First principles modeling of electron tunneling between defects in m-HfO2

Abstract

a b s t r a c tDefect assisted electron transfer processes in metal-oxide materials play a key role in a diverse range of effects of relevance to microelectronic applications. However, extracting the key parameters governing such processes experimentally is a challenging problem. Here, we present a first principles based investigation into electron transfer between oxygen vacancy defects in the high-k dielectric material HfO 2 . By calculating electron transfer parameters for defects separated by up to 15 Å we show that there is a crossover from coherent to incoherent electron transfer at about 5 Å. These results can provide invaluable input into numerical simulations of electron transfer, which can be used to model and understand important effects such as trap-assisted tunneling in advanced logic and memory devices.

Hematite(001)-liquid water interface from hybrid density functional-based molecular dynamics

“…In addition, the simulations reported here and in previous work [18] provide a solid basis for investigation of the nature and energetics of excess hole and electron in hematite/water interfaces, relevant to water splitting photocatalysis [5], crystal growth [80] and biogeochemical transformations [81,82]. The constrained density functional theory method that was previously applied to calculation of electron transfer parameters for hole tunneling in oxide materials [83][84][85] may be extended to such interface problems. Work along these lines is currently ongoing in our laboratory.…”

Hole Polaron Migration in Bulk Phases of TiO2 Using Hybrid Density Functional Theory

“…The electronic coupling constant H ab is then estimated as the difference between the adiabatic and diabatic energies at the transition state. We note a more accurate approach would be to obtain the diabatic solutions at the transition state using constrained DFT and then diagonalizing to obtain the electronic coupling constant as we have done in previous studies. − However, the high computational cost of these calculations and large number of pathways make this prohibitive at the present time.…”

“… 6 , 43 − 45 There are many previous applications of the approach to model polaron hopping in TiO 2 , Fe 2 O 3 , and organic semiconductors as well as electron transfer between point defects in crystals. 22 , 26 , 46 − 48 , 55 , 56 Here, we employ MEHAM with the common approximation that the hole hopping process can be described as a one-dimensional process coupling to a single generalized phonon mode. We note that although we consider a single phonon mode, it includes displacements of all atoms and the wavefunction is not constrained in any way, so it is not the case that adjacent atoms are not involved (in general they all are).…”

“…Furthermore, calculation of barriers to hole hopping are far less affected by finite size effects since the hole remains localized throughout transition. To model polaron hopping, we employ the MEHAM model, which is able to describe the charge-transfer processes in both the adiabatic and non-adiabatic limits and is well suited to describing small polaron hopping in TiO 2 . ,− There are many previous applications of the approach to model polaron hopping in TiO 2 , Fe 2 O 3 , and organic semiconductors as well as electron transfer between point defects in crystals. ,,− ,, Here, we employ MEHAM with the common approximation that the hole hopping process can be described as a one-dimensional process coupling to a single generalized phonon mode. We note that although we consider a single phonon mode, it includes displacements of all atoms and the wavefunction is not constrained in any way, so it is not the case that adjacent atoms are not involved (in general they all are).…”

“…However, the size of the SIE in these calculations is unknown (and could be significant given the large Hubbard U value used of 10 eV). Although hybrid functional methods have been used together with MEHAM theory to investigate electron transfer process in some materials, for example, MgO and HfO 2 , − it is yet to be applied to bulk phases of TiO 2 (including brookite or TiO 2 -B). Furthermore, previous studies have not compared activation energies for thermal ionization of the polaron against activation energies for hole hopping at the same level of theory which is needed in order to determine the migration mechanism.…”