Simulation of transient current through PMMA thin films based on a random walk model

A piecewise continuous, time dependent diffusive coupling in a classical one-dimensional randomly pinned charge density wave model has been used for the analysis of experimentally observed transient current data for polymethyl methacrylate. Satisfactory agreement has confirmed that this can be a dynamical model for the behavior of the transient current. The analysis also suggests the presence of three different regimes in the decay of the transient current.

Figure 1

CDW fit of current at $3.25\mathrm{MV}∕\mathrm{m}$. Both the measured current $(+)$ and simulated CDW polarization current $(\times )$ are normalized and drawn versus the number of time steps $\left(n\right)$.

Figure 2

CDW fit of a current at $2.50\mathrm{MV}∕\mathrm{m}$ [current $(+)$, simulation $(\times )$].

Figure 3

CDW fit of a current at $2.0\mathrm{MV}∕\mathrm{m}$ [current $(+)$, simulation $(\times )$].

Figure 4

Power spectrum analysis of the observed current at $2\mathrm{MV}∕\mathrm{m}$. The slope of the straight line is equal to $-0.98$.

Figure 5

Plot of $\log F\left(n\right)$ vs $\log n$ for the time series of the $x$ component of Lorenz equations showing the crossover.

Figure 6

$\log \left[F\right(n\left)\right]$ vs $\log \left(n\right)$ with three different scaling exponents for the measured current $(+)$ at $3.25\mathrm{MV}∕\mathrm{m}$ and the simulation $\left(x\right)$.The inset show the scaling exponents for the current.

Figure 7

$\log \left[F\right(n\left)\right]$ vs $\log \left(n\right)$ with three different scaling exponents for the measured current $(+)$ at $2.50\mathrm{MV}∕\mathrm{m}$ and the simulation. The inset show the scaling exponents for the current.

Figure 8

$\log \left[F\right(n\left)\right]$ vs $\log \left(n\right)$ with three different scaling exponents for the measured current $(+)$ at $2.00\mathrm{MV}∕\mathrm{m}$ and the simulation $\left(x\right)$. The inset shows the scaling exponents for the current.