Effect of dielectric environment on exciton spectrum of silicon quantum fibers

The problem of an exciton in a silicon quantium fiber $2\div4$ nm in diameter with permittivity $\varepsilon_i$ on a medium with permittivity $\varepsilon_e$ has been solved numerically. It was found that, if $\varepsilon_e<\varepsilon_i$ the exciton radius was smaller and the binding energy higher than for $\varepsilon_e=\varepsilon_i$. Conversely, with $\varepsilon_e>\varepsilon_i$, the exciton radius increased, while the binding energy sharply decreased. This explains the experimental data on dielectric quenching of exciton luminescence of porous silicon.