The Physics of Non–Equilibrium Reliability Phenomena

Chapter B Defect Properties

To gain further insight into the resulting Si dangling bond defects their properties upon charge capture have been investigated. Three different types of defects have been selected and the formation energies for neutral and negatively/positively charged states have been calculated. The selected defects including the corresponding spin density can be see in Fig. B.1: a) a sub–interfacial (one layer away from the interface) Si trivalently back–bonded to three other Si atoms with no other O atoms in the direct vicinity, b) a Si–DB directly at the interface with an oxygen atom \(\SI {1.9}{\angstrom }\) away and c) a Si–DB back–bonded to two Si’s and one O atom (rendering in compatible to a \(P_\mathrm {b1}\)–type structure). All defects possess an unpaired electron, as indicated by the spin density, with no other defect present in the model. Subsequently, the different charge states, neutral, negative and positive, of each defect have been calculated. The results are shown in in Fig. B.1, which shows the difference in the electron density with respect to the neutral configuration. Blue refers to an increase of electron density, whereas the red translucent profiles indicate a decrease of electron density. Clearly visible is that the added electron (or hole) is indeed localized within the direct vicinity of the Si–DBs. However, particularly the positive charge state for configurations b) and c) suggests that the hole is shared between the Si and the O (Fig. B.1 middle and right). This, however, is to be expected, since oxygen is slightly negatively charged in the SiO\(_2\) network, see Chap. 3.

In order to reliably extract the formation energies for the different charge states of the interface defects, the electrostatic correction methodology presented in [200] and implemented in the sxdefectalign2d program has been applied. All results together with the corresponding Mulliken charges with respect to the neutral configuration are shown in Figs. B.2 and B.3. The model potential is in very good agreement with the electrostatic potential from DFT for both charge states, \(Q=+1/-1\), of the Si–DB, as can be seen in the lower panels of the respective figures. A reasonable dielectric profile was used throughout the calculation and the spatial placement of the Gaussian model charge is further supported by the Mulliken charges shown in Figs. B.2 and B.3. The correction constant was found by aligning the model and the DFT potential far away from the defect, by considering the average over the oscillations within the DFT potential which result from microscopic screening. Finally, with the extracted corrections, the formation energies for the different charge states could be reliably calculated, see Sec. 3.1