Deep electron and hole polarons and bipolarons in amorphous oxide

Abstract

Amorphous (a)-HfO2 is a prototype high dielectric constant insulator with wide technological applications. Using ab initio calculations we show that excess electrons and holes can trap in aHfO2 in energetically much deeper polaron states than in the crystalline monoclinic phase. The electrons and holes localize at precursor sites, such as elongated Hf-O bonds or under-coordinated Hf and O atoms and the polaronic relaxation is amplified by the local disorder of amorphous network. Single electron polarons produce states in the gap at ∼2 eV below the bottom of the conduction band with average trapping energies of 1.0 eV. Two electrons can form even deeper bipolaron states on the same site. Holes are typically localized on under-coordinated O ions with average trapping energies of 1.4 eV. These results advance our general understanding of charge trapping in amorphous oxides by demonstrating that deep polaron states are inherent and do not require any bond rupture to form precursor sites.Electron and hole states with energy levels lying deep in the bandgap impair the dielectric quality of insulating layers. In particular, electron transitions facilitated by these states account for multitude of degradation phenomena including enhanced leakage current and charge trapping eventually leading to the dielectric barrier failure and breakdown. Routinely, however, these deep electron states are seen as not inherent to the perfect material but rather associated with the presence of defects and/or impurity centers in the atomic network of an insulator. This belief offers some hope that imperfections can be eliminated by using more clean and optimized synthesis and proper processing of the insulators. On the other hand, self-trapping of excess charges in the form of small electron and hole polarons is well known to occur even in perfect crystalline oxide insulators. However, it is usually shallow, with trapping energies of the order of 0.2 eV (see e.g. [1-3]). As a result, the electron and hole polarons are mobile at room temperature in crystalline reduced TiO 2 and NiO [4], CeO 2 [5, 6], doped ZrO 2 [7,8], and in plethora of other oxides (see e.g. [1,[9][10][11][12]). The intrinsic localization of excess electrons and holes in noncrystalline materials and liquids has also been a subject of extensive experimental and theoretical studies pioneered in [13]. Structural disorder typically induces shallow electron states near the bottom of the conduction band, below the so-called mobility edge (see, e.g. [14] . In these systems, the polaronic relaxation is amplified by the local disorder of amorphous network.Here we turn to amorphous (a)-HfO 2 , which represents a wide class of high dielectric constant oxides recently emerged as the major contenders to replace SiO 2 in a broad spectrum of nano-electronic devices ranging from deep-scaled transistors to DRAM and non-volatile memory cells (see, e.g. [21,22]). Amorphous oxides make the backbone of most electronic devices and charge trapping appears to be the key factor determining devic...

Interactions of hydrogen with amorphous hafnium oxide

“…[40], we observe spontaneous localization of one and two extra electrons in deep states in each considered system. In 60% cases precursor sites for this localization are the Hf atoms which have at least three oxygen neighbors with the distance longer than 2.16Å.…”

“…The distributions of Hf-O and Hf-Hf bond lengths obtained after the DFT cell and geometry optimization of neutral cells are discussed in Ref. [40]. Hf ions are 5-7 coordinated and O ions are 2-4 coordinated.…”

“…The densities of the produced models are ranging from 8.6 to 9.2 g cm −3 . These models exhibit wide distributions of bond lengths and atomic coordinations [40].…”

“…Nine periodic models of a-HfO 2 , each containing 324 atoms, have been generated using classical molecular dynamics and a melt and quench procedure in an NPT ensemble, as discussed in more detail in Ref. [40]. The densities of the produced models are ranging from 8.6 to 9.2 g cm −3 .…”

“…In this work we used the methodology described in our recent paper [40]. To create initial models a-HfO 2 structures we used pair potentials developed in Ref.…”