[Paper Review] Polaron mobility in oxygen-deficient and lithium doped tungsten trioxide

N. G. Bondarenko, Olle Eriksson+1 more|arXiv (Cornell University)|Sep 20, 2015

Ga2O3 and related materials3 citations

TL;DR

This study investigates polaron formation and mobility in oxygen-deficient and lithium-doped monoclinic tungsten trioxide using DFT+U and HSE06 calculations. It finds that oxygen vacancies stabilize immobile W⁵⁺–W⁵⁺ bipolarons, while Li doping enables mobile polarons with activation energies of 98–124 meV, particularly along the [001] direction.

ABSTRACT

Electron localization and polaron mobility in oxygen deficient as well as Li doped monoclinic tungsten trioxide have been studied. We show that small polarons formed in the presence of oxygen vacancy prefer the bipolaronic $W^{5+}- W^{5+}$ configuration whereas the $W^{6+}- W^{4+}$ configuration is found to be metastable. Our calculations suggest that bipolarons are tightly bound by the vacancy and therefore largely immobile. On the contrary, polarons formed as a result of Li intercalation can be mobile, the activation energy for polaron jumping in this case varies between 98 and 124 meV depending on the crystallographic direction. The formation of $W^{5+}- W^{5+}$ bipolarons in $Li-WO_{3}$ is possible. When situated along $[001]$ the bipolaronic configuration is 8 meV lower in energy than two separate $W^{5+}$ polarons.

Motivation & Objective

• To understand the electronic and structural stability of polarons in oxygen-deficient and Li-doped WO₃.
• To determine whether W⁵⁺–W⁵⁺ bipolarons or W⁶⁺–W⁴⁺ configurations are energetically favored around defects.
• To calculate activation energy barriers for polaron migration in both oxygen-vacancy and Li-doped systems.
• To clarify the role of defects and dopants in determining polaron mobility and electrochromic response in WO₃.

Proposed method

• Employed DFT+U with Hubbard U parameters of 6 eV for W 4d and 9 eV for O 2p states to accurately describe localized d-electrons in WO₃.
• Used the projector augmented-wave (PAW) method within VASP for electronic structure calculations on large supercells.
• Applied the nudged elastic band (NEB) method to compute activation energy barriers for polaron hopping between W sites.
• Performed geometry optimization and energy evaluation for various defect configurations, including isolated and paired W⁵⁺ states.
• Compared results from DFT+U with HSE06 functional to validate the accuracy of the chosen functional for polaronic systems.
• Analyzed charge density distributions to visualize electron localization and polaronic states in different configurations.

Experimental results

Research questions

• RQ1 Which polaronic configuration—W⁵⁺–W⁵⁺ or W⁶⁺–W⁴⁺—is energetically favored in oxygen-vacancy-doped WO₃?
• RQ2 What is the activation energy barrier for polaron migration in oxygen-deficient WO₃, and how does it depend on crystallographic direction?
• RQ3 How does Li intercalation affect polaron formation and mobility compared to oxygen vacancies?
• RQ4 Is the W⁴⁺ state a stable configuration in Li-doped WO₃, or is it metastable and likely to form only in defective systems?
• RQ5 What is the relative stability of W⁵⁺–W⁵⁺ bipolarons along different crystallographic directions in Li-doped WO₃?

Key findings

• The W⁵⁺–W⁵⁺ bipolaronic configuration is the most stable around oxygen vacancies, with the [001]-aligned configuration being 8 meV lower in energy than the next-nearest-neighbor W⁵⁺–W⁵⁺ pair.
• Polarons formed in oxygen-deficient WO₃ are tightly bound to the vacancy and exhibit negligible mobility due to high activation barriers.
• The W⁶⁺–W⁴⁺ configuration is metastable with a 150 meV activation barrier for transition from the W⁵⁺–W⁵⁺ state.
• In Li-doped WO₃, polarons are mobile with activation energies ranging from 98 to 124 meV, depending on the crystallographic direction.
• The [001]-aligned W⁵⁺–W⁵⁺ bipolaron in Li-doped WO₃ is the most stable configuration, lying 8 meV below the corresponding next-nearest-neighbor pair.
• The W⁴⁺ state is energetically unfavorable in pristine Li-doped WO₃, being over 300 meV higher in energy than any W⁵⁺–W⁵⁺ configuration, indicating it likely arises only in defective systems with oxygen vacancies.