  In this paper we report results from a neutron irradiation campaign of
Ultra-Fast Silicon Detectors (UFSD) with fluences of 1e14, 3e14, 6e14, 1e15,
3e15, 6e15 n/cm2. The UFSD used in this study are circular 50 micro-meter thick
Low-Gain Avalanche Detectors (LGAD), with a 1.0 mm diameter active area. They
have been produced by Hamamatsu Photonics (HPK), Japan, with pre-radiation
internal gain in the range 10-100 depending on the bias voltage. The sensors
were tested pre-irradiation and post-irradiation with minimum ionizing particle
(MIPs) from a 90Sr based \b{eta}-source. The leakage current, internal gain and
the timing resolution were measured as a function of bias voltage at -20C and
-30C. The timing resolution was extracted from the time difference with a
second calibrated UFSD in coincidence, using the constant fraction method for
both. The dependence of the gain upon the irradiation fluence is consistent
with the concept of acceptor removal and the gain decreases from about 80
pre-irradiation to 7 after a fluence of 6e15 n/cm2. Consequently, the timing
resolution was found to deteriorate from 20 ps to 50 ps. The results indicate
that the most accurate time resolution is obtained at a value of the constant
fraction discriminator (CFD) threshold used to determine the time of arrival
varying with fluence, from 10% pre-radiation to 60% at the highest fluence. Key
changes to the pulse shape induced by irradiation, i.e. (i) a reduce
sensitivity of the pulse shape on the initial non-uniform charge deposition,
(ii) the shortening of the rise time and (iii) the reduced pulse height, were
compared with the WF2 simulation program and found to be in agreement.
