Monte Carlo simulations of charge carrier mobility in semiconducting polymer field-effect transistors

We have incorporated the gate potential and the Coulomb interaction potential between charge carriers in studies of the transport behavior of a field-effect-transistor device based on a conjugated polymer as electroactive material. The basic transport process is described by the Miller-Abrahams type of hopping rate, and the Monte Carlo approach is used to calculate the charge carrier distribution in the conducing channel as well as the mobilities of the carriers as a function of source-drain electric field, temperature, and carrier concentration. The simulations show that the charge carriers are confined to a conducting channel with thickness of about $5–6\mathrm{nm}$. With a Gaussian energetic disorder of $0.14\mathrm{eV}$, typical for materials of this type, the transport is nondispersive with a Gaussian distribution in the distance traveled by the carriers. The mobility is enhanced in the conducting channel as compared to a true bulk transport process, and the logarithm of the mobility is shown to increase linearly with source-drain electric field and inverse temperature.

Figure 1

(Color online) Charge carrier density in the active material of the OFET as a function of the distance $z$ from the oxide interface for $V_g=-10$ (190 particles), $V_g=-20$ (380 particles), and $V_g=-30$ (570 particles), and $E_{SD}=0.2\frac{\sigma }{ea}=1.75\times {10}^5\mathrm{V}∕\mathrm{cm}$.

Figure 2

(Color online) Histograms of the number of charge carriers versus displacement along the $x$ axis for a gate voltage $V_g=-10\mathrm{V}$ and total number of charge carriers $N=190$. The snapshots of the histograms are taken at $t_1=3.6\mathrm{ms}$, $t_2=7.2\mathrm{ms}$, $t_3=10.8\mathrm{ms}$, $t_4=14.4\mathrm{ms}$, $t_5=18.0\mathrm{ms}$, and $t_6=21.6\mathrm{ms}$ corresponding to $1\times {10}^4$, $2\times {10}^4$, $3\times {10}^4$, $4\times {10}^4$, $5\times {10}^4$, and $6\times {10}^4$ MCTSs. $E_{SD}=0.2\frac{\sigma }{ea}=1.75\times {10}^5\mathrm{V}∕\mathrm{cm}$.

Figure 3

(Color online) Same as Fig. 2 but for a gate voltage $V_g=-20\mathrm{V}$ and total number of charge carriers $N=380$. The snapshots taken at $t_1^{\prime }=2.1\mathrm{ms}$, $t_2^{\prime }=4.2\mathrm{ms}$, $t_3^{\prime }=6.4\mathrm{ms}$, $t_4^{\prime }=8.5\mathrm{ms}$, $t_5^{\prime }=10.6\mathrm{ms}$, and $t_6^{\prime }=12.7\mathrm{ms}$.

Figure 4

Mobility vs MCTS for $V_g=-10$ (190 particles), $V_g=-20$ (380 particles), and $V_g=-30$ (570 particles), and $E_{SD}=0.2\frac{\sigma }{ea}=1.75\times {10}^5\mathrm{V}∕\mathrm{cm}$.

Figure 5

Mobility vs electric field $E_{SD}$ at different temperatures. The pairs of curves with open and filled symbols are the results with and without the gate field applied but keeping the number of particles constant. The gate voltage is $V_g=-10\mathrm{V}$ (190 particles).

Figure 6

Mobility vs inverse temperature. The gate voltage is $V_g=-10\mathrm{V}$ (190 particles).