Footprint and lateral gate length are fixed at 20 nm. Only the recess depth changes. Watch the channel path, the HZO grain count and how far apart the "0" and "1" threshold distributions sit.
Model: L_eff = L_g + 2·max(0, d − x_j) with x_j = 5 nm. Grains N = L_eff·W/g² (W = 30 nm, g = 10 nm). σ(V_t) = 0.9 V/√N. DIBL = 600·exp(−L_eff/16 nm) mV/V. Memory window 1.8 V, V_R = 1.2 V. Margin = MW − 6σ − DIBL·0.5 V. These are scaling laws for intuition, not calibrated TCAD. Corner field crowding, sidewall interface traps and orientation-dependent HZO texture are not included.