Dielectric screening versus quantum confinement of phosphorus donors in silicon nanocrystals investigated by magnetic resonance

We monitor the localization of donor wave functions when going from the bulk to nanoscales by electrically detected magnetic resonance of P-doped Si nanocrystal networks. Analysis of the P hyperfine splitting shows that for nanocrystals with radii above $\sim 6\text{nm}$ donor localization is dominated by a reduction in dielectric screening relative to the bulk rather than by quantum confinement. Screening effects become negligible only for radii below $\sim 2\text{nm}$, where quantum confinement dominates. Thus, hyperfine interactions can serve as sensitive probes to study basic properties of doped nanocrystals and provide data to critically test theoretical models.

Figure 1

(Color online) (a) Hydrogenlike model of a donor impurity in a bulk semiconductor. (b) Quantum confinement and (c) dielectric confinement models of a donor impurity in a semiconductor NC. Dashed and solid traces represent electron probability density ${\left|\Psi \left(r\right)\right|}^2$ and potential energy $V\left(r\right)$, respectively. Dotted traces in (b) and (c) correspond to the bulk situation.

Figure 2

EDMR spectra of P-doped Si-NCs with 14 to 2.8 nm mean radii for $\Delta \theta \sim 80°$ (solid traces). Due to the detection method, spectra show first derivatives of the resonant current changes. Dotted traces depict simulated $\text{hf}\left({}^{31}\text{P}\right)$ line shapes.

Figure 3

(Color online) Experimental dependence of ${}^{31}\text{P}$ hfs on NCs mean radius (filled circles), together with the dependencies obtained from the (i) quantum confinement model (dotted trace), (ii) dielectric confinement model (dash-dotted trace), and (iii) full model (solid trace). The EPR hfs (open circles) and corresponding fitting with a $R^{-3}$ law (dashed trace) reported by Fujii et al. (Ref. 12) for Si-NCs embedded in $a{\text{-SiO}}_2$ are also shown. Horizontal and vertical error bars represent the size distribution interval that contains 70% of the NCs and the peak-to-peak width of the high-field $\text{hf}\left({}^{31}\text{P}\right)$ resonance, respectively. The horizontal gray line indicates the value $A_{\text{bulk}}$.