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We performed Monte-Carlo simulations of X-ray interactions and charge transport within a photon counting cadmium zinc telluride (CZT) detector. We study various physical processes affecting the width and shape of detected pulses and find that the energy resolution depends on the pulse width variance. One impact factor (and main topic of this work) is the temporal splitting of pulses due to the simultaneous creation of two or more charge clouds by K-fluorescence within the same pixel. Measured energies are underestimated if the timing constants of detector and electronics are below or in the order of the arrival time differences of the charge clouds. Pulse temporal splitting is of minor relevance if other effects like charge sharing or polarization by hole trapping are present which cause a stronger degradation of the pulse height spectrum.