Simulation Studies of CdTe Pixel Detectors C. P. Lambropoulos Member, IEEE, K. E. Karafasoulis, V. A. Gnatyuk, and S. Levytskyi Abstract–We have performed simulation studies of CdTe pixel detectors using the commercial SDEVICE simulator by SYNOPSYS. We have incorporated energy levels and concentrations of defects in the band gap using the information by published compensation models. We have performed I-V simulation experiments. We simulated the transient behavior of the detectors due to the bombardment with alpha particles and X-ray photons. The simulation of the interaction with alpha particles required the description of the dependency on energy of the Bragg peak in CdTe, which we included in the material database file of CdTe. We investigated the relation of the charge collected at neighbor pixels with the depth of interaction of X ray quanta. The study has the following purposes: (a) To provide realistic current waveforms as input to electronics simulations needed for the development of pixel readout electronics. (b) To evaluate methods for the extraction of the depth of interaction. (c) To incorporate to this device simulator as much detailed information as possible about the material, about the electrodes and about the defects that degrade its performance and explore through numerical simulation their effect on charge collection. I. INTRODUCTION HE detailed and accurate modeling of CdTe detectors is a demanding task due to the lack of consistent information about various material parameters, as well as the fact that the compensation mechanism details have not been clarified yet. In this study we used the commercial device simulator SDEVICE[1] by SYNOPSYS. The equations which we solved were: The Poisson equation TRAP A D N N n p q ρ ϕ ε - - + - - = ∇ ⋅ ∇ ) ( coupled with the electron continuity equation ( ) ) ( t n R q nq net n n ∂ ∂ + = Φ ∇ - ⋅ ∇ μ and with the hole continuity equation Manuscript received November 4, 2008. This work was supported in part by a Greek-Ukrainian Bilateral Collaboration and by the ESA Project "CDTE Crystallization and Related Compounds" under the contract no. 14240 CCN02. K.E. Karafasoulis was with the Electronics Sensors and Communications Laboratory, Technological Educational Institute of Chalkida, Psahna-Evia, 34400 Greece. He is now with the Greek Atomic Energy Commission P.O. Box 60092, Agia Paraskevi, Attiki 15310 Greece (e-mail: ckaraf@gmail.com). C. P. Lambropoulos is with the Electronics, Sensors and Communications Laboratory and the Aircraft Technology Department, Technological Educational Institute of Chalkida, Psahna-Evia, 34400 Greece (e-mail: lambrop@teihal.gr). V. A. Gnatyuk is with the Shizuoka University, Research Institute of Electronics, 3-5-1 Johoku, Hamamatsu, Shizuoka 4328011 Japan, on leave from the National Academy of Sciences of Ukraine, VE Lashkaryov Institute of Semiconductor Physics, Kiev, UA-03028 Ukraine (e-mail: gnatyuk@ua.fm). S. Levytskyi is with the National Academy of Sciences of Ukraine, VE Lashkaryov Institute of Semiconductor Physics, Kiev, UA-03028 Ukraine (e- mail:levytskyi@ua.fm). ( ) ) ( t p R q pq net p p ∂ ∂ + = Φ ∇ - ⋅ ∇ μ Where φ is the electrostatic potential computed as the difference from a reference potential which is the Fermi potential of the intrinsic material, Φ n and Φ p are the quasi- Fermi potentials for electrons and holes respectively, R net is the net electron – hole recombination rate, N D and N A are the ionized donor and acceptor concentrations, ρ TRAP is the charge density contributed by traps and fixed charges. The values of the main parameters used are collected in Table 1: TABLE I MATERIAL PARAMETERS Parameter Value ε r relative permittivity of CdTe 10.6 Bandgap (@300 o K) 1.52 Electron effective mass 0.096 Hole effective mass 0.43 Electron affinity 4.28eV Electron mobility (@300 o K) 1000cm 2 /V·s Hole mobility (@300 o K) 80cm 2 /V·s The first objective of our study was to create a model for the material consistent with well established experimental results. This would make us confident about the results of the charge transport simulations, which was our second objective. The information contained in the materials database of the simulator is elementary. The material is described as a pure homogeneous crystal without any defects, while some parameters have default values, which are wrong, because they are borrowed from Silicon. One example is the Brag peak position used in the generation term of the continuity equations when the charge deposition from an alpha particle is simulated. We used the SRIM package [2] to simulate the spectra of the energy deposited by alpha particles with different energies impinging on CdTe. Then we extracted the parameters of the fit of a second order polynomial which relates the position of the Brag peak to the energy of the alpha particle and used it in the generation term (see [1] pp 431- 432): ( ) ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - ⋅ - + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + - ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - ⋅ ⋅ = 2 2 1 2 1 2 2 2 2 2 2 1 2 1 exp ) ( 2 1 exp ) 2 ( ) , , , ( a a u c e c w w v s t t s k t w v u G au t m π if 3 1 a a u + ≤ , else 0 ) , , , ( = t w v u G Where u is the coordinate along the alpha particle path, v and w are the coordinates orthogonal to u, α 1 is the position of the Brag peak obtained from the relation: 2 2 1 0 1 E b E b b a + + = . The scaling factor k is obtained from the constraint that the integral of the generation term over space and time is equal to T