The density of states from the B3LYP(20%) calculation with the Figgen basis set was obtained for the four Si/HfO2 interface structures and it is shown in figure 7.5. We observe that the Fermi
level and the band gap for the Si/HfO2 structure is pushed above that of the bulk Si B3LYP
conduction band minimum. This does not seem to be in agreement with the relative offsets of bulk Si, mononclinic and amorphous HfO2 previously calculated and presented in section 5.3. If
controlled for this offset the total DOS of Si/HfO2 interfaces does reduce to a superposition of
the bulk Si, amorphous HfO2 and defect level gap states, similar to the total DOS of the Si/SiO2
structures was a superposition of Si, SiO2 and defect states.
The atom projection of the Si atoms in inner layers of the Si slab is used to determine the valence band maximum (VBM) and the conduction band minimum (CBM) of the interface structures. The density of states for near the gap region for the four Si/HfO2 structures is shown in figure 7.6.
For reference, the 0 eV level was set at the structure’s VBM. The cell 1 and cell 1 ox structures present a spin polarisation while cell 2 ox and cell 3 ox have an identical spin up - spin down density of states. The absolute position of the Fermi level varies from cell to cell by0.7eV. It has been shown in Chapter 5 that bulk Si and bulk (monoclinic and amorphous) HfO2 have a defect
free gap region. This leads us to observe that, as was the case for Si/SiO2 interface structures,
the presence of the interface layer causes such gap states to appear. Unlike Si atoms in SiO2, Hf
atoms in HfO2 have more variability in their O coordination and do not tend to form clear bonding
patterns such as the the tetrahedra present in SiO2. As shown in section 4.2 Hf-Si bonds have
also been shown to create interface states, and we should also account for them.
The contributions of Hf atoms with various degrees of O coordination to the total DOS of Si/HfO2
interface structures is shown in figure 7.7. The summed atom projected DOS contributions of Hf atoms of a given contribution are summed and the 0 eV level is set at the VBM. Sixfold O coordinated Hf atoms are shown to produce the largest number of states above the VBM with clear sharp localised states — however it must be taken into account that sixfold coordinated O atoms appear more frequently than all the other Hf atom coordinations combined. Fivefold coordinated Hf atoms create more diffuse states throughout the gap. As shown in the Hf-O coordination distribution chart from figure 7.3a, the relative frequency of fivefold and sevenfold coordinated Hf atoms is relatively similar. Figure 7.7 shows that fivefold O coordinated Hf atoms are way more likely to produce states throughout the gap region than sevenfold coordinated Hf. Fourfold and eightfold O coordinated atoms also are equally likely to appear in our structures, but a clear symmetry exists in the number of gap states they produce — fourfold O coordinated Hf atoms produce clear localised peaks in the gap region while eightfold coordinated Hf atoms contribute the least to the distribution of gap states.
Clearly having a high O coordination is a significant factor in reducing the number of gap states produced by Hf atoms. In order to accurately determine the effect of various coordination numbers for Hf atoms in producing gap states we computed the relative contributions to the band gap for each individual atom. Figure 7.8 shows the the average integrated atom projected DOS between the VBM and CBM for each individual atom of a given O coordination. The average value of the
Figure 7.6: Gap density of states for Si/HfO2 interface structures calculated at the B3LYP(20%)
level. The Fermi level for each structure is marked with a red line. The0eV level marks the VBM for each individual structure. Shaded areas represend the valence band and the conduction band regions for the Si/HfO2 interface structures.
Figure 7.7: Hf DOS contribution for different O coordination values. A coordination sphere of
3˚A is considered around each Hf atom and the coordination number represents the number of O atoms within that sphere. The contribution is summed for each coordination number. The zero eV level represents the VBM for each structure and the shaded area marks the valence band.
integrated dos (Ω¯) for atoms of coordination k1 is ¯ Ω = 1 N N X i Z CBM VBM PDOSi(E) (7.1)
where the indexiiterates over allN atoms of coordinationk, averaging over the integrals between the valence band minimum and conduction band maximum of the projected density of states of k-fold coordinated atom i (PDOSi(E)). It is immediately obvious that having a full oxygen coordination is paramount in decreasing the number of gap states, as the average value of the integrated Hf atom projected gap DOS decreases with higher O coordination numbers. An Hf atom with 4 oxygen atoms in its coordination sphere is very likely to create gap states when having another Hf or Si atom within3 ˚A. Hf atoms with an O coordination of 7 or 8 are roughly as likely to produce gap states. Sixfold O coordinations for Hf atoms are also present in amorphous HfO2
(cf the distribution in figure 7.3a). As bulk amorphous HfO2 has a clear band gap, this leads
to the conclusion that mere sixfold O coordination for Hf atoms is not enough to explain the creation of gap states. The majority of sixfold coordinated Hf atoms that produce states in the band gap above the average level of sevenfold and eightfold coordinated Hf atoms have at least one Hf within their coordination sphere – which leads to the point that for Hf atoms with an O coordination larger than 6 is effective at screening out the interaction with other Hf atoms. In analysing the effect of Hf-Si bonding for creating interface states we calculated the DOS contribution of Si atoms with at least one Hf atom within a3 ˚A coordination shell. We observed that the presence of a Si atom within the3˚A coordination shell of a Hf atom does not necessarily result in the formation of a gap state. As shown in Chapter 4, theoretical studies on (001)Si interfaces with monoclinic and cubic HfO2 show that choosing an interface that bonds surface
Si to Hf atoms in stead of O atoms from the oxide results in metallic states [127]. During the PBE optimisation oxygen migrates from the HfO2 layer to the Si surface. Figure 7.10 shows the
oxygen mass density profile along the vertical z axis of the interface structures with the oxygen mass density in the amorphous HfO2 structure shown for reference. The oxygen density in the
structures is lower and more spread on the vertical axis than the one in amorphous HfO2regardless 1
Figure 7.8: Average integrated projected gap DOS for diferent coordinations of Hf atoms as per equation 7.1. Hf atoms are sevenfold coordinated in m-HfO2. Hf atoms in Si/HfO2 interface
structures are more likely to produce significant gap states if their coordination number is less than 7.
of whether an initially oxidised Si slab was used or not. The immediate conclusion would be that O atoms adsorbed at the Si interface prevent Hf-Si bonds from creating gap states. The O migration does have the effect of favouring the creation of Hf-Hf bonds in the oxide as well as fourfold and fivefold coordinated Hf atoms which are more likely to create gap states.