3. Selected results

Reduction of the EOT to the target value is a major technological and scientific problem. EOT is increased by oxidation of the substrate during the growth and by the presence of a silicate layer at the interface (Pr silicate has a dielectric constant lower than that of Pr2O3, although it is higher than that of SiO2). To this end, we have addressed several issues. For example, we have:

Another group of problems has to do with the need to reduce the density of charge traps in order to keep the leakage currents and threshold voltage under control. In this context, we have for example:

3.1. Chemically sharp Pr₂O₃/Si(001) and Pr₂O₃/Si(111) interface

A good matching between lattice spacing of the oxide and of the Si(001) substrate occurs when the (110) axis of the oxide is normal to the substrate, and the (100) axis of the film is parallel to the (110) axis of the substrate. In this configuration, each three Si atoms find a corresponding pair of Pr atoms. Two of these three Si atoms become now dimerized, which leaves the Si surface with four dangling bonds per each 3×1 unit, that is, two Si dangling bonds per each Pr atom on the oxide side. If the oxide had the composition of PrO₂, this would mean that there are four oxygen atoms per these two Pr atoms; the position of these O atoms would roughly match the position of the dangling bonds and each of the interfacial Si atoms could be oxidized. However, in Pr₂O₃ stoichiometry there are only three O atoms available for this purpose, leaving in each 3×1 unit one Si dangling bond without an oxygen partner.

An additional important factor is a charge mismatch between these materials. Bulk Pr₂O₃ is strongly ionic: one can assume that each Pr atom gives three electrons away and each O atom captures two electrons. But since O atoms at the interface form bonds (predominantly covalent) with Si atoms, they are only partially involved in the charge transfer from metal atoms. As a consequence, each interfacial Pr₂O₃ moiety donates two electrons which cannot be localized on the existing anions if the oxide is stoichiometric.

Green oxygen atoms are inserted to satisfy the electron counting rule

We find that in the ideal case of pure Pr₂O₃/Si(001) film (no silicate) these electrons are trapped by additional O located in the second Pr layer (the structure labeled 0(SiPr) in the energy diagram in the next Section); in the figure, these oxygen atoms are indicated by green shading. The stoichiometry of Pr oxide in the interfacial atomic layer becomes now Pr₂, but the Pr atoms in this layer are in the Pr(III) state as in bulk Pr₂O₃, not in Pr(IV) state as in bulk PrO₂. This is because the electrons needed to complete the valence shells of these additional oxygen atoms arrive from Si atoms and not from Pr atoms.

Stoichiometric interface with silicon "dangling bonds"

In stoichiometric Pr₂O₃/Si(001), the sesquioxide composition of the interface is maintained by removing some oxygen atoms moves from Si-O-Pr sites. This creates Si-Pr "bonds", which are in this case predominantly ionic, with a negatively charged Si dangling bond stabilized by electrostatic attraction with two Pr⁺³ neighbors (the structure labeled 1(SiPr) in the energy diagram in the next Section). This dangling bond is not active electrically, because the electrostatic interaction with the positively charged neighbors moves the (0/-) electron transition state into the valence band of silicon. The removal of oxygen from the interface does not change the interface into metallic, because the amount of electrons taken away from Pr atoms to localized states does not change. The only difference is that some of these electrons go now to Si dangling bonds and not to oxygen atoms. Note that the concentration of oxygen atoms in the first Pr oxide layer remains the same as in PrO₂. The interface becomes metallic only when the oxygen is lost from this oxide layer.

The same electron counting rule, which results in oxygen enrichment, is responsible for this oxygen enrichment of the first oxide layer in Pr₂O₃/Si(001), is also responsible for the behavior of oxygen at Pr₂O₃/Si(111) interface. Non-metallic character of the interface is maintained by the addition of oxygen to the first atomic layer of the oxide until PrO₂ stoichiometry is achieved. As in the case of Pr₂O₃/Si(001), the Pr atoms in this layer are Pr(III) as in bulk Pr₂O₃, not Pr(IV) as in bulk PrO₂. This is a general rule. No matter if the film is Pr₂O₃, PrO₂, or PrO_x, the first layer of the oxide on top of silicon consists of Pr^IIIO₂. Indeed, all valence orbitals of Si which are not saturated by Si atoms are used in covalent bonds with oxygen atoms of the oxide. In order to conserve the charge neutrality of the interface, all oxygen vacancy sites in the interface layer of cubic Pr₂O₃ have to be filled with oxygen; otherwise, the metal atoms in the interface layer donate electrons to silicon, the interface becomes metallic, and the interface energy increases. So exactly this amount of oxygen as is needed to fill the vacancy sites is needed to keep the interface semiconducting.

There are two possible arrangements of the first atomic layers of oxide with respect to Si(111) substrate. They differ by the stacking order of (111) layers and are named after this order as type-A and type-B interface. For A-type interface, the stacking of Pr oxide layers in the cubic film follows the stacking of Si(111) double layers, while for B-type interface there is a stacking fault at the interface. The stacking fault corresponds to 180° rotation of A-type film around an oxygen atom connected to Si. The essential difference between these configurations is the relative position of metal atoms in the first layer of the oxide and unoxidized Si atoms in the first (111) double layer. In B-type films, the metal and Si atoms are in registry, while in A-type films they are out of registry and the first in-registry Si atom belongs to the second (111) double layer. In B-type films, the metal and Si atoms are in registry, while in A-type films they are out of registry and the first in-registry Si atom belongs to the second (111) double layer.

These two geometries are associated with different strength of the electrostatic interaction between the metal atoms and the electrons in Si-Si bonds at the interface, as well as with the Si core. From ab initio calculations we obtain that type-B interface is energetically preferred over type-A interface, in agreement with experimental observation. The computed energy difference is relatively small (about 40 meV per interface Pr atom), which is reflected in experiment in the presence of a small fraction of A-type domains. During oxidation of the substrate, these domains convert to B-type, which in turn is consistent with the increase of the computed energy difference Si-Si bonds in the substrate are oxidized, and with the interpretation of the energy difference as coming predominantly from electrostatics.

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