You migth need to be more specific. Why are the trap levels exactly at midgap? Is it something related to the particular system you are studying? In principal, the trap states could be anywhere in the gap. Additionally, an in gap current could arise from charge carriers being thermally activated from donor levels present midgap. This current is easier to measure, as one simply has to follow how the current at VG = 0 evolves with temperature. If it is high enough to be measured....
In the case of oxide traps, which method are you planning to use to measure them?