Figure 1

Diagram showing the rates and rate coefficients of PP formation and dissociation in an organic semiconductor. Polarons travel through the material until two of them become Coulombically coupled, forming PPs of singlet $\left(G_S\right)$ or triplet $\left(G_T\right)$ content. These pairs may either dissociate back to free polarons $\left(d_S,d_T\right)$ or become highly coupled, forming excitons (singlet, SE, or triplet, TE), which may recombine either radiatively or nonradiatively. PPs may undergo intersystem crossing, incoherently moving between singlet and triplet configurations due to interacting with the environment (with the rate $k_{SR}$).Reuse & Permissions

Figure 2

(Color online) The steady-state solution for the two spin populations (bottom), and the difference in population (top) as a function of spin mixing time, for the case of electrical injection $\left(G_T=3G_S\right)$. Here, $\rho =0.5$. At small ${\tau }_{SR}$, the population distribution approaches the thermal distribution, and at high ${\tau }_{SR}$ it is determined by the generation and recombination rates.Reuse & Permissions

Figure 3

(Color online) The steady-state solution for the two spin populations (bottom), and the difference in population (top) as a function of spin mixing time, for the case of optical excitation $\left(G_T=0\right)$. Here, $\rho =0.99$. At small ${\tau }_{SR}$, the population distribution approaches the thermal distribution, and at high ${\tau }_{SR}$ it is determined by the generation and recombination rates.Reuse & Permissions

Figure 4

(Color online) Rate coefficients, ${\Gamma }_{1,2}$ [see Eqs. (9, 10)] for the double exponential transient recovery following PP population manipulation, modeled using the realistic values given in Table . As can be seen, ${\Gamma }_1$ is always less than ${\Gamma }_2$, and ${\Gamma }_2$ is always greater than $k_{SR}$.Reuse & Permissions

Figure 5

The two limiting cases of spin relaxation for which the rate coefficients are determined. Intuitively, the limit for $k_{SR}\to 0$ corresponds to two independent systems, whereas the limiting case $k_{SR}\to \infty$ generates a single system with dissociation and recombination rates given by Boltzmann factor weighted averages.Reuse & Permissions

Figure 6

(Color online) Calculated transient response of the current through a forward biased OLED following electron-spin-resonant excitation-induced mixing between the singlet and triplet PP spin configurations, as a function of time after the pulse, and the intersystem crossing time ${\tau }_{SR}$. The data are modeled using the parameters noted in the figure and normalized by $\Delta n$. The transient is observed to follow an enhancement-quenching form.Reuse & Permissions

Figure 7

(Color online) Comparison between numerically generated and experimentally measured current transients following resonant spin manipulation between the singlet and triplet states. The experimental data were obtained on an MEH-PPV OLED operating in the forward bias configuration at a temperature of 15 K. The transient has an enhancement-quenching signal, well fit by a biexponential function with time constants $1/{\Gamma }_1=30.8\mu \text{s}$ and $1/{\Gamma }_2=8.5\mu \text{s}$. The initial rise at short times $\left(t<6\mu \text{s}\right)$ is due to the rise time of the amplifier used in these experiments. Numerically generated transient signal as a function of the time after microwave excitation are shown for a range of fixed intersystem crossing times ${\tau }_{SR}$. The data are modeled using the parameters noted in the figure. The transient is also observed to follow an enhancement-quenching form. The magnitude of the simulated data was scaled to match the experimental data. At long ${\tau }_{SR}$, variations in ${\tau }_{SR}$ have little effect on the form of the transient. As ${\tau }_{SR}$ is reduced, it begins to dominate the time constant of the enhancement part of the transient (positive $\Delta I$). If the value of ${\tau }_{SR}$ used in the simulation is smaller than ${\Gamma }_2$, then the simulation cannot reproduce the experimental data.Reuse & Permissions