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Blue‐shift of E 2 critical point resonance in optical second‐harmonic spectrum of Si nanocrystals
Author(s) -
Mendoza Bernardo S.,
Wei Junwei,
Downer Michael C.
Publication year - 2012
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.201100718
Subject(s) - blueshift , resonance (particle physics) , nanocrystal , atomic physics , harmonic , dielectric , molecular physics , materials science , harmonic spectrum , second harmonic generation , energy (signal processing) , dielectric function , optics , condensed matter physics , analytical chemistry (journal) , physics , chemistry , optoelectronics , nanotechnology , high harmonic generation , photoluminescence , quantum mechanics , laser , chromatography
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.