In trimethylamine, 'N' atom is $\mathrm{s}{\mathrm{p}}^3$ -hybridized.

Due to the presence of lone pair in $\mathrm{s}{\mathrm{p}}^3$ -hybrid orbital, the geometry of $(\mathrm{C}{\mathrm{H}}_3{)}_3\mathrm{N}$ becomes pyramidal around nitrogen.

This lone pair of electrons can be donated to electron-deficient species, e.g., $(\mathrm{C}{\mathrm{H}}_3{)}_3\mathrm{N}\to \mathrm{B}{\mathrm{F}}_3$ . This lone pair cannot be transferred to carbon atom, because carbon atom has no d-orbital in its valence shell.
In $(\mathrm{S}\mathrm{i}{\mathrm{H}}_3{)}_3\mathrm{N},$ the 'N' atom is $\mathrm{s}{\mathrm{p}}^2$ -hybridized.

The orientation of three $\mathrm{s}{\mathrm{p}}^2$ -hybrid orbitals is plane-triangular, therefore, the geometry around 'N' becomes plane-triangular. Here the lone pair of electrons is transferred to vacant d-orbitals to each of three silicon atoms forming $\mathrm{p}\mathrm{\pi }-\mathrm{d}\mathrm{\pi }$ multiple bonds. Consequently, ${\left(\mathrm{S}\mathrm{i}{\mathrm{H}}_3\right)}_3\mathrm{N}$ has no donor properties. For example
$(\mathrm{S}\mathrm{i}{\mathrm{H}}_3{)}_3\mathrm{N}+\mathrm{B}{\mathrm{F}}_3\to$ No reaction.