Figure 4.

Theoretical investigation of the TiON–TiO_2–x interface and the trap-assisted recombination model. (a) Ab initio DFT+U calculations of the electron–phonon scattering time of TiN. The strong electron–phonon coupling of TiN results in thermalization with the lattice within the resolution of our system. Inset shows a comparison of calculated Au and TiON lifetimes with Au showing 2 orders of magnitude longer lifetimes. (b) Proposed trap-assisted recombination model at the TiON–TiO_2–x interface with the associated lifetimes observable in our measurements associated with shallow trap occupation (τ_Sh), deep trap occupation (τ_De), and recombination (τ_Re). (c) Experimental data showing the shallow and deep trap occupation lifetimes along with the exponential rise time of the signal (τ₀) and the amount of energy lost to occupying traps (s + d) and the amount remaining in the free carriers (δ).