Extraction of Cu diffusivities in dielectric materials by numerical calculation and capacitance-voltage measurement

A rigorous method of obtaining the Cu diffusivities in various SiO ₂-based dielectric materials is proposed. The diffusion profile of Cu ions in a dielectric material is first simulated and the resulting flatband voltage shift (ΔV_FB) is compared with the experimental results obtained by C-V measurements after bias-temperature stressing (BTS). The evolution of the Cu concentration in dielectric materials is evaluated using a one-dimensional finite differential method with two unknown parameters, the diffusivity, and the maximum solid solubility of Cu ions in the dielectric material. C-V measurements are conducted at 1 MHz to measure the ΔV _FB value of Cu/SiO₂/Si capacitors before and after BTS at an electric field of +1.0 MV/cm and in the temperature range between 200 and 275°C. With this process, the Cu diffusivities in thermally grown SiO ₂, oxynitride and SiO₂ deposited by plasma-enhanced chemical vapor deposition, and methyl-doped SiO₂ are found to be 2.22 × 10^-3 exp(-1.54 eV/kT), 3.09 × 10^-5 exp(-1.34 eV/kT), 2.59 × 10^-5 exp(-1.18 eV/kT), and 6.07 × 10^-9 exp(-0.71 eV/kT), respectively.