Layout of the LHCb detector: vertex locator (VELO), Ring-Image Cherenkov counters (RICH1 and RICH2), tracking stations upstream (TT) and downstream (T1-T3) of the spectrometer dipole magnet, scintillating pad detector used for trigger purposes (SPD), pre-shower detector (PS) and electromagnetic calorimeter (ECAL), hadronic calorimeter (HCAL), and muon stations (M1-M5). LHCb uses a right-handed cartesian coordinate system with its origin at the nominal interaction point, the $z$-axis pointing along the LHC beam axis and the $y$ axis pointing upwards.

Layout of the TT, with the LHC beam pipe passing through an opening in the centre of the detection layers. The four detection layers are labelled TTaX, TTaU, TTbV and TTbX. The four different types of read-out sectors employed in each of the detection layers are indicated by different shading: read-out sectors close to the beam pipe consist of a single silicon sensor, other read-out sectors consist of two, three or four silicon sensors that are connected together in series.

Left: evolution of the integrated luminosity for $pp$ collisions in each year of LHC operation. Right: expected 1- $\mathrm{ Me V}$ neutron equivalent fluence per proton-proton collision, with the TTaU detector layer overlaid. These results were obtained from a Fluka simulation of the LHCb detector, assuming a proton-proton collision energy of 14 TeV.

Evolution of the leakage current for the different HV channels connected to one-sensor read-out sectors in TT as a function of (a) the delivered integrated luminosity measured and (b) time. The red curves show channels in the detector layer TTaU, the blue one in TTbV. The predicted evolution is shown in black while the grey band shows its uncertainty, computed from the uncertainty on the model parameters, on the Fluka simulation and on the temperature measurements. The uncertainty does not account for the range of fluence expected across the sectors shown.

Signal height distribution for hits associated to tracks in the TT for two different bias voltage values. The fitted distribution is described in the text.

Pulse shapes recorded in the TT for two different bias voltage values. The fitted function is shown in Eq. (6).

Integrated charge as a function of the applied bias voltage for a central TT read-out sector measured in the CCE scans from (a) April 2012 and (b) September 2017. The decrease of $V_\text{depl}$ is clearly visible.

Distributions for all analysed read-out sectors of (a) the ratio $r$ defined in Eq.7; (b) the relative difference between $V_\text{depl}$ and $V_\text{depl}^\text{2011-07-04}$ as discussed in the main text; (c) the differences in $V_\text{depl}$ obtained from a fifth-order spline and from a linear interpolation. The solid black line in (a) highlights the value of the average $\overline{r}$.

Measured effective depletion voltage (red points) in the area of two TT sensors: one just above the beam pipe (a) and one further away (b), whose positions are indicated in Figure 11(a). The black point and error bars correspond to the CCE scan used to calibrate the ratio $r$. The statistical contribution to the total uncertainty is indicated by the solid error bars. The predicted evolution of the depletion voltage, based on the initial depletion voltage measured after sensor production, the running conditions and the Hamburg model, is shown as a solid black line. The grey bands show the uncertainty on the predicted evolution of $V_\text{depl}$, while the black dashed lines account for the $\pm 2.5$ V uncertainty on the measurement of the initial depletion voltage $V^0_\text{depl}$ in $C-V$ scans.

Measured evolution of $V_\text{depl}$ as a function of the 1-MeV neutron equivalent fluence obtained from the running conditions and Fluka for a TT sector in the area close to the beam pipe (a) and for all of the read-out sectors in the TT (b). The innermost sectors are subdivided in regions separating tracks traversing the detector at a distance larger or smaller than 75 mm from the beam axis. The error bars of the data points display the sum of the statistical and systematic uncertainty. The solid black curve shows the predictions based on the stable damage part of the Hamburg model, the grey shaded region its uncertainty due to the parameter uncertainty of the model. The initial depletion voltage $V^0_{\text{depl}}$ for the Hamburg model prediction in (b) is averaged among all sectors, and the dashed black lines show the standard deviation of the distribution of the initial $V^0_\text{depl}$ values.

Sketch highlighting the TT sectors analysed during the various CCE scans (a). The greyed out sectors were excluded due to poor statistics. The two sectors highlighted with dashes, just above the beam pipe and below the beam pipe on the left hand side, are those which evolution is shown in Figure 9(a) and Figure 9(b), respectively. Absolute change in $V_\text{depl}$ in the innermost region of TT in January 2013 and September 2018 is shown in (b) and (c) respectively. The white sector in (c) became inoperative in August 2017 due to an HV connector issue.

Animated gif made out of all figures.

Parameters for the leakage current predictions.

Summary of CCE scans dates and corresponding integrated delivered luminosity.

Parameters for the depletion voltage simulation by the Hamburg model [10].