Electronic structure and effective mass analysis of doped TiO$_2$ (anatase) systems using DFT+$U$

TL;DR

This study uses DFT+U to analyze how various dopants affect the electronic structure and charge carrier effective masses in TiO$_2$ anatase, revealing dopant-specific modifications to conductivity and transparency.

Contribution

It systematically computes U parameters via linear response and evaluates the impact of multiple dopants on TiO$_2$'s electronic properties, providing new insights into doping effects.

Findings

Cr, Mo form mid-gap states reducing transparency

Nb, Ta, W induce n-type conductivity near conduction band

Dopants increase effective mass and band non-parabolicity

Abstract

In this work, electronic structure of several doped TiO$_2$ anatase systems is computed using DFT+$U$. Effective masses of charge carriers are also computed to quantify how the dopant atoms perturb the bands of the host anatase material. $U$ is computed systematically for all the dopants using the linear response method rather than using fitting procedures to physically known quantities. A combination of $d$ and $f$ block elements (Nb, Ta, V, Mo, W, Cr, La, Cu, Co and Ce) are considered as dopants. Depending upon the energies of their outer $d$ or $f$ electrons, the dopants are found to form defect states at various positions in the band structure of host anatase system. Some dopants like Cr, Mo etc. form mid-gap states, which could reduce transparency. Other dopants like Nb, Ta and W are found to have the Fermi levels positioned near the conduction band edge, indicating these systems to exhibit $n$-type conductivity. From the effective mass analysis, dopants are found to increase the effective mass of charge carriers and the non-parabolic nature of bands. Based on electronic structure and effective mass analysis, Nb, Ta and W are identified to exhibit higher transparency and conductivity as compared to the other dopants considered here. The theoretical results presented here, increase our understanding and show the potential of dopants to alter the properties in anatase TiO$_2$.