Photon counting detectors (PCD) are promising as next generation detectors for spectral imaging applications. Sensors based on cadmium telluride (CdTe) and silicon (Si) are already in experimental use and sensors based on gallium arsenide (GaAs) , a promising material for PCDs are being researched[1]. These materials suffer from different undesirable phenomena such as escape of Compton scatter, fluorescence escape and charge sharing.These events can result in multi-counting of a single incident photon in neighbor pixels. Accurately modeling these effects can be crucial for detector design and for model based correction. In this paper, we derive an accurate model for multi-counting events and correlations to compare the expected performance of CdTe, GaAs and Si. Detectors based on these materials differ in their structure in their practical use. CdTe is used face-on and is on the order of 3mm in thickness. We simulate the correlations in a 3*3 pixel grid, with each pixel being 500*500 μm². GaAs and Si need to be much thicker and are oriented edge-on in our simulation. We use a 6cm deep structure for Si and 1 cm for GaAs, again with each pixel being 500*500 μm². Mean and covariance matrices are deduced using spatio-energy functions estimated from Monte Carlo simulation and a material-specific, energy-independent spherical charge cloud model (give the radii for the three materials). Then we use the Cramer-Rao lower bound (CRLB) to estimate the variance of the estimated basis material thicknesses for the three detectors.