  Pixelated silicon detectors are state-of-the-art technology to achieve
precise tracking and vertexing at collider experiments, designed to accurately
measure the hit position of incoming particles in high rate and radiation
environments. The detector requirements become extremely demanding for
operation at the High-Luminosity LHC, where up to 200 interactions will overlap
in the same bunch crossing on top of the process of interest. Additionally,
fluences up to 2.3 10^16 cm^-2 1 MeV neutron equivalent at 3.0 cm distance from
the beam are expected for an integrated luminosity of 3000 fb^-1. In the last
decades, the pixel pitch has constantly been reduced to cope with the
experiment's needs of achieving higher position resolution and maintaining low
pixel occupancy per channel. The spatial resolution improves with a decreased
pixel size but it degrades with radiation damage. Therefore, prototype sensor
modules for the upgrade of the experiments at the HL-LHC need to be tested
after being irradiated. This paper describes position resolution measurements
on planar prototype sensors with 100x25 um^2 pixels for the CMS Phase-2
Upgrade. It reviews the dependence of the position resolution on the relative
inclination angle between the incoming particle trajectory and the sensor, the
charge threshold applied by the readout chip, and the bias voltage. A precision
setup with three parallel planes of sensors has been used to investigate the
performance of sensors irradiated to fluences up to F_eq = 3.6 10^15 cm-2. The
measurements were performed with a 5 GeV electron beam. A spatial resolution of
3.2 +\- 0.1 um is found for non-irradiated sensors, at the optimal angle for
charge sharing. The resolution is 5.0 +/- 0.2 um for a proton-irradiated sensor
at F_eq = 2.1 10^15 cm-2 and a neutron-irradiated sensor at F_eq = 3.6 10^15
cm^-2.
