Ultra-Fast Silicon Detectors (UFSDs) are n-in-p silicon detectors that implement moderate gain (typically 5 to 25) using a thin highly doped p++ layer between the high resistivity p-bulk and the junction of the sensor. The presence of gain allows excellent time measurement for impinging minimum ionizing charged particles. An important design consideration is the sensor thickness, which has a strong impact on the achievable time resolution. We present the result of measurements for LGADs of thickness between 20 micro-m and 50 micro-m. The data are fit to a formula that captures the impact of both electronic jitter and Landau fluctuations on the time resolution. The data illustrate the importance of having a saturated electron drift velocity and a large signal-to-noise in order to achieve good time resolution. Sensors of 20 micro-m thickness offer the potential of 10 to 15 ps time resolution per measurement, a significant improvement over the value for the 50 micro-m sensors that have been typically used to date.
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