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We present a physics-based model for ferroelectric/negative capacitance transistors (FEFETs/ NCFETs) without an inter-layer metal between ferroelectric and dielectric in the gate stack. The model self-consistently solves 2D Poisson's equation, non-equilibrium Green's function (NEGF) based charge and transport equations, and multi-domain Landau Khalatnikov (LK) equations with the domain interaction term. The proposed simulation framework captures the variation of ferroelectric (FE) polarization (P) along the gate length due to non-uniform electric field (E) along the channel. To calibrate the LK equations, we fabricate and characterize 10nm HZO films. Based on the calibrated model, we analyze the gate/drain voltage dependence of P distribution in the FE and its effect on the channel potential and current-voltage characteristics. Our results highlight the importance of larger domain interaction to boost the benefits of FEFETs with subthreshold swing (SS) as small as ~50mV/decade achieved at room temperature. As domain interaction increases, the characteristics of FEFETs without inter-layer metal (SS, negative drain induced barrier lowering (DIBL), negative output conductance) approach those of FEFETs with inter-layer metal.