Co-planar grid detectors utilizing single carrier sensing techniques, offer a practical solution for developing compound semiconductor gamma-ray detectors with high resolving power. We present an analytical model for describing the response of co-planar grid detector. The response of a co-planar grid detector is shown to be affected by intrinsic lateral inhomogeneity, which is inherent to its design. We evaluate the effect of both lateral and bulk inhomogeneities and show that the resolution of a co-planar grid detector is dominated by inhomogeneous broadening of the signal and not by Fano or electronic noise.