Charge dynamics of individual conductance channels within a percolation network of a nano-patterned nanocrystal quantum dot solid

TL;DR

The paper addresses the challenge of unclear charge transport in colloidal quantum dot solids caused by disorder. It introduces nano-patterned PbS QD solids (~$70$ nm) to create a defect-free, periodically packed system that reveals intrinsic transport across about $N\lesssim40$ channels, with conductance noise exceeding $100\%$ of the mean current and a spectral form $S(\omega)\propto \omega^{-0.68}$. A stochastic quasi-1D percolation-path model explains the observations, including trap-induced channel switching and voltage-driven opening of channels. The study uncovers Lévy-type statistics in single-channel dynamics (e.g., $p(\tau_{off})\propto \tau^{-(1+\mu)}$ with $\mu$ in the ~0.1–0.6 range, and $\langle I_{\omega}\rangle\propto \omega^{-\mu}$ with $\mu\approx0.68$–0.72), along with attractor states arising from long-range Coulomb interactions. These insights provide a path toward rational design of defect-free QD solids with tunable periodic potentials and establish a platform for probing collective charge/spin phenomena and Lévy statistics in solid-state transport.

Abstract

Colloidal nanocrystal quantum dots (QD) enable the bottom-up assembly of designer solids. Among the multitudinous applications of QD solids, there has been great success in exploiting the tunable optical properties for LED displays, lighting, bioimaging and diagnostics. Applications dependent on electrical properties such as solar cells, photodetectors, and transistors have fallen short of their full potential because of poor control over electrical properties, and some of applications with the most promise for novelty, such as a solid-state quantum simulator for quantum computation and spintronics, are stagnant. Lack of clarity on the charge transport mechanism has been a significant barrier to progress, particularly as numerous sources of disorder are present. In this work, we make advancements in a nano-patterning technique to fabricate a 70-nm wide QD solid that is also free of several sources of structural defects. Owing to the small size and structural integrity, we isolate the charge dynamics of a single conductance channel within a percolation network. We tune parameters to measure ~10 channels, and with a time-resolved measurement, we find conductance noise that exceeds 100% of the average current. From observation of the long-time dynamics of the charge transport, including random telegraph noise, colored noise and attractor states, we model the transport with stochastic quasi-one-dimensional percolation paths. With this insight into the charge transport of QD solids unimpeded by structural defects, we provide a path for the rational design of a QD solid with electrical properties that reflect the underlying tunable, periodic potential.

Figures (5)

• Figure 1: (a) Films of semiconductor nanocrystals patterned with nanoscale dimensions and free of structural defects such as grain boundaries and cracks. The films are comprised of Zn$_{0.5}$Cd$_{0.5}$Se$-$Zn$_{0.5}$Cd$_{0.5}$S core$-$shell nanocrystals (cross-hatch pattern) and CdSe (dot pattern). The blue dot pattern is false color to improve visibility. (b) $\textit{n}-$butylamine-capped PbS nanocrystals form the active region of an inverted field-effect transistor. Transmission electron micrograph shows the close$-$packed array. (c)-(e) IV curves of $\textit{n}-$butylamine-capped PbS nanocrystals that are drop$-$cast and nanopatterned to 450$-$nm wide and 70$-$nm wide at its narrowest point respectively. Insets are scanning electron micrographs showing that nanopatterning results in arrays that are structurally continuous, in contrast to drop$-$cast films. With the elimination of clustering, the zero$-$bias conductance increases by a factor of $\sim$180. For sufficiently narrow channels, current noise arises. The gold electrodes on each side of the film are not shown.
• Figure 2: (a) Current versus drain-source voltage in the nanocrystal array displayed in Fig. \ref{['fig:Size']}(e). (inset) Current versus time with a bandwidth of 0.0002 - 1 Hz at V$_{ds}$=25.5 V. (b) The average current (blue) and the standard deviation of the current (red) versus drain-source voltage. Lines are fits to an exponential in V$_{ds}$. (c) Current noise varies proportionally to the average current, an indication that conductance fluctuations give rise to the noise. (d) Fourier transform of the noise at V$_{ds}$=13 V. The noise fits to a power law as shown in red. The green dashed line shows 1$/$f noise for contrast.
• Figure 3: (a) Current versus time at a temperature of 295 K with a voltage bias of $V_{ds}=13 V$. The black line is a fit to a power law decay of the current transient. (b) The Fourier transform of the current decay from panel a (blue line) fits to a power law with a comparable power as the Fourier transform of the current noise. (c) Current versus time at a temperature of 77 K with a voltage bias of $V_{ds}=40 V$. (d) Magnification of the signal in panel c between 105 and 140 seconds. The waiting time between events is $\tau_{off}$. (e) Histogram of the waiting times $\tau_{off}$ from panel c fit to $p(\tau)=a/\tau^{1+\mu}$ where $\mu=0.098\pm0.12$. The inset is the histogram on a log-log plot. (f) Total charge transmitted over time, $<Q(t)>$, calculated from the current in panel a (blue circles) and in panel c (black line). Red line is a fit to $<Q(t)>\propto t^{\mu}$. (g) Current versus time at temperature of 295 K for an even longer time than in panel a. We observe three regimes with different values of the average current. The inset is a magnification of regime III.
• Figure 4: (a) Percolation paths representing the mechanism of the current transients. The red paths represent the conduction channels that dominate the current, and the blue paths represent connected paths with slower rates of charge transmission. As traps fill over time, represented by x, the long screening length cause reductions in the tunnel rates of nearby channels, shown by the diminished color. The rate of the dominant red paths gradually diminishes. (b) Percolation paths representing the discrete shift to an attractor state of lower conductance. Filling of traps sufficiently nearby to several dominant red channels diminish the rate below the resolution limit. The blue paths become dominant.
• Figure 5: (a) Current versus source-drain voltage as a function of temperature. The inset shows the current noise versus temperature. The noise calculated from time traces of the current at V$_{ds}$ = 44 V for ten minutes with a bandwidth of 0.002 - 100 Hz. (b) Current versus source-drain voltage as a function of gate voltage. The inset shows that the relative noise as a function of negative gate voltage.