Charge Losses in Silicon Sensors and Electric-Field Studies at the Si-SiO$_2$ Interface

Electric fields and charge losses in silicon sensors before and after irradiation with x-rays, protons, neutrons or mixed irradiation are studied in charge-collection measurements. Electron-hole pairs ($eh$ pairs) are generated at different positions in the sensor using sub-ns pulsed laser light of different wavelengths. Light of 1063 nm, 830 nm and 660 nm wavelength is used to generate $eh$ pairs along the whole sensor depth, a few $\mu$m below the surface and very close to the surface, respectively. Segmented p$^+$n silicon strip sensors are used to study the electric field below the SiO$_2$ separating the strip implants. The sensors are investigated before and after irradiation with 12 keV x-rays to a dose of 1 MGy. It is found that the electric field close to the Si-SiO$_2$ interface depends on both the irradiation dose and the biasing history. For the non-irradiated sensors the observed dependence of the electric field on biasing history and humidity is qualitatively as expected from simulations of the electrostatic potential for different boundary conditions at the surface. Depending on the biasing history incomplete collection of electrons, full charge collection or incomplete collection of holes is observed. After the bias voltage is changed, the amount of observed charge losses is time dependent with time constants being a function of humidity. For the irradiated sensors an increased effective oxide charge density and more electron losses are observed compared to the non-irradiated sensors. Due to positive oxide charges which are always present at the Si-SiO$_2$ interface an electron-accumulation layer forms, if the oxide charge is not compensated by charges on top of the passivation. If negative charges overcompensate the oxide charge, a hole-accumulation layer forms. In both cases the number of accumulated charges can be temporarily increased by incomplete charge collection of either electrons or holes. How many additional charge carriers can be added to the accumulation layer and when the accumulation layer returns to steady state is investigated. Irradiated silicon pad sensors are used to study the charge-collection efficiency (CCE) of charge carriers generated using laser light of 1063 nm wavelength, as a function of bulk material, active sensor thickness, voltage, temperature, particle type (for the irradiation) and fluence. As a cross check the CCE is also determined for charge carriers generated by electrons from a $^{90}$Sr-source. A precision of 3 \% in the CCE is achieved. Sensors of n-doped and p-doped silicon are compared, as well as sensors of different crystal-growing methods (magnetic Czochralski (MCz) and float zone (FZ)). The sensor thickness varies from 200 $\mu$m (MCz and FZ) to 320 $\mu$m (FZ). The 320 $\mu$m thick FZ sensors underwent a dopant-diffusion process (dd-FZ) to reduce the active sensor thickness. For the irradiation both protons of different energies (23 MeV and 23 GeV) and reactor neutrons ($\sim$1 MeV) are used. The achieved fluences are between $3\cdot10^{14}$ cm$^{-2}$ and $1.3\cdot10^{16}$ cm$^{-2}$ 1 MeV-neutron equivalent. The CCE is used to calculate the signal corresponding to a minimum-ionising particle (mip) traversing the sensor and to calculate the effective distance the generated charge carriers drift. While little difference in CCE between the 200 $\mu$m thick MCz and FZ materials is found, the dd-FZ materials of both $\sim$200 $\mu$m and $\sim$300 $\mu$m active thickness have a lower CCE, corresponding also to a shorter effective drift distance. The CCE and the effective drift distance are also calculated for $eh$ pairs generated close to the sensor surface using laser light of 660 nm wavelength. The measurements are not compatible with a position-independent trapping probability, and qualitative agreement with a position-dependent occupation of radiation-induced trapping centres due to the dark current is found.