Role of Polaron Pair Diffusion and Surface Losses in Organic Semiconductor Devices

By applying Monte Carlo simulations we find that the extraction of bound polaron pairs (PP) at the electrodes is an important loss factor limiting the efficiency of organic optoelectronic and photovoltaic devices. Based upon this finding, we develop a unified analytic model consisting of exact Onsager theory describing the dissociation of PP in organic donor-acceptor heterojunctions, the Sokel-Hughes model for the extraction of free polarons at the electrodes, as well as of PP diffusion leading to the aforementioned loss mechanism, which was not considered previously. Our approach allows us to describe the simulation details on a macroscopic scale and to gain fundamental insights, which is important in view of developing an optimized photovoltaic device configuration.

Figure 1

Probability of surface losses vs electric field found by Monte Carlo simulation of $1:1$ donor-acceptor blends at 300 K with ${\tau }_{\mathrm{eff}}=100\mathrm{ns}$ (device length $l=100\mathrm{nm}$, dielectric constant $ϵ=3.0$). (a) Absolute probability for surface loss ($p_{\mathrm{loss}}$) is significant at low fields and for long donor conjugation lengths (CL). (b) $p_{\mathrm{loss}}$ relative to the sum of all losses—in the bulk ($p_{\mathrm{rec}}$) and at the surface—becomes the dominant loss mechanism for increasing CL and increasing field.

Figure 2

Probability distribution $p_{D_{\mathrm{PP}}}$ of polaron pair diffusion lengths from Monte Carlo simulation (circles) of a $1:1$ donor-acceptor blend at 300 K with ${\tau }_{\mathrm{eff}}=100\mathrm{ns}$ (device length $l=100\mathrm{nm}$, dielectric constant $ϵ=3.0$). The dashed lines indicate the fitted contributions of the two identified diffusion processes, with diffusion lengths of 2 respectively, 9 nm, the solid line representing the sum of both.

Figure 3

Combination of dissociation theory (left triangle) and drift and diffusion model (right triangle). PP dissociation probability $p_{\mathrm{diss}}$ results from competitive rates of the individual PP loss processes $K_i$ and leads to net current with $p_{\mathrm{SH}}$. Direct surface loss of PP ($K_{\mathrm{loss}}$) has not been addressed before.

Figure 4

Probability for net photocurrent $p_{\mathrm{ext}}$ and PP dissociation $p_{\mathrm{int}}$ from Monte Carlo simulation (markers; $1:1$ donor-acceptor blend, $\mathrm{CL}=6$, ${\tau }_{\mathrm{eff}}=100\mathrm{ns}$, 300 K, $l=100\mathrm{nm}$, $ϵ=3.0$, and no mirror charge effects) and analytic calculations (fit; $D_{\mathrm{PP}}=3.8\times {10}^{-10}{\mathrm{m}}^2/\mathrm{s}$, $l_{\mathrm{eff}}=22\mathrm{nm}$, $r_{\mathrm{PP}}=3.0\mathrm{nm}$, $\mu =4.3\times {10}^{-8}{\mathrm{m}}^2/\mathrm{V}\mathrm{s}$, ${\tau }_{\mathrm{eff}}=100\mathrm{ns}$, 300 K, $l=100\mathrm{nm}$ and $ϵ=3.0$). For comparison, calculations without PP diffusion ($D_{\mathrm{PP}}=0{\mathrm{m}}^2/\mathrm{s}$) and without virtual device shortening ($l_{\mathrm{eff}}=100\mathrm{nm}$) are shown.