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A staircase approximation method is deployed to model nonuniform field in the multiplication region and its surrounding ambient of a thin avalanche photodiode (APD). To the best of our knowledge, this is the first instance of introducing an equivalent circuit model that is taking the effect of the electric field profile in a thin APD's multiplication region and its surroundings into account. This equivalent circuit model that is developed from the carriers' rate equations also includes the effect of the tunneling current. The tunneling current that can be induced as a small current injected into the multiplication region results in an enhanced model behavior at high reverse bias voltages near breakdown. The output current obtained from the proposed model is compared with available experimental data. This comparison reveals excellent model accuracy, in regard to the current levels and prediction of breakdown voltages for both photo and dark currents. Moreover, simulations demonstrate ability of the present model for gain-bandwidth analysis.