Precise energy calibration of pixel detector working in time-over-threshold mode

The semiconductor pixel detector Timepix (256x256 pixels with pitch of 55 μm) is a successor of the Medipix2 device. Each Timepix pixel can be independently operated in one of three possible modes: (1) counting of the detected particles; (2) measurement of the particle energy; and (3) measurement of the time of interaction. The energy measurement in the second mode is performed via the determination of the 'time-over-threshold' (TOT). The energy measurement with the Timepix detector in TOT mode requires knowledge of the energy calibration of each pixel of the matrix. Such calibration is very nonlinear in the low energy range and can be described by a surrogate function depending on four parameters. The determination of all these parameters can be performed by measurement and evaluation of the response of each pixel in at least four calibration points. The procedure is extremely demanding: it requires the analysis of at least 250 thousand spectra and the performance of 330 thousand least-squares fits. In this article, it is demonstrated that even better result can be achieved with only two or three calibration points halving the number of least-squares fits needed. The method is based on precise analysis of the shape of spectral peaks. The article also discusses the performance of energy calibrated device for spectrometry of heavy charged particles.