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Recent studies show disordered materials such as amorphous silicon (a-Si), in spite of their low mobility, can efficiently amplify photocurrent via carrier multiplication process. Detectors with a thin (~40nm) a-Si multiplication layer has demonstrated single photon sensitivity at high speed under room temperature. It is believed that the abundance of bandtail states that cause low mobility of the amorphous materials actually contribute to the detector’s superior performance because carrier impact ionization involving these states, which can be modeled by donor-acceptor pairs (DAPs), relax the k-selection rule of the many-body carrier multiplication process. Our paper presents a theoretical framework to calculate the carrier multiplication process in a-Si or other disordered materials involving DAPs. Our analysis also establishes the relations between detector characteristics and key parameters such as the density of band tail states, layer thickness, and applied electric field. DAP assisted carrier multiplication rate is computed first. Carrier multiplication coefficients for electrons and holes under given applied field are then calculated using a trial distribution function that satisfies both the continuity equation and the energy balance equation. Our analysis shows that thinner a-Si gives rise to higher multiplication efficiency than thicker a-Si because of its higher carrier kinetic energy when the layer thickness is shorter than the length of energy relaxation by phonon scattering. Using the calculated carrier multiplication coefficients, voltage dependent gain of the device is computed and the results agree well with the measured results of a-Si cycling excitation process (CEP) detectors. [ABSTRACT FROM AUTHOR]