The 3D scene presses a whole nanowire array uniformly along its polar axis. This 2D build reproduces the other historical nanogenerator mechanism instead — the original 2006 Wang & Song design — where a single conductive AFM tip rasters sideways across a row of upright ZnO nanowires, bending whichever one it currently touches like a point-loaded cantilever. The physics is genuinely independent: bending stress instead of uniform compression, one active wire at a time instead of a parallel array, and a rectifying Schottky contact instead of a resistive divider.
Cantilever, point force F at the free end (height L):
Bending moment at the base: M(0) = F · L
Outer-fiber stress: σ_max = M(0) · r / I , I = πr⁴/4
Transverse piezoelectric potential (d31 mode):
g31 = d31 / ε11
Voc = g31 · σ_max · 2r (signed — flips with bend direction)
Schottky-rectified output (ideal reverse-biased diode contact):
VL = max(0, Voc) · RL /(RL + Rs) [Ohmic contact: VL = Voc · RL /(RL+Rs), no clamp]
PL = VL² / RL
- Tip loading force — the AFM cantilever's contact force in nanonewtons; sets the bending moment and hence the peak stress and open-circuit voltage.
- Raster scan frequency — how fast the tip sweeps back and forth across the row; each full sweep bends the contacted wire once in each direction.
- External load RL — the circuit the rectified pulse train drives; deliverable power is maximised when RL is matched to the single contacted wire's internal resistance.
- Nanowire row density — spacing between wires; denser rows mean more contact events (voltage pulses) per sweep, not lower internal resistance as in the parallel-array 3D scene.
- Contact type — Schottky clips the reverse-direction half of every pulse to zero, so the sweep's two opposite-sign bends still add up to a net positive DC-like output; Ohmic passes both signs through unrectified, so a full sweep averages out to almost nothing. This is the actual mechanism that lets a real bending-mode nanogenerator deliver usable power from an alternating strain, and it is why devices are deliberately built with a rectifying contact.
Real devices output far less than this idealised d31 relation predicts — free carriers inside the semiconducting ZnO screen part of the piezopotential, exactly as noted for the 3D array's d33 relation. Numbers here are similarly an unscreened upper bound, useful for seeing the trend rather than as a literal voltmeter reading.