  A detailed understanding of the material properties that affect the splitting
between the two low-lying valley states in Si/SiGe heterostructures will be
increasingly important as the number of spin qubits is increased. Scanning gate
microscopy has been proposed as a method to measure the spatial variation of
the valley splitting as a tip-induced dot is moved around in the plane of the
Si quantum well. We develop a simulation using an electrostatic model of the
scanning gate microscope tip and the overlapping gate structure combined with
an approximate solution to the three-dimensional Schr\"odinger-Poisson equation
in the device stack. Using this simulation, we show that a tip-induced quantum
dot formed near source and drain electrodes can be adiabatically moved to a
region far from the gate electrodes. We argue that by spatially translating the
tip-induced dot across a defect in the Si/SiGe interface, changes in valley
splitting can be detected.
