Blue‐shift of E 2 critical point resonance in optical second‐harmonic spectrum of Si nanocrystals

The E 2 critical point (CP) resonance in the second‐harmonic spectrum of silica‐embedded Si nanocrystals (NCs) of 3 and 5 nm average diameter is observed to be blue‐shifted by 0.5 eV from its energy (4.4 eV) in the linear dielectric response ε ( ω ) of the same samples. In contrast, the E 1 CP resonance (3.4 eV) and a third resonance intermediate in energy (3.8 eV) between E 1 and E 2 occur at nearly the same energy in both linear and nonlinear spectra. We explain the anomalous E 2 blue‐shift by calculating the second‐harmonic response function Δ ( ω ) of the NCs analytically from the measured ε ( ω ) using a dipolium model. The analysis shows that the E 2 blue‐shift originates from the screening factors of the form [ ε (2 ω ) + 2] −1 and [2 ε (2 ω ) + 3] −1 that are unique to second‐harmonic generation (SHG) from nanospheres. Strong interaction between E 2 and $E'_{1} $ (5.3 eV in bulk c‐Si) resonant contributions to this factor pulls the E 2 peak response toward the higher $E'_{1} $ energy while negligibly influencing lower energy resonances.