  In silicon spin qubits, the valley splitting must be tuned far away from the
qubit Zeeman splitting to prevent fast qubit relaxation. In this work, we study
in detail how the valley splitting depends on the electric and magnetic fields
as well as the quantum dot geometry for both ideal and disordered Si/SiGe
interfaces. We theoretically model a realistic electrostatically defined
quantum dot and find the exact ground and excited states for the out-of-plane
electron motion. This enables us to find the electron envelope function and its
dependence on the electric and magnetic fields. For a quantum dot with an ideal
interface, the slight cyclotron motion of electrons driven by an in-plane
magnetic field slightly increases the valley splitting. Importantly, our
modeling makes it possible to analyze the effect of arbitrary configurations of
interface disorders. In agreement with previous studies, we show that interface
steps can significantly reduce the valley splitting. Interestingly, depending
on where the interface steps are located, the magnetic field can increase or
further suppress the valley splitting. Moreover, the valley splitting can scale
linearly or, in the presence of interface steps, non-linearly with the electric
field.
