This paper addresses the lack of understanding of the origin of negative capacitance (NC) effect in the hafnium zirconium oxide (HZO) ferroelectric (FE) gate stack and proposes a new circuit-compatible hybrid compact model for NC field-effect transistors (NCFETs). The model supports Landau and Preisach FE models, encompassing multiple FE domains, FE leakage, and FE damping. The proposed model is experimentally validated, and the intrinsic switching speed of HZO is predicted. It is revealed that the NC effect in HZO stems from a mismatch in free charge and polarization switching rates. Performance evaluation of the model reveals that HZO-NCFET achieves ∼1.18x and ∼9.17x higher amplification at low and high frequencies compared to its PZT-NCFET counterpart. Our study demonstrates the superior ON-current (2.74 mA/µm) of the Engineered Leaky-HZO NCFET, surpassing FinFET and Germanium-source L-shaped TFET by ∼7.89x and ∼4.81x, respectively. This study briefly examines the direct causes of the negative drain-induced barrier lowering effect and negative differential resistance effect in Landau NCFETs. Furthermore, we emphasize the crucial role of FE thickness in determining the magnitude of the NC effect, offering valuable insights for the design and optimization of NC-based devices and circuits. Analysis of the Miller effect in NCFET-based inverters demonstrates significant improvements owing to high ON-current and voltage amplification, making them suitable for high-speed NCFET-based circuitry. Landau and Preisach NCFET-based inverters exhibit (50.70%, 51.34%) lower overshoots and (28.45%, 28.61%) reduced propagation delay compared to the NC nanowire FET-based inverter. Moreover, NCFET-based 2:1 fork circuits significantly reduce (46.69%, 51.37%) critical clock skew compared to CMOS FET-based circuits, showcasing the potential of NCFET technology in addressing timing violations in random logic paths. Furthermore, the Landau and Preisach NCFET-based ring oscillators (ROs) achieve (39.97%, 49.38%) and (52.65%, 62.92%) higher oscillation frequencies (fOSC) compared to state-of-the-art graphene FET-RO and CMOS-RO, respectively. The 15-stage Leaky-HZO and Engineered Leaky-HZO NCFET-ROs outperform the double gate-FET-RO by ∼2.19x and ∼16.69x in terms of fOSC, highlighting their superior performance in frequency-domain metrics. These findings demonstrate the potential of NCFET-based digital and mixed-signal circuits for high-performance integrated circuit designs.