Immediate recapture in the trapping-detrapping process of a single charge carrier

Abstract

Previously we have shown that pure 1/f noise arises from the trapping-detrapping process when traps are heterogeneous. Namely, the trapping-detrapping process relies on the assumption that detrapping rates of individual trapping centers in the condensed matter are random and uniformly distributed. Another assumption underlying the trapping-detrapping process was that both trapping and detrapping times need to have non-zero duration. Here we violate the latter assumption by introducing immediate recapture of the charge carrier. We show that 1/f noise will still be observed, though the range of frequencies over which it will be observed shifts to the lower frequency range as the immediate recapture probability increases.

Figures (5)

• Figure 1: Sample signal generated by the trapping--detrapping of a single charge carrier. Relevant notation: $\tau_{i}$ -- detrapping time (gap duration), $\theta_{i}$ -- trapping time (pulse duration), $a$ -- current generated by a free--drifting charge carrier (pulse height).
• Figure 2: Probability density function of the detrapping time distribution under the assumption that individual detrapping rates are uniformly distributed in $\left[\gamma_{\text{min}},\gamma_{\text{max}}\right]$ (red curve), Eq. \ref{['eq:escape-time-pdf']}. The probability density function was obtained with $\gamma_{\text{min}}=10^{-3}$ and $\gamma_{\text{max}}=10$. Black dashed curves correspond to the exponential probability density functions with fixed rates: $\gamma_{\tau}=10^{-3}$, $2.78\times10^{-3}$, $7.74\times10^{-3}$, $2.15\times10^{-2}$, $5.99\times10^{-2}$, $1.67\times10^{-1}$, $4.64\times10^{-1}$, $1.29$, $3.59$, and $10$. Normalization of the exponential probability density functions was adjusted for the visualization purposes, but it remains proportional to their respective contributions.
• Figure 3: Rescaled simulated PSD curves of the trapping--detrapping process with immediate recapture mechanism. Common simulation parameters: $T=10^{6}$, $\gamma_{\text{min}}=10^{-4}$, $\gamma_{\text{max}}=10^{4}$, $a=1$, $\gamma_{\theta}=1$.
• Figure 4: Rescaled simulated PSD curves of the trapping--detrapping process with immediate ejection mechanism. Common simulation parameters: $T=10^{6}$, $\gamma_{\text{min}}=10^{-4}$, $\gamma_{\text{max}}=10^{4}$, $a=1$, $\gamma_{\theta}=1$.
• Figure 5: Simulated conditional PSD curves of the trapping--detrapping process with immediate ejection mechanism. Common simulation parameters: $T_{\text{min}}=10^{6}$, $N_{\text{min}}=10^{6}$, $\gamma_{\text{min}}=10^{-2}$, $\gamma_{\text{max}}=10^{4}$, $a=1$, $\gamma_{\theta}=1$.