Optimization of planar pixel detector

T. Habermann Planar pixel detectors L W H ground U

T. Habermann Distortion effects a)Surface leakage current (10 – 20 pA) E.L. Hull, R.H.Pell, …NIMA 364(1995) b) Effects of the enclosure

T. Habermann poissons equation for the potential : electric field : boundary conditions : Electric field calculation in germanium

T. Habermann applied potential : U = V 20mm 80mm d Detector geometry 2-dimensional pixel (φ = U) ground (φ = 0) pixel width : d = mm

T. Habermann Electric field calculation 2-dimensional 2-dimensional poisson equation : x y H L

T. Habermann Finite-Volume-Method The region is divided into N rectangular controlvolumes (CV). The potential is approximated in the center of this CV’s → For every CV we get an equation of the form : a P Φ P - a w Φ W - a N Φ N - a E Φ E - a S Φ S = b P → linear system of equations with N variables : AΦ=b 2-d grid 3-d grid (“Computational Methods for Fluid Dynamics”, J.H.Ferziger,M.Peric)

T. Habermann Potential in germanium 12x12 grid points U 0 = 3000V H = 0.02 m L = 0.02 m

T. Habermann Potential in germanium 50x50 grid points U 0 = 3000V H = 0.02 m L = 0.02 m 2 pixel width : m distance to the edge : m

T. Habermann Convergency Flux in y-direction at the top surface vs number of grid points in x-direction (= number of grid points in y-direction) relative error vs # of grid points in x-direction

T. Habermann outlook further examination of convergency behaviour (→ adjustment of the numerical method for better convergency) 3d model examination of the electric field and reconstruction of the expected effects : distortion caused by the enclosure distortion caused by surface leakage current How do the free parameters influence these effects ? (distance between pixels, pixelsize, size of the capsule,...) GOAL : Minimize the electric field distortion by choosing the right parameter values

T. Habermann Model of the coupled system Contact conditions : Parameters : distance from the left chamber wall L V = [ ] mm contact surface charge density ρ S = [ ] μC/m^3 pixel size L P = [ ] mm applied voltage U = [ ] V (→648 different parameter sets)

T. Habermann Finite volumes for the coupled system

T. Habermann Results : Field distortion caused by surface charge density

T. Habermann Results : depth of affected region in dependence of surface charge density pixelsize= 16mm L1 = 15mm

T. Habermann Results : different pixel sizes L P = 2mm L P = 10mm

T. Habermann Results : depth of affected region in dependence of pixel size

T. Habermann Results : depth of affected region in dependence of applied voltage

T. Habermann Results : depletion voltage electric field propagation for small (2mm) pixelsize and 3000V applied voltage :

T. Habermann Results : depletion voltage in dependence of pixel size pixel size = 20mm → planar detector according to Glenn Knoll V d = 2177,22 V simulated V d =2176,32 V

T. Habermann Results : depletion voltage in dependence crystal thickness

T. Habermann outlook investigation of the electric field strength inside the germanium in dependence of pixel size,... investigation of the electric field in dependence of the crystal thickness 3d model another solver could be used to decrease memory usage and calculation time (essential for 3d calculations)...