  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 $3\times10^{14}$ 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.
