Optimum Segmentation and Thickness of Silicon Pixel Detectors for Signal to Noise Ratio and Timing Resolution

In Silicon Pixel Detector systems the pixel size and detector thickness are often determined by spatial resolution and material budget requirements. Nevertheless, in some applications there is, within certain limits, freedom in the choice of these parameters. It is therefore interesting to understand what are the optimum pixel size and detector thickness which maximize Signal to Noise Ratio (SNR) and/or Timing Resolution (TR). To be accurate this optimization problem has to take into account detector parameters such as specific leakage current, operating temperature and specific capacitances and technology parameters such as noise characteristics, oxide thickness, power supply voltage and many others. To help understanding what the optimum detector segmentation and thickness are, we wrote an optimization routine which considers all the above mentioned parameters and which optimizes the size of the input transistor of the charge amplifier for each detector segmentation or thickness considered. SNR and TR require different optimization procedures. In particular, for TR it is important to consider the detector speed, and this requires proper modeling through 3D detector simulations.