Perovskite Ion Migration & J-V Hysteresis

Bias Sweep

FORWARD SCAN

Scan rate 0.20 V/s

Ion mobility μ 1.00×

Vacancy density 50%

Temperature 300 K

Live Readouts

Applied V

0.00 V

Current J

0.0 mA/cm²

Hysteresis index (last full cycle)

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Forward (low→high V) Reverse (high→low V)

How it works

Perovskite absorbers (e.g. MAPbI₃) contain mobile point defects — chiefly iodide vacancies — that drift under the cell's internal field like a slow, solid-state electrolyte:

Drift-diffusion:  J_ion = -D ∂c/∂x + μ·E·c
Einstein relation: D = μ·k_BT / q
Arrhenius mobility: μ(T) = μ₀·exp[-E_a/k_B (1/T - 1/T₀)]

Ions pile up at the perovskite/transport-layer interfaces, building a polarization charge that screens part of the applied bias. The diode only "feels" the screened voltage:

V_eff(t) = V(t) - α·⟨x_ion⟩(t)
J(V_eff) = J_sc - J₀·[exp(V_eff / nV_t) - 1]

Because ⟨x_ion⟩ lags the applied voltage by the ion relaxation time (set by mobility and vacancy density), the forward (low→high V) and reverse (high→low V) sweeps trace different J-V paths — the hallmark scan-rate-dependent hysteresis reported in perovskite solar cells.

Scan rate — how fast V(t) sweeps; slow scans let ions keep up (less hysteresis), fast scans outrun them (more hysteresis), fastest scans also outrun them the other way once ions can't move at all.
Ion mobility μ — sets the drift speed and, via the Einstein relation, the diffusion/jitter of the spheres.
Vacancy density — how many mobile ions exist (visualized instance count) and how strongly they screen the field.
Temperature — mobility follows an Arrhenius law with a ~0.35 eV migration barrier, so hysteresis collapses at high T and worsens in the cold — matching real device measurements.

Units here are normalized for a responsive, illustrative animation — real ionic mobilities in halide perovskites are of order 10⁻⁸–10⁻¹⁰ cm²/V·s with relaxation times of seconds.

Mobile ion vacancies Electron transport layer Hole transport layer

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