Vanadium interactions in crystalline silicon

The properties of interstitial vanadium $\left({\mathrm{V}}_i\right)$ in Si and its interactions with the vacancy and the self-interstitial, as well as with hydrogen, are calculated using first-principles techniques. The stable configurations, gap levels, and binding energies agree well with the available experimental data. The nudged-elastic-band method is used to calculate the activation energies for diffusion of ${\mathrm{V}}_i$ in various charge states. They range from 1.46 (for ${{\mathrm{V}}_i}^{+}$) to 2.04 eV (for ${{\mathrm{V}}_i}^{-}$). The (trigonal) $\{{\mathrm{V}}_i,\mathrm{H}\}$ pair has a binding energy of 1.15 eV, a donor level at $E_c-0.61\mathrm{eV}$, and possibly an acceptor level $E_c-0.07\mathrm{eV}$. Substitutional vanadium $\left({\mathrm{V}}_s\right)$ can also trap H interstitials and form electrically active $\{{\mathrm{V}}_s,\mathrm{H}\}$ and $\{{\mathrm{V}}_s,\mathrm{H},\mathrm{H}\}$ complexes.

Figure 1

Migration barrier along the T-H-T sites for ${}^1{{\mathrm{V}}_i}^{+}$ obtained with seven images using the NEB method. $q$ is a generalized coordinate. The curves in the other charge states are very similar.

Figure 2

The $\{{\mathrm{I}}_{\mathrm{Si}},{\mathrm{V}}_i\}$ defect. The Si atoms are blue (light gray) and V is black.

Figure 3

The ${\{{\mathrm{V}}_i,\mathrm{H}\}}^{+}$ complex. The Si atoms are light gray (blue), V is dark gray, and H is white.

Figure 4

The $\{{\mathrm{V}}_s,\mathrm{H}\}$ complex. The Si atoms are light gray (blue), V is dark gray, and H is white.

Figure 5

The $\{{\mathrm{V}}_s,\mathrm{H},\mathrm{H}\}$ complex. The Si atoms are light gray (blue), V is dark gray, and H is white.

Figure 6

Comparison of the calculated (dashed lines) and measured (solid lines [22]) gap levels associated with ${\mathrm{V}}_i$ and $\{{\mathrm{V}}_i,\mathrm{H}\}$. The calculated acceptor level of $\{{\mathrm{V}}_i,\mathrm{H}\}$ is close to the conduction band, well within the accepted error bar for the marker method. The $E_5$ DLTS line reported in Ref. [22] (question mark) may be associated with some other VH complex.