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            <title xml:lang="en">A measurement of Lorentz angle and spatial resolution of radiation hard silicon pixel sensors</title>
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              <p>Silicon pixel sensors developed by the ATLAS collaboration to meet LHC requirements and to withstand hadronic irradiation to fluences of up to $10^{15} n_eq/cm^{2}$ have been evaluated using a test beam facility at CERN providing a magnetic field. The Lorentz angle was measured and found to alter from 9.0 deg. before irradiation, when the detectors operated at 150 V bias at B=1.48 T, to 3.1 deg after irradiation and operating at 600 V bias at 1.01 T. In addition to the effect due to magnetic field variation, this change is explained by the variation of the electric field inside the detectors arising from the different bias conditions. The depletion depths of irradiated sensors at various bias voltages were also measured. At 600 V bias 280 micron thick sensors depleted to ~200 micron after irradiation at the design fluence of 1 10^{15} 1 MeV n_eq/cm2 and were almost fully depleted at a fluence of 0.5 * 10^{15} 1 MeV n_eq/cm2. The spatial resolution was measured for angles of incidence between 0 deg and 30 deg. The optimal value was found to be better than 5.3 micron before irradiation and 7.4 micron after irradiation.</p>
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