When I cut at 1/4" depth and 1/2" width, it works fine. When I increase it to 3/8" depth the wood splinters.
In addition to the Answer given by @Steven already, it may be a good idea to score the fibers that outline the sides of the cut prior to performing routing operations. Oak is notorious for splintering due to its open grain.
This can easily be done with a knife and a straight-edge:
or with a table saw, running the piece backwards over the blade:
Note that the table saw method should only be attempted if you have the piece securely fastened on something like a miter sled. See the referenced web page for further details, or this video.