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Low Gain Avalanche Detectors (LGADs) are silicon sensors with a built-incharge multiplication layer providing a gain of typically 10 to 50. Due to thecombination of high signal-to-noise ratio and short rise time, thin LGADsprovide good time resolutions.  LGADs with an active thickness of about 45 $\mu$m were produced at CNMBarcelona. Their gains and time resolutions were studied in beam tests for twodifferent multiplication layer implantation doses, as well as before and afterirradiation with neutrons up to $10^{15}$ n$_{eq}$/cm$^2$.  The gain showed the expected decrease at a fixed voltage for a lower initialimplantation dose, as well as for a higher fluence due to effective acceptorremoval in the multiplication layer. Time resolutions below 30 ps were obtainedat the highest applied voltages for both implantation doses before irradiation.Also after an intermediate fluence of $3\times10^{14}$ n$_{eq}$/cm$^2$, similarvalues were measured since a higher applicable reverse bias voltage couldrecover most of the pre-irradiation gain. At $10^{15}$ n$_{eq}$/cm$^2$, thetime resolution at the maximum applicable voltage of 620 V during the beam testwas measured to be 57 ps since the voltage stability was not good enough tocompensate for the gain layer loss. The time resolutions were found to followapproximately a universal function of gain for all implantation doses andfluences.

Gain and time resolution of 45 $\mu$m thin Low Gain Avalanche Detectors before and after irradiation up to a fluence of $10^{15}$ n$_{eq}$/cm$^2$