  The ATLAS Inner Tracker (ITk) upgrade for the High-Luminosity LHC (HL-LHC)
requires a radiation-tolerant pixel readout chip, which must withstand a total
ionising dose (TID) of up to 1 Grad. The readout ASIC for the ITk upgrade has
been designed by the RD53 collaboration using 65 nm CMOS technology. In order
to characterise the radiation tolerance of the chip digital logic, the RD53
ASICs include ring oscillators, which can be used to measure gate delay
degradation. Extensive X-ray irradiation studies of the ring oscillators have
been performed on the ITk Pixel pre-production readout ASIC, ITkPixV1. A
dependence of radiation damage on dose rate has been observed in 65 nm CMOS
technology. This paper aims to quantify the dose rate dependence of TID damage
to the ITkPix ring oscillators and, therefore, the ITkPix ASIC digital logic.
X-ray irradiations at different dose rates between 20 krad/h and 30 Mrad/h are
compared. A dose rate dependence is observed, with 2-3 times more damage at the
lowest dose rate of 20 krad/h, compared to 4 Mrad/h. The dose rate dependence
was also observed to be dependent on transistor size and type.
