3.7. A generic atomistic model for positive fixed charge in dielectric oxides on Si
The origin of intrinsic fixed charges is unclear even in SiO2, although its relation to the excess of silicon has been recognized. We argue that the positive fixed charge in SiO2 comes from a triple-coordinated oxygen atom that is associated with a Si dangling bond arising from an incompletely oxidized Si atom injected into the oxide during the process of thermal oxidation. We adapt a similar model to explain the appearance of fixed charges in Pr2O3 and in transition metal oxides and rare earth metal oxides in general.
To begin with, note that in silicon oxynitride, each Si atom is bonded to four oxygen or nitrogen atoms, each O atom is bonded to two Si atoms, and each N atom is bonded to three Si atoms. This saturates all the valances; the oxynitride is an insulator. Similarly, a nitrogen atom can be incorporated into the amorphous SiO2 network without generating any localized states when it becomes bonded to sp3 orbitals of three Si neighbors. Each Si atom remains fourfold and each O atom remains twofold coordinated, but the impurity N atom is threefold coordinated.
| |
 | |
SiNcO+ (or O3+) configuration in SiO2 resembles that of nitrogen in SiO2 |
This is the white atom in the figure. One can view this configuration as a Si dangling bond (e.g., of the Si atom painted in pink) saturated by a N atom substituting a nearby O site. Imagine now that this threefold-coordinated, group-V nitrogen atom is now replaced by a group-VI oxygen atom. This oxygen atom has one electron more than needed to saturate the valences of Si, and therefore the additional electron is donated to the conduction band (CB) or bonded only weakly on the defect. Since the CB bottom of SiO2 is 3 eV above the CB bottom of the Si substrate, the electron is then transferred to the substrate and a fixed charge is formed in the SiO2 film. We name this defect a Silicon-related Nitrogen Coordinated Oxygen (SiNcO) defect. Formally, it is a so-called valence alternation defect and is labelled as O3+, with the subscript 3 indicating that the valence of oxygen inreased to 3, and the "+" sign designating the charge of the defect in the standard notation. We use here the name SiNcO as it allows us to give the common name to a family of conceptually similar, positively charged defects based on valence alternated oxygen but with various number of neighbors, as is common for oxygen in high-k oxides.
We have verified that SiNcO is indeed a donor which donates an electron to the Si substrate on which the SiO2 film is grown. Our first attempts to estimate the formation energy of this defect indicate that it is noticeably (be 1.5-2 eV) smaller than the formation energy of a Si dangling bond in SiO2.
We now return to the case of Pr2O3. We computed that the presence of oxygen in the ambient (as during post-deposition annealing) promotes dissolution of Si atoms from the substrate into the Pr2O3 film. In particular, energy is gained when a Pr atom is replaced by a Si atom taken from the substrate and subsequently oxidized to Pr oxide. In an otherwise perfect lattice, such a substitutional SiPr has a dangling Si bond, which introduces electron transition states in the the upper part of the Si band gap. In an amorphous network or at a grain boundary, this dangling bond may arrange itself next to an oxygen atom from the oxide, thus forming a SiNcO similar to that in SiO2. We will now estimate the formation energy of such a defect.
| |
 | |
Two model configurations of SiNcO+ in Pr2O3 |
Building a model of such a configuration in order to verify the conjunction that such a defect would act as a fixed charge would be a tedious task. Instead, we have placed an interstitial SiH3 molecule in two configurations in crystalline Pr2O3: in the perfect crystal and in a Pr2O3 void created in an otherwise perfect crystal. In both cases, the defect behaves as expected: it delivers a positive fixed charge. However, the formation energies ESi-NcO (with respect to Si-Si bond in disilane, Si2H6) is very different: when computed for the Fermi level corresponding to that of intrinsic Si, it amounts to 2.4 eV in the first configuration, and to -1.2 eV in the second configuration. The difference comes apparently from the high compressive stress in the first configuration: the Si atom is forced to a site close to three Pr atoms (note that in spite of that, a regular bond with the oxygen atom is formed). In contrast to that, the second configuration allows the Si atom to find a place reasonably distant from the Pr neighbors without compromising the Si-O bond length. This leads to a significant lowering of the formation energy in the second configuration. We will treat these two formation energies as the upper and lower bound estimate of the bond energy between the dangling bond of Si and an NcO atom in Pr2O3.
In order to estimate the SiNcO formation energy we still need an estimate of the energy of a regular bond between Si atom and an O atom in Pr2O3. For this purpose, we will use the energy computed in Section on Formation of the interfacial silicate for the SiO2 molecule dissolved in Pr2O3. The formation energy 4ESi-OPr of this defect with respect to SiO2 is about 1.2 eV and corresponds to the formation of four regular Si-O bonds in Pr2O3. Since the SiNcO defect has three such bonds and one SiNcO bond, we are now in a position to estimate its formation energy E:
E = ESi-NcO + 3 ESi-OPr
| |
 | |
Energetics of defect formation in Pr oxides |
The result has been already been plotted as a function of the chemical potential of oxygen in the energy diagram of native point defects; here we repeated this diagram again for convenience The two thin red dash-dot line correspond to the upper and lower bounds, while the line labeled SiNcO+ corresponds to their arithmetic average. We see that SiNcO+ is the energetically most favorable defect in the regime of oxygen chemical potentials already slightly (about 0.5 eV) above the equilibrium with SiO2, if the average value is taken as the estimate of its formation energy. Even in the pessimistic case (the upper bound estimate) the formation energy of SiNcO is only slightly higher than the formation energy of the oxygen interstitial Oi-2 when the chemical potential of oxygen approaches the equilibrium between Pr2O3 and PrO2. What is even more significant, both formation energies (the upper limit for SiNcO+ and the energy of Oi-2 are clearly negative in this limit, meaning that these defects are formed spontaneously.
We expect that the SiNcO formation energy is low also in other metal oxides. The reason is that the low energy of SiNcO is caused by the oxidation of the Si atom. Even when the SiNcO formation energy is estimated from quite unfavorable atomic configurations (SiO2 interstitial in Pr2O3 and SiH3 interstitial in the perfect Pr2O3 lattice, the fact that Si-O bonds are formed overweighs the geometrical constraints associated with the particular defect site. Since the presence of metal neighbors to these O atoms affects the strength of this bond only moderately (as proven by the fact that amorphous silicates stable up to several hundred degrees C can be obtained not only with "silifilic" rare-earth oxides but also with "silifobic" materials such as HfO2 and TiO2, the appearance of SiNcO as a major positive fixed charge source in, e.g., HfO2/Si(001), seems plausible. More to the point, HfO2 is purposely grown on Si in amorphous form, and this is the amorphous host that is the natural environment for the SiNcO atomic configuration.