Blender Tip: Solidify modifier intersections (Read vid description)
Solidify modifier in blender is made for 3d animation speed. It does NOT do the extra processing needed to create proper solids. It won't examine to prevent intersections (at present).
A couple methods ARE often very useful in addressing the issue in many cases:
Method 1: Move other edges away from sharp bends.
Method 2: Use a vertex group (assigned in the solidify modifier) to adjust thicknesses as needed.
Neither of these handles all cases, but they do help with many.