Potential-Induced Degradation (PID) is a leakage-driven power loss seen in grid-tied c-Si modules. When the array's negative terminal is far below ground (common with transformerless inverters), sodium ions from the soda-lime cover glass drift under the field through the EVA/glass interface toward the grounded aluminum frame — or, for a negatively biased array, migrate from glass into the cell's anti-reflective coating near the frame edge, forming a shunting path that polarizes the cell surface.
The ion front follows a drift-diffusion law from a fixed-concentration boundary at the frame edge, whose classic solution is the complementary error function:
C(d,t) = C0 · erfc( d / (2·√(D·t)) )
D(T) = D0 · exp(−Ea / (kB·T)) [Arrhenius]
D_eff = D(T) · (|V|/Vref) · (RH/100)^1.5
Here d is distance from the frame edge, t is elapsed stress time, D(T) is the Arrhenius ion diffusivity (Ea ≈ 0.8 eV, matching reported PID activation energies), and the effective rate is boosted by system voltage (drift field strength) and humidity (surface ionic conduction on the glass, per IEC 62804's damp-heat/bias protocol).
- Voltage bias — sets the electric field pulling Na⁺ toward the cells; more negative accelerates the front.
- Temperature — enters through the Arrhenius factor; every +10 °C roughly doubles the diffusivity here.
- Humidity — raises glass-surface conductivity, supplying more mobile ions.
- Cells nearest the grounded frame have the shortest leakage path and degrade first, exactly as PID appears in the field — edge rows go first, the center lags behind.
Consequences modeled: local shunt resistance collapses, module power output drops, and array leakage current (through the encapsulant to the frame) rises — the same three symptoms field technicians measure with a Suns-VOC/EL scan and an insulation-resistance meter.