M.Sc Thesis | |

M.Sc Student | Dolgin Madlena |
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Subject | Statistical, Electrostatic and Numerical Models of Spectral Performance of 2D-Arrays of Gamma-Ray Spectrometers |

Department | Department of Electrical and Computer Engineering |

Supervisor | PROFESSOR EMERITUS Yael Nemirovsky |

The spectrometers for gamma-ray and X-ray photons made of semiinsulating semiconductors are of the great interest due to their high spatial and energy resolution.

In our study the electrostatic, statistical and numerical models for spectral performance of two-dimensional (2D) array of gamma ray spectrometers are developed. The modeling is done by the following steps:

· Calculation of the three dimensional (3D) field in the device.

· Calculation of the charge induced on the anodes.

· Derivation of the charge transport expression.

· Derivation of expression for the probability density of random point of absorption.

· Statistical modeling of the measured signal, namely derivation of expression for pulse height spectrum.

Hence, in the first part of this research the 3D non-uniform field in the device, determined by the geometrical design of the device is calculated using three methods: numerical Finite Elements Method (FEM) using the commercial 3D software, semianalytic Moments (MM) and Fourier Series Expansion (FSE) methods implemented in Matlab. The efficient and the fast method (FSE), which exploits the device periodicity is chosen for future modeling of the device. In the second part, the charge induced on the anodes is calculated by the two semianalytical methods mentioned above. The deviation of the solutions derived by the different methods is less than 2% and point at their convergence to the exact one. However, the comparison of these solutions with approximation presented in previous studies reveals 7% average deviation.

The analytical charge transport expression is derived considering the phenomenon of multiple trapping-detrapping of the carriers in semiinsulating semiconductors. Finally, the pulse height spectrum is modeled statistically considering a random point of absorption and a random drift length for each carrier. The pulse height spectrum is calculated as a function of the geometrical design, photon energy, electron and hole mobility, mean trapping and mean detrapping times and the applied voltage as well as the shaping time.

The model developed in our research enables optimization of the geometrical design of the 2D array of anodes according to the electrical properties of a given semiconductor material, in order to improve spectral performance.