A modeling tool for detector resolution and incomplete charge collection † Jorge E. Fernández, Viviana Scot and Lorenzo Sabbatucci* The detector response function of X-ray and gamma-ray detectors is obtained from the convolution of the energy deposition spec- trum with the detector resolution function. The energy deposition spectrum can be computed by using deterministic or Monte Carlo codes, while the energy resolution depends specifically on the detection mechanism, which is characteristic of the single de- tector. In a first approximation, the energy resolution can be modeled using a normalized Gaussian distribution having its full width at half maximum expressed in terms of specific semiempirical formulas for solid-state detectors, scintillators, and gas pro- portional counters. However, this approach is not sufficient with some solid-state detectors. It is frequent to find that the peaks show a deviation from the Gaussian shape: a long flat shelf structure from the peak centroid to the lower energies and an asym- metry that can be described with an exponential decay on the left side of the peak. These two effects have been introduced in the new tool RESOLUTION by adapting empirical models found in literature. RESOLUTION can be tailored to the specific detector by analyzing measured monochromatic peaks by means of the following strategies: (1) in a first approximation, a Gaussian shape is assumed in order to determine the full width at half maximum parameters, (2) if it is noted a flat background on the left side of the peak, then a shelf function is added, and (3) if a departure of the Gaussian is observed, then an exponential tail function is added. RESOLUTION gives a very precise description of the line shape. Copyright © 2015 John Wiley & Sons, Ltd. Introduction A detailed description of the detector response function (DRF) is of fundamental importance to understand properly the meaning of the measured spectra. The DRF can be computed from the convo- lution of the energy deposition spectrum, which depends on the physical properties of the detector (such as composition, thickness, and geometry), with the detector resolution function. While the en- ergy deposition spectrum is frequently computed by means of de- terministic and Monte Carlo codes, the energy resolution and the other artifacts proper of the detection system are usually not or only partially considered. The post processing code RESOLUTION [1] was developed to model the detector resolution function, which is necessary to obtain the DRF. This paper presents an upgraded version of the model introduced by Fernández and Scot, [1] which is now capable to take into account the shelf structure and the ex- ponential tail that, for solid-state detectors (SSD), are superimposed to the Gaussian peak in the low-energy side. In a first approximation, the energy resolution is computed by using a normalized Gaussian distribution whose full width at half maximum (FWHM) depends on few empirical parameters, which are different for each type of detector: semiconductors detectors (SSD), scintillators, and gas proportional counters. It is worth noting that in the case of SSD, the peaks show a deviation from the Gaussian shape, with the presence of a long flat shelf structure from the peak centroid to the lower energies, and an asymmetry in the left side of the Gaussian that can be described with an exponential decay. Some authors [2,3] attribute these artifacts to incomplete charge collection (like carrier trapping and charge escape). Other authors show that the interactions between the metal contact and the detector material produce a low-energy shelf structure, with defined steps. [4] Papp [5] points out the effect of the signal processing electronics on the evo- lution of the electronic signal and, from the details of the electron transport processes, proposes an approximate analytical function to describe the detector response. The line shape can be modeled with analytical [6] or semiempirical formulas. [2,3,7] Between them, the so- called HYPERMET [2] function represents a general semiempirical model, which was initially proposed for describing the line shape of a Ge detector. Campbell et al. [3] tested the HYPERMET function also in the case of Si(Li) detectors with satisfactory results. Usually, the HYPERMET function is fitted to a given measured spectrum. An alternative approach is at the basis of the RESOLUTION tool: it is developed to add the energy resolution to a simulated energy- deposition distribution, by allowing the direct comparison with an experimental spectrum. The tool RESOLUTION includes now the de- scription of the deviation from the Gaussian shape in the full energy peaks by using an adaptation of the HYPERMET model. The characteristic of the model and the main features of the code are illustrated with examples for pure (Ge) and composite detectors (CdTe), which show an excellent agreement with the measurement. Theoretical model Energy resolution Mathematically, the measured spectrum I m (E) can be expressed as a convolution: [1,8] I m E ðÞ¼ ∫ RE′; E ð Þ ϕ E′ ð Þ IE′ ð Þ dE′ (1) * Correspondence to: Lorenzo Sabbatucci, Laboratory of Montecuccolino, Department of Industrial Engineering (DIN), Alma Mater Studiorum University of Bologna, via dei Colli, 16, Bologna I-40136, Italy. E-mail: lorenzo.sabbatucci2@ unibo.it † Presented at the European Conference on X-Ray Spectrometry, Bologna, Italy, 15-20 June 2014 Laboratory of Montecuccolino, Department of Industrial Engineering (DIN), Alma Mater Studiorum University of Bologna, via dei Colli, 16, Bologna I-40136, Italy X-Ray Spectrom. 2015, 44, 177–182 Copyright © 2015 John Wiley & Sons, Ltd. Research article Received: 30 September 2014 Revised: 19 January 2015 Accepted: 19 January 2015 Published online in Wiley Online Library: 4 March 2015 (wileyonlinelibrary.com) DOI 10.1002/xrs.2597 177