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To use double-gate (DG) MOSFET for mixed-signal circuit applications, especially for circuits in which the two gates are independently driven, such as in the case of dynamic-threshold and fixed-potential-plane operations, physical compact models that are valid for all modes of operations are necessary for accurate design and analysis. Employing physically rigorous current-voltage (I-V) relationship in subthreshold and above-threshold regions as asymptotic cases, we have constructed a model that joins the two operating regions by using carrier-screening functions. We have included consistently source/drain series resistance, low drain-field mobility, and small-geometry effects of drain-induced barrier lowering (DIBL), MOS interface mobility, velocity saturation and channel-length modulation (CLM) with validation from two-dimensional (2-D) distributed simulation. All model parameters can be extracted from large-signal I-V characteristics in dc conditions with given geometrical data. Parameter extraction methods and verification from simulation are presented in Part II.