Exploring Charge Hopping Transport in Amorphous HfO2: an Approach Combing Ab Initio Methods and Model Hamiltonian

Charge hopping transport is typically modeled by Marcus theory with the coupling strengths and activation energies extracted from the constrained density functional theory. However, such a method may not be a practical route for amorphous materials due to the tremendous amount of hopping paths, therefore computationally unreachable. This work presents a general approach combining the a b initio method and model Hamiltonian, yielding similar results to constrained density functional theory. Such an approach is computationally efficient, allowing us to consider all 23 220 hopping paths between oxygen vacancies in our demonstrated amorphous hafnium dioxide model containing 324 atoms. Based on these hopping rates, charge mobility in amorphous hafnium dioxide is investigated as a function of oxygen vacancies concentration. It is found that a minimum oxygen vacancies concentration of 0.7 x 10(21) cm(-3) is required to enable the connectivity of the charge hopping network.