Engineering & Science
Mott-Gurney Space-Charge-Limited Current (SCLC) Law for OLEDs & Perovskites
Calculate trap-free solid-state space-charge-limited current density J = (9/8) * eps_r * eps_0 * mu * (V^2 / L^3) (A/m^2) to extract carrier mobility in organic OLEDs, polymers, and halide perovskites.
Why OLED and perovskite current scales as V^2 / L^3 instead of Ohm’s Law!
In low-doped wide-bandgap semiconductors—organic light-emitting diodes (OLEDs), conjugated polymers, and halide perovskite solar cells—injected charge carriers from an ohmic contact quickly outnumber equilibrium thermal carriers, building up an electrostatic space-charge cloud inside the film of thickness L (m)! Nevill Mott and Ronald Gurney (1940) proved that drift-limited solid-state current obeys a quadratic V^2 / L^3 power law (distinct from vacuum Child-Langmuir V^1.5 / d^2): J_MG = (9 / 8) * eps_r * eps_0 * mu * (V^2 / L^3)!
Device physicists sweep J-V curves on hole-only or electron-only diodes specifically to extract bulk carrier mobility mu (m^2/(V*s)) without Hall-effect contacts! Across an L = 100 nm (1.0e-7 m) organic transport layer with relative permittivity eps_r = 3.5 and mobility mu = 1.0e-7 m^2/(V*s) (10^-3 cm^2/(V*s)), applying V = 5.0 V drives J = 87,158.41 A/m^2 (8.72 A/cm^2); doubling bias to V = 10.0 V quadruples current 4x to 348,633.64 A/m^2!
| Applied Bias & Film Thickness (eps_r = 3.5, mu = 1e-7 m^2/Vs) | Scaling Law V^2 / L^3 | Mott-Gurney Current J (A/m^2) | mA/cm^2 Equivalent |
|---|---|---|---|
| V = 5.0 V across L = 100 nm (1e-7 m) | 2.50e22 V^2/m^3 | 87,158.41 A/m^2 | 8,715.8 mA/cm^2 |
| Doubled Bias V = 10.0 V (L = 100 nm) | 1.00e23 V^2/m^3 (4x) | 348,633.64 A/m^2 | 34,863.4 mA/cm^2 |
| Doubled Thickness L = 200 nm at V = 5.0 V | 3.125e21 V^2/m^3 (1/8x) | 10,894.80 A/m^2 | 1,089.5 mA/cm^2 |
Mott-Gurney SCLC Current Density J (A/m^2) = (9/8) * eps_r * eps_0 * mu * (V^2 / L^3)
Uses vacuum permittivity eps_0 = 8.8541878e-12 F/m across eps_r (B2), mobility mu (B3), voltage V (B4), and thickness L (m, B5).
=IF(OR(B2 <= 0, B3 <= 0, B4 < 0, B5 <= 0), "Invalid SCLC Inputs", ROUND((9 / 8) * B2 * 0.0000000000088541878 * B3 * ((B4 ^ 2) / (B5 ^ 3)), 2))Extracted SCLC Carrier Mobility mu (cm^2/(V*s)) From Measured Current Density
Converts SI mobility mu (m^2/(V*s)) into standard semiconductor report units cm^2/(V*s) (* 10,000).
=IF(OR(B2 <= 0, B3 <= 0, B5 <= 0), "Invalid SCLC Inputs", ROUND(B3 * 10000, 6))Try the example
Use the original values or change them to test your understanding.