Exciton Charge Separation at a Donor–Acceptor Junction

Junction Conditions

Electric field F 50 V/µm

Temperature T 300 K

CT-state separation a 1.5 nm

Exciton diffusion length L_D 8 nm

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Dissociation probability P_diss(F,T)

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Internal quantum eff.

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Photocurrent (rel.)

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Excitons generated

Free pairs formed

How it works

Light absorbed in the donor layer of an organic solar cell creates a tightly-bound, neutral Frenkel exciton, not a free charge. It has to diffuse to the donor–acceptor interface before it decays, then split into a free electron and hole — this simulation models both steps.

1. Diffusion (random walk). Each yellow exciton takes isotropic random steps with diffusion coefficient D = L_D²/τ, where τ ≈ 300 ps is a typical exciton lifetime. If it decays before reaching the interface, that photon is lost (a short flash marks it) — this is why L_D directly limits how thick a donor layer can usefully be.

2. Dissociation (Onsager–Braun theory). At the interface the exciton forms a Coulomb-bound charge-transfer (CT) state of separation a, with binding energy

E_b = e² / (4π ε₀ ε_r a)

Thermal energy and the applied field F compete against this binding energy. The field-assisted escape rate follows Onsager's classic result, in Braun's series form:

k_d(0) = ν₀ · exp(−E_b / k_B T)
b = e³F / (8π ε₀ ε_r k_B² T²)
f(b) = 1 + b + b²/3 + b³/18 + b⁴/180 + ...
k_d(F) = k_d(0) · f(b)
P_diss = k_d(F) / (k_d(F) + k_f)

k_f is the intrinsic CT-state recombination rate. A stronger field, higher temperature, or smaller CT separation all raise P_diss — exactly the trade-offs real organic-photovoltaic materials are engineered around. Dissociated pairs (cyan electron, magenta hole) drift apart under the field and are collected at the electrodes as photocurrent; failed CT states recombine at the interface instead (an amber flash).

Exciton (donor) Free electron Free hole Lost / recombined

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