  Fluctuations of electric fields can change the position of a gate-defined
quantum dot in a semiconductor heterostructure. In the presence of magnetic
field gradient, these stochastic shifts of electron's wavefunction lead to
fluctuations of electron's spin splitting. The resulting spin dephasing due to
charge noise limits the coherence times of spin qubits in isotopically purified
Si/SiGe quantum dots. We investigate the spin splitting noise caused by such
process caused by microscopic motion of charges at the semiconductor-oxide
interface. We compare effects of isotropic and planar displacement of the
charges, and estimate their densities and typical displacement magnitudes that
can reproduce experimentally observed spin splitting noise spectra. We predict
that for defect density of $10^{10}$ cm$^{-2}$, visible correlations between
noises in spin splitting and in energy of electron's ground state in the
quantum dot, are expected.
