  Recent interest in pile-up mitigation through fast timing at the HL-LHC has
focused attention on technologies that now achieve minimum ionising particle
(MIP) time resolution of 30 picoseconds or less. The constraints of technical
maturity and radiation tolerance narrowed the options in this rapidly
developing field for the ATLAS and CMS upgrades to low gain avalanche detectors
and silicon photomultipliers. In a variety of applications where occupancies
and doses are lower, devices with pixel elements of order 1 cm$^2$,
nevertheless achieving 30 ps, would be attractive. In this paper, deep diffused
Avalanche Photo Diodes (APDs) are examined as candidate timing detectors for
HL-LHC applications. Devices with an active area of $8 \times 8$ mm$^2$ are
characterised using a pulsed infrared laser and, in some cases, high energy
particle beams.The timing performance as well as the uniformity of response are
examined. The effects of radiation damage on current, signal amplitude, noise,
and timing of the APDs are evaluated using detectors with an active area of $2
\times 2$ mm$^2$. These detectors were irradiated with neutrons up to a a 1-MeV
neutrons fluence $\Phi_{eq} = 10^{15}$ cm$^{-2}$. Their timing performance was
characterised using a pulsed infrared laser. While a time resolution of $27 \pm
1$ ps was obtained in a beam test using an $8 \times 8$ mm$^2$ sensor, the
present study only demonstrates that gain loss can be compensated by increased
detector bias up to fluences of $\Phi_{eq} = 6 \cdot 10^{13}$ cm$^{-2}$. So it
possibly falls short of the $\Phi_{eq} = 10^{14}$ cm$^{-2}$ requirement for the
CMS barrel over the lifetime of the HL-LHC.
