MOSFET VDS = VGS - VTN: Understanding Zero Inversion Charge & Conductance

When VDS (drain-source voltage) equals VGS (gate-source voltage) minus VTN (threshold voltage), i.e., VDS = VGS - VTN, the MOSFET operates at its threshold voltage, representing an edge case scenario. This condition has two significant implications:

1. Zero Inversion Charge Density at the Drain: This means no charge accumulation at the drain terminal, resulting in zero drain current flow. The MOSFET enters the cut-off region, with no conductive channel formed.

2. Zero Incremental Conductance: The MOSFET's conductance remains constant, implying that the drain current doesn't change with variations in the drain voltage.

In essence, when VDS = VGS - VTN, the MOSFET is on the verge of turning on but remains off, with no drain current and insensitivity to drain voltage changes.