  A slanting magnetic field is usually used to realize a slight hybridization
between the spin and orbital degrees of freedom in a semiconductor quantum dot,
such that the spin is manipulable by an external oscillating electric field.
Here we show that, the longitudinal slanting field mediates a longitudinal
driving term in the electric-dipole spin resonance, such that the spin
population inversion exhibits a modulated Rabi oscillation. Fortunately, we can
reduce this modulation by increasing the static magnetic field. The
longitudinal slanting field also mediates a spin-1/f-charge noise interaction,
which causes the pure dephasing of the spin qubit. Choosing proper spectrum
function strength, we find the spin dephasing time is about $T^{*}_{2}=20$
$\mu$s and the spin echo time is about $T^{\rm echo}_{2}=100$ $\mu$s in a Si
quantum dot. We also propose several strategies to alleviate the spin
dephasing, such as lowering the experimental temperature, reducing the quantum
dot size, engineering the slanting field, or using the dynamical decoupling
scheme.
