Low Gain Avalanche Detectors (LGADs) are silicon sensors with a built-in charge multiplication layer providing a gain of typically 10 to 50. Due to the combination of high signal-to-noise ratio and short rise time, thin LGADs provide good time resolutions. LGADs with an active thickness of about 45 $mu$m were produced at CNM Barcelona. Their gains and time resolutions were studied in beam tests for two different multiplication layer implantation doses, as well as before and after irradiation with neutrons up to $10^{15}$ n$_{eq}$/cm$^2$. The gain showed the expected decrease at a fixed voltage for a lower initial implantation dose, as well as for a higher fluence due to effective acceptor removal in the multiplication layer. Time resolutions below 30 ps were obtained at the highest applied voltages for both implantation doses before irradiation. Also after an intermediate fluence of $3times10^{14}$ n$_{eq}$/cm$^2$, similar values were measured since a higher applicable reverse bias voltage could recover most of the pre-irradiation gain. At $10^{15}$ n$_{eq}$/cm$^2$, the time resolution at the maximum applicable voltage of 620 V during the beam test was measured to be 57 ps since the voltage stability was not good enough to compensate for the gain layer loss. The time resolutions were found to follow approximately a universal function of gain for all implantation doses and fluences.
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