Analytical approach for 3D detectors engineering

Different constructions of silicon 3D detectors are analyzed and tabulated using possible combinations of two simple elements: the p-n junction and the ohmic columns. A simplified model of the operation of cylindrical p-n junctions in 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 the bias, and a semi-spherical “dead” tip with a maximal electric field due to the focusing effect. Consideration of these fragments allows a description of the detector operation with two main parameters: the pinch-off voltage and the maximal operational voltage; these parameters may be evaluated analytically using the information about the detector material and the detector geometry. This approach makes it possible to extrapolate these critical parameters to 3D detector operation in the upgraded LHC.