  Electrons confined in silicon quantum dots exhibit orbital, spin, and valley
degrees of freedom. The valley degree of freedom originates from the bulk
bandstructure of silicon, which has six degenerate electronic minima. The
degeneracy can be lifted in silicon quantum wells due to strain and electronic
confinement, but the "valley splitting" of the two lowest lying valleys is
known to be sensitive to atomic-scale disorder. Large valley splittings are
desirable to have a well-defined spin qubit. In addition, an understanding of
the inter-valley tunnel coupling that couples different valleys in adjacent
quantum dots is extremely important, as the resulting gaps in the energy level
diagram may affect the fidelity of charge and spin transfer protocols in
silicon quantum dot arrays. Here we use microwave spectroscopy to probe spatial
variations in the valley splitting, and the intra- and inter-valley tunnel
couplings ($t_{ij}$ and $t'_{ij}$) that couple dots $i$ and $j$ in a triple
quantum dot (TQD). We uncover large spatial variations in the ratio of
inter-valley to intra-valley tunnel couplings $t_{12}'/t_{12}=0.90$ and
$t_{23}'/t_{23}=0.56$. By tuning the interdot tunnel barrier we also show that
$t'_{ij}$ scales linearly with $t_{ij}$, as expected from theory. The results
indicate strong interactions between different valley states on neighboring
dots, which we attribute to local inhomogeneities in the silicon quantum well.
