mid-gap work function

**Mid-Gap Work Function** is a **metal gate work function value positioned at the center of the silicon bandgap** — approximately 4.6 eV, equidistant from the conduction band edge (4.05 eV) and valence band edge (5.17 eV). **What Is Mid-Gap Work Function?** - **Value**: $Phi_m approx 4.5-4.7$ eV = $(E_c + E_v)/2 = 4.61$ eV for Si. - **Materials**: TiN as-deposited typically has $Phi_m approx 4.6$ eV (naturally mid-gap). - **Symmetric $V_t$**: A mid-gap gate material produces equal $|V_t|$ for NMOS and PMOS on undoped channels. **Why It Matters** - **FD-SOI**: Mid-gap work function is ideal for FD-SOI because $V_t$ is tuned by back-gate biasing rather than gate metal engineering. - **Simplification**: A single gate metal for both NMOS and PMOS reduces process complexity. - **Trade-off**: Mid-gap gives moderate $V_t$ for both device types but cannot achieve the ultra-low $V_t$ needed for high-performance. **Mid-Gap Work Function** is **the neutral gear of gate engineering** — a balanced starting point that can be adapted through biasing or further metal tuning.