Electric field throughout a semiconductor
In a bar of ideal semiconductor with one side grounded and the other at some nonzero voltage you will have a constant electric field through the bar.
Another answer addresses the band structure of semicondcutors, which seems unnecessary to answer this question, but since it was brought up I will comment on it as well. The electric field present in a semiconductor is proportional to the derivative of the conduction and valence band edges. This is guaranteed to be a constant when there is no net charge. If there is net charge the field will change across the semiconductor and your bands will bend. In your example of an ideal semiconductor there is no net charge anywhere within the semiconductor and therefore the electric field must be constant.
In a practical block of semiconductor you will have to apply your bias somehow, and that is usually through a metal-semiconductor contact. These introduce some diode behavior and will change the field a bit.