During fast charging, lithium plates unevenly onto the anode and grows needle-like dendrites through the electrolyte toward the cathode. In a liquid electrolyte nothing resists the tip mechanically, so growth speed tracks current density almost linearly and branching is chaotic — a tip that bridges the gap shorts the cell and can trigger thermal runaway.
A solid electrolyte can physically squeeze back. The Monroe–Newman stability criterion says a dendrite tip is mechanically arrested once the electrolyte's shear modulus exceeds roughly twice that of lithium metal (2 × 4.9 ≈ 9.8 GPa). Below that threshold the solid still slows growth but doesn't stop it; above it, growth speed collapses toward zero and the dendrite stalls before reaching the cathode.
v_tip ∝ C-rate × suppression(G)
suppression(G) = liquid ? 1 : clamp(1 − 0.9·G/9.8, 0.03, 1)
short-circuit when penetration ≥ 100%
- Charge rate (C-rate) — how fast lithium ions are driven onto the anode; higher current pumps the dendrite tip forward faster in both electrolytes.
- Shear modulus — solid-state electrolyte stiffness only; below ≈9.8 GPa dendrites still creep through, above it they are mechanically pinched off.
- Penetration — how far the tallest dendrite has crossed the anode–cathode gap; 100% is an internal short.
This is the concrete safety trade-off behind "solid-state batteries": the same mechanical stiffness that suppresses dendrites is also what makes solid electrolytes harder to manufacture defect-free at scale, and it does nothing by itself to raise energy density — that gain comes separately, from being able to pair a stiff electrolyte with a pure lithium-metal anode instead of graphite.