & / / (eV) Erd (eV)

1 0.39 0.31 1.33 2 0.58 0.16 1.65 3 0.23 0.12 1.26 Mean 0.40 0.2 1.4 Range 0.35 0.2 0.4 Stable configuration

Table 5.1: Energetics and geometry of stable configuration for Og* the amorphous sample. Einc gives the incorporation energy, Faff the vertical electron affinity for an electron with energy corresponding the bottom of the Si conduction band, and Erei is the relaxation energy after electron capture. Note that in the case of three species, the RMS spread of the distribution will be equal to half of the range.

and use crystalline host structures. This result shows the significance of disorder for the energetics of oxidising species. In chapter 7, I will analyse in detail the depen­ dence of O2, incorporation energy on the geometry and properties of the amorphous Si02 network. As it is shown there, the size of the void is the crucial factor. The amorphous structure provides bigger voids than a — quartz and hence the lower incorporation energies. This will have consequences for the diffusion energies, too. The barriers in amorphous material will depend on the size of the voids and the size of the rings providing a passage from one void to another. As shown in chapter 7, the barriers for 0°* diffusion in the amorphous model will be significantly higher than in a — quartz (mainly due to much lower stable site energies).

The interstitial molecule has an average electron affinity of 0.2 eV with a small spread of values (RMS of 0.1 eV). The electron affinity of 0°^ in the amorphous material is lower by 0.5 eV than the one in a — quartz which can be attributed to difference in electrostatic potential in the centres of the bigger voids of the amorphous sample and in the voids of a — quartz.

% 02i +

Site Einc (eV) Eaff (eV) (eV)

1 -1.25 -1.18 1.96 2 -1.23 -1.01 1.93 3 -1.15 -1.18 2.20 Mean -1.2 -1.1 2.0 Range 0.1 0.2 0.3 Stable configuration

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Table 5.2: Energetics and geometry of stable configuration for in the amorphous sample. Einc gives the incorporation energy, Ea/f the vertical electron affinity for an electron with energy corresponding the bottom of the Si conduction band, and Erei is the relaxation energy after electron capture. Note th at in the case of three species, the RMS spread of the distribution will be equal to half of the range.

5.2

Negative interstitial molecular oxygen in

a — S i Û 2

Table 5.2 gives the results for incorporation of into the amorphous structure. The configurations in the Table were obtained by charging and relaxation of the neutral molecular species (Table 5.1). The initial conclusion is that mainly single bonded configuration of is stable in the bigger voids of amorphous material; the corresponding geometry in a — quartz would be configuration (A) of Fig. 4.3. To check this, I performed several calculations trying to stabilise in the amorphous sample the double-bonded (bridging) configurations (B) and (C) of Fig. 4.3. In all cases, I recovered the single-bonded configuration. Its average incorporation energy is -1.2 eV, which is 1.1 eV lower than the energy of single-bonded configuration in a —quartz. The molecule in a single-bonded configuration aligns its longitudinal axis towards the middle of the void to maximise its distance from the SiÜ2 network. The

situation is analogous to the neutral oxygen molecule with the difference of the bond between the molecule and the network Si. The voids of the amorphous structure are generally bigger and hence the negative molecule can have significantly lower incorporation energy than in a — quartz. From this perspective it can be argued that the double-bonded configuration of in a; — quartz is stabilised by the smaller volume of the voids. Hence, it is possible that the double-bonded configuration can be stable in smaller voids of a — Si02^ though with high incorporation energy. The

5 Oxygen species in amorphous SiÜ2

mechanism of diffusion in a —quartz, presented in sec. 4.2, involves the double­ bonded (bridging) configuration, which is not stable in the bigger voids of SiÜQ. Hence, it can be expected th at the diffusion energy in amorphous sample will be significantly higher than in a — quartz.

The average electron affinity of in amorphous material is 0.2 eV lower than the affinity of the same type of configuration in a — quartz. The spread of values in the amorphous sample is very small.

5.3

Double-negative interstitial molecular oxygen

in

Q, — S i0 2

As in the case of a — quartz, in the amorphous sample can have many different types of stable configurations. Table 5.3 gives the energetics and geometries for the three molecular species. The mean incorporation energy is -2.1 eV, which is just 0.2 eV lower than in ct — quartz. The RMS spread of values is very small. The energies of these different stable structures appear rather insensitive to the size of voids. In fact, they can be very compact as in the case (A), bridge across a six-membered ring as configuration (B) or sit on a top of a four-membered ring as configuration (C) not extending much into the void. The configuration (C) shows also a three­ fold coordinated oxygen, similarly to one of the configurations in a — quartz. The insensitivity of the incorporation energy to the void size, the similarity in stable configurations and their incorporation energies in crystalline and amorphous phases and the multitude of stable geometries may be the consequence of Coulomb inter­ action being the dominating contribution to the bonding between the molecule and the Si02 network (due to the two excess electrons localised on the species). These similarities indicate that the diffusion mechanism and the barriers should be similar in a — quartz and a — SiÜ2‘ Again, it is not possible to localise another

Stable configurations

o i r

Site E i n c (eV) Config.

1 -2.04 (A) 2 -2.15 (B) 3 -2.18 (C) Mean -2.1 Range 0.1 A) B) C) ^0-0^ / \ Si— 0 —0 — Si: \ / \l/ / / \ Si— 0 —0 O l\\

Table 5.3: Energetics and geometries of stable configurations for in the amor­ phous sample. Einc gives the incorporation energy, Eaff the vertical elec­ tron affinity for an electron with energy corresponding the bottom of the Si conduction band, and Erei is the relaxation energy after electron capture. Note that in the case of three species, the RMS spread of the distribution will be equal to half of the range.

5.4

Neutral interstitial atomic oxygen in

a

S i O ,

Similarly to a — quartz, there are two stable configurations of Of per site in the amorphous sample. They are generally different in energy. Here, I quote only the results for the lower-energy configurations. Table 5.4 gives the energetics of the species at the seven chosen sites. The average incorporation energy of 1.9 eV is just 0.1 eV lower than the corresponding energy in a — quartz. However, the RMS spread of 0.3 eV makes the result significantly different from the picture obtained in crystalline phase. Intuitive explanation to the big spread of energies would relate it to the different local environments of the defects encountered in the amorphous material. However, as it is shown in chapter 6 and ref. [83], the big variations in Of incorporation energy can be linked to the medium- and longer-range elastic interactions and strain fields in the amorphous structure. Since Of stable configu­ rations and their average energetics in a — SiÜ2 and a — quartz are similar, it can

be expected that the diffusion barriers should be comparable, though big spread of energies is likely to be present in the case of the amorphous material. The Of mean electron affinity of -0.4 eV with a very modest spread of values is marginally lover

5 Oxygen species in amorphous Si02

OS’ OS' + e -

Site Einc (eV) Eaff (eV) Erei (eV)

1 1.73 -0.41 3.31 2 1.91 -0.44 3.17 3 1.65 -0.36 3.25 4 2.28 -0.34 3.46 5 1.76 -0.44 3.21 6 2.24 -0.43 3.37 7 1.63 -0.23 2.81 Mean 1.89 -0.38 3.23 RMS 0.27 0.07 0.21 Range 0.65 0.2 0.6 Stable configuration SSKH / S i S

Table 5.4: Energetics and geometry of stable configurations for 0 ° in the amorphous sample. Einc gives the incorporation energy, Ea/f the vertical electron affinity for an electron with energy corresponding the bottom of the Si conduction band, and Erei is the relaxation energy after electron capture. than the electron affinity in a — quartz.

5.5

Negative interstitial atomic oxygen in a — Si02

The stable configurations of in the amorphous sample are very similar to the stable configurations in a — quartz. Table 5.5 summarises the results for the seven sites. As it can be seen, the relaxation upon electron capture by the neutral in­ terstitial atom can either lead to single-bonded configuration (A) or double-bonded configuration (B) of with generally similar energies. The average incorporation energy of -0.9 eV is 0.2 eV lower than in a — quartz. The spread of values is big and comparable with the neutral atomic oxygen. The diffusion mechanism and barriers are expected to be similar to a — quartz due to the similarity in stable configurations and their energetics, though big spread of energies is likely to be found in the amor­ phous sample. The electron affinities were calculated for the configurations of Table 5.5. The mean electron affinity of 0.0 eV has a significant spread but mainly due to configurations (A) having average Eaff of -0.14 eV and configurations (B) having higher mean of 0.19 eV. Contrary to a — quartz^ it is always possible to lo­ calise a second excess electron vertically (no atomic relaxation) on all configurations

o r O r + e- — ^ o r Site Einc (eV) Config. (eV) Erei (eV)

1 -1.18 (B) 0.19 1.73 2 -0.83 (B) 0.11 1.69 3 -1.25 (A) -0.15 2.00 4 -0.85 (B) 0.15 1.62 5 -0.56 (A) -0.09 2.20 6 -0.70 (B) 0.32 1.56 7 -0.95 _(A) -0.18 1.81 Mean -0.90 - 0.05 1.80 RMS 0.25 - 0.19 0.23 Range 0.7 - 0.5 0.6 Stable configurations A) B) \ O

psii

Table 5.5: Energetics and geometry of stable configurations for 0 ~ in the amorphous sample. Einc gives the incorporation energy, Eaff the vertical electron affinity for an electron with energy corresponding the bottom of the Si conduction band, and Erei is the relaxation energy after electron capture. of type (A).

5.6

Double-negative interstitial atom ic oxygen in

a — S i0 2

As in the case of a — quartz, Of “ in the amorphous SiO i has only one type of stable configuration. Table 5.6. The seven double-negative configurations were obtained by localisation of a second excess electron on 0*“ (Table 5.5) and relaxation of their geometries. I did not attem pt to find the lowest energy configuration at each site by rotation of the Of~ complex. The mean incorporation energy for the double­ negative atomic oxygen in the amorphous sample of -2.75 eV is similar to a —quartz. The spread of results is significant and comparable with the other atomic interstitial species in a —Si02> The diffusion mechanism and barriers are expected to be similar

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