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A fully three-dimensional model of a semiconductor gamma-ray detector is presented. The model takes into account the gamma-ray and charge collection physical phenomena involved in the detection process and models the readout electronic response and noise. The model successively involves the Monte Carlo simulation of the photon transport, the finite element transient computation of the adjoint transport equation, and the electronic signal processing including an accurate noise model. The simulation is possible because the solution of the adjoint equation allows us to obtain a continuous mapping of the induced charge collection efficiency (at any time and any interaction point) with a single 3D transient finite element computation. The simulation outputs are pulse height spectra and biparametric (rise time versus pulse height) spectra. The model has been validated on two applications. The first application is a CdZnTe monolithic pixelated detector at medical energies. The detector dimension is 10x10x5 mm, with a pixel size of 2x2 mm, and a 2.5 mm pitch. The second application is a gamma-ray spectrometric single-channel probe for 200 keV to 2 MeV photons combining a small anode and the capacitive Frisch grid structure. The detector dimension is 10x10x9 mm. Simulated and experimental results are compared. In both cases, the comparison between simulated and experimental spectra is qualitatively good for pulse height spectra as well as biparametric spectra.