Time resolution of silicon pixel sensors

We derive expressions for the time resolution of silicon detectors, using the Landau theory and a PAI model for describing the charge deposit of high energy particles. First we use the centroid time of the induced signal and derive analytic expressions for the three components contributing to the time resolution, namely charge deposit fluctuations, noise and fluctuations of the signal shape due to weighting field variations. Then we derive expressions for the time resolution using leading edge discrimination of the signal for various electronics shaping times. Time resolution of silicon detectors with internal gain is discussed as well.