I am making a 3D logo.
When I create a text object and use solidify mod to make it thicker it does this:
When I don't use the solid mod, and instead convert it to a curve to do a curve extrusion it does this:
Why is it doing this?
The missing fill in your curves is caused by overlap. If the curves self intersect Blender doesn't know how to fill them correctly.
Either:
Again if you are working with curves don't use the solidify modifier, instead use the curve extrude option which should yield better results.
That being said, I think you started on the wrong foot, if you plan on curving your object the way you show in the image you will never get a clean solution from curves. Because of the triangle based topology of curve object you will never get a clean smooth curvature.
You can try and minimize it by using a Subsurf modifier but it will generally maintain it's triangulated appearance.
You should do this from scratch with a mesh object with an even quad based topology