The innermost part of the tracking detector of the ATLAS experiment consists mainly of planar n$^+$-in-n silicon pixel sensors. During the phase-0 upgrade, the Insertable B-Layer (IBL) was installed closest to the beam pipe. Its pixels are arranged with a pitch of $250,mu$m$,times,50,mu$m with a rectangular shaped n$^+$ implantation. Based on this design modified pixel designs have been developed in Dortmund. Six of these new pixel designs are arranged in structures of ten columns and were placed beside structures with the standard design on one sensor. Because of a special guard ring design, each structure can be powered and investigated separately. Several of these sensors were bump bonded to FE-I4 read-out chips. One of these modules was irradiated with reactor neutrons up to a fluence of $5 times 10^{15} , n_{text{eq}}text{cm}^{-2}$. This contribution presents important sensor characteristics, charge collection determined with radioactive sources and hit efficiency measurements, performed in laboratory and test beam, of this irradiated device. It is shown that the new modified designs perform similar or better than the IBL standard design in terms of charge collection and tracking efficiency, at the cost of a slightly increased leakage current.