Analytical model for 3D detectors parameterization

A simplified model of operation of the cylindrical p–n junctions in silicon 3D detectors is proposed. To do this, two distinct fragments are recognized in the p–n junction column: a cylindrical space charge region whose radius increases with bias and a semispherical “dead” tip with a maximal electric field due to the focusing effect. For description of the detector operation, three main parameters, namely the pinch-off voltage, the full-depletion voltage and the maximal operational voltage, are introduced and evaluated analytically using the detector material properties and geometry. This approach makes it possible to extrapolate these critical parameters to 3D detector operation in the upgraded LHC. By using possible combinations of two simple elements, the p–n junction and the ohmic column, the different configurations of 3D detectors are analyzed and tabulated.