Trapping time of excitons in Si nanocrystals embedded in a ${\mathbf{SiO}}_{\mathbf{2}}$ matrix

Silicon (Si) nanocrystals (NCs) are of great interest for many applications, ranging from photovoltaics to optoelectonics. The photoluminescence quantum yield of Si NCs dispersed in ${\mathrm{SiO}}_2$ is limited, suggesting the existence of very efficient processes of nonradiative recombination, among which the formation of a self-trapped exciton state on the surface of the NC. In order to improve the external quantum efficiency of these systems, the carrier relaxation and recombination need to be understood more thoroughly. For that purpose, we perform transient-induced absorption spectroscopy on Si NCs embedded in a ${\mathrm{SiO}}_2$ matrix over a broad probe range for NCs of average sizes from 2.5 to 5.5 nm. The self-trapping of free excitons on surface-related states is experimentally and theoretically discussed and found to be dependent on the NC size. These results offer more insight into the self-trapped exciton state and are important to increase the optical performance of Si NCs.

Figure 1

Schematic of the adiabatic vibrational potentials, including the STE state, in the framework of the Huang-Rhys model within a configuration coordinate diagram. Potential 1 corresponds to the system before an excitation is created, and adiabatic potentials 2 and 3 correspond to the ground ($E_{g,\mathrm{exc}}$) and excited ($E_{\mathrm{EXC}}$) exciton states in the NC, respectively. Potential 4 represents the STE with energy $E_{\mathrm{STE}},{\varepsilon }_{\mathrm{opt}}$ is the threshold energy of optical ionization from the STE state, and ${\varepsilon }_T$ is the energy of the thermal ionization of an electron from the ground exciton state to the STE state. Arrow $C$ shows the process of the exciton capture from the excited state to the STE state, and $T$ demonstrates the process of the thermally stimulated tunneling from the ground state in potential 4 to potential 2.

Figure 2

Probe energy dependence of the IA transients. Normalized IA intensity transients for the sample with an average NC diameter of $d_{\mathrm{NC}}=5.5\mathrm{nm}$ with the probe energy set to below ($E_{\mathrm{probe}}=1.8\mathrm{eV}$, black curve) and above ($E_{\mathrm{probe}}=3.0\mathrm{eV}$, red curve) the STE ionization threshold energy of this sample. In the inset, a zoom into the first 30 ps is shown.

Figure 3

Influence of the NC size on the IA transients. Normalized IA intensity transients for a probe energy of $E_{\mathrm{probe}}=1.8\mathrm{eV}$ for samples with different average NC sizes $d_{\mathrm{NC}}$ of 2.5 (blue), 4 (olive), and 5.5 nm (black).

Figure 4

Comparison of the experimentally determined initial IA decay time constant and the theoretically estimated STE capture time. The probe energy dependence of the time constant, determined by fitting the initial IA transients to a single exponential function for three samples with average NC sizes of $d_{\mathrm{NC}}=2.5$ (blue), 4 (olive), and 5.5 nm (black). For comparison, the theoretically estimated STE capture times, multiplied by factor 2, for the three NC sizes are indicated with dashed lines in the same color as the corresponding experimental values.