Leakage Current

Radiation damage also causes an increase in the detector current $I$, which is strictly proportional to the equivalent fluence $\Phi_{\rm eq}$ and the sensitive volume $V$,

$$\Delta I=\alpha\,\Phi_{\rm eq}\,V\quad,$$ (2.26)

where $\alpha$ is the current related damage rate, which is independent on material type and resistivity. The leakage current in silicon detectors is strongly temperature dependent according to

$$I \propto T^2\,e^{-\frac{E_g}{2kT}}\quad,$$ (2.27)

where $T$ is the operating temperature, $E_g$ the band gap and $k$ the Boltzmann constant. According to eq. , there is a factor of approximately 15 between the leakage currents at room temperature and at $-10^{\circ}\,\rm C$. Thus, also the proportional factor $\alpha$ as given in eq.  shows the same temperature dependence. At room temperature, values between $4$ and $10\cdot 10^{-17}\,\rm A/cm$ are stated for the current related damage rate, depending on the measurement method.

After irradiation, the increased current is still changing. There is a beneficial short-term effect called ``annealing'' with a time constant of a few days at room temperature. Unfortunately, it is followed by a deterioration effect called ``reverse annealing'' in the long run (about one year at room temperature). Both effects are strongly temperature dependent. At room temperature, the annealing first causes the leakage current to decrease, while later it rises due to reverse annealing process until it finally saturates at a value which is significantly above the initial level. At $-10^{\circ}\,\rm C$ however, both effects are virtually frozen, so the detector current remains constant. Thus, irradiated detectors in general should be operated and stored at low temperature, while it is favorable to shortly expose them to room temperature (for handling, service, transportation etc.) to take advantage of the beneficial annealing.