The aim of the TT-PET project is to develop a small animal TOF-PET scanner with 30 ps time resolution, intended to be inserted in an existing MRI scanner. The basic idea of the TT-PET project is to use a stack of layers of high-Z photon-converter and 100 micro-m thick silicon sensors, to build a scanner with 0.5 x 0.5 x 0.2$mm^3 granularity, with precise depth-of-interaction measurement. The development of a monolithic silicon detector with high timing performaces represents the main challenge of the project. We will show the last results of the R & D activity devoted to the realisation of this detector, together with the expected performances of the scanner obtained with a custom simulation framework.