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This paper presents a physical description of two specific aspects in drain-extended MOS transistors, i.e., quasi-saturation and impact-ionization effects. The 2-D device simulator Medici provides the physical insights, and both the unique features are originally attributed to the Kirk effect. The transistor dc model is derived from regional analysis of carrier transport in the intrinsic MOS and the drift region. The substrate-current equations, considering extra impact-ionization factors in the drift region, are also rigorously derived. The proposed model is primarily validated by MATLAB program and exhibits excellent scalability for various transistor dimensions, drift-region doping concentration, and voltage-handling capability.