Combined effect of energetic and spatial disorder on the trap-limited electron diffusion coefficient of metal-oxide nanostructures

We have extended the random walk numerical simulation (RWNS) method with exponential distribution of trap states so that disordered morphologies of metal-oxide nanostructures are taken into account. By using a stochastic cluster model we generate random packings of nanoparticles with texture parameters (porosity, roughness factor) commonly found in TiO2 and related nanostructurk We then place electron traps according to two alternative models: in the so-called r(2) model, traps are located on the surface of the nanoparticles, whereas in the r(3) model, the traps are distributed throughout the whole material. RWNS simulations with exponential distribution of trap states are carried out for different porosities and particles sizes. It is observed that the total number of traps in the simulation sample is the key parameter that governs the behavior of the diffusion coefficient. Both models reproduce the experimental dependence on the porosity although only the r(2) model explains the increase of the diffusion coefficient with the particle size. The numerical method utilized here can be considered as a first step toward a full and realistic modelization of electron transport in nanostructured devices.