Comprehensive description of blinking-dynamics regimes in single direct-band-gap silicon nanocrystals

Blinking dynamics of strain-engineered direct-band-gap Si nanocrystals is measured over a broad interval of time scales and excitation intensities. The measured data are at first described using the autocorrelation function approach. Then, the relationship between the shape of the autocorrelation function and the distributions of on and off times is discussed. An original numerical approach allowing us to deduce and quantify the corresponding on- and off-times distributions is proposed. Both the autocorrelation function and the distribution of on and off times are observed to follow a broken-power-law function, for which we introduce an analytical formula. The broken-power-law function signifies a change in the power-law dynamics at short time scales (the power-law exponent changes on the time scale of 1--20 ms). Under the lowest excitation intensities, both the autocorrelation function and the distribution of on times are flat, implying the existence of a nonblinking regime. In addition to the broken-power-law dynamics, the end of the on-times distribution is also cut off by an exponential tail. All these temporal regimes are observed to be independent of excitation intensity for the lowest excitation intensities, whereas at higher excitation intensities, excitation intensity dependence appears. The distribution of off times is observed to be more robust, with changes occurring at higher excitation intensity than in the case of the on-times distribution. The different observed regimes are discussed in detail and a qualitative model including the emission of a trion is proposed.