Three-Dimensional Percolation and Performance of Nanocrystal Field-Effect Transistors

The understanding of charge transport through films of semiconductor nanocrystals (NCs) is fundamental for most applications envisaged for these materials, e.g., light-emitting diodes, solar cells, and thin-film field-effect transistors (FETs). In this work, we show that three-dimensional film-thickness-dependent percolation effects taking place above the percolation threshold strongly affect the charge transport in NC films and greatly determine the performance of NC devices such as NC FETs. We use thin films of Si NCs with a wide range of thicknesses controllable by spray coating of NC inks to thoroughly investigate the electronic properties and charge transport in thin NC films. We find a steep (superlinear) increase of the electrical conductivity with increasing film thickness, which is not observed in bulk semiconductor thin films with bandlike charge transport. We explain this increase by an exponentially increasing number of charge percolation paths in a system dominated by hopping charge transport. Thin-film NC FETs reveal thickness-independent field-effect mobilities and threshold voltages, whereas on:off current ratios decrease quickly with increasing film thickness. We show that the steep enhancement of electrical conductivity with increasing film thickness provided by three-dimensional percolation effects is, in fact, responsible for the dramatic degradation of NC FET performance observed with increasing film thickness. Our work demonstrates that the performance of NC FETs is much more critically sensitive to film thickness than in conventional FET-based bulk semiconductor materials.

Figure 1

(a) High-magnification SEM image of HF-etched Si NCs (H terminated). (b) Size distribution of Si NCs in (a). The red dotted line is a fit of a log-normal distribution with a count median diameter $d_{\mathrm{H}\text{term}}=10\pm 2\mathrm{nm}$. (c) SEM image of a FET electrode structure covered with a thin Si NC film obtained under an angle of 60°. (d) Surface profile of the FET structure in (c).

Figure 2

Drain-source $I\text{−}V$ characteristics of NC FETs (floating gate) with $L=160\pm 60\mathrm{nm}$ (blue), $L=320\pm 100\mathrm{nm}$ (green), and $L=1073\pm 190\mathrm{nm}$ (orange) in a semilog scale (a) and a log-log scale (b). The filled symbols correspond to measurements with increasing voltage; the open symbols to measurements with decreasing voltage. The dashed lines in (b) symbolize linear and superlinear $I\text{−}V$ dependences, respectively.

Figure 3

(a) Conductance $G$ of NC FETs as a function of the film thickness. The data are extracted from fitting $I\text{−}V$ dependences measured with floating gate, as shown in Fig. 2. (b) Conductivity $\sigma$ of the NC FETs calculated from $G$ values given in (a) and the corresponding film thickness, respectively. The different symbols and colors correspond to different sample series.

Figure 4

Output characteristics of NC FETs with (a) $L=160\pm 60\mathrm{nm}$, (b) $L=320\pm 100\mathrm{nm}$, and (c) $L=1073\pm 190\mathrm{nm}$ film thickness. (d) shows the data in (c) subtracted by the output characteristic obtained at $V_G=0\mathrm{V}$. The voltages given on the right axis correspond to the applied $V_G$.

Figure 5

Transfer characteristics of NC FETs with $L=160\pm 60\mathrm{nm}$ (blue), $L=320\pm 100\mathrm{nm}$ (green), and $L=1073\pm 190\mathrm{nm}$ (orange) film thickness. The filled (open) symbols correspond to a measurement with increasing (decreasing) voltage. The dashed lines represent linear fits to the data, whose intersection with $I_{\mathrm{off}}$ is equal to $V_G$. (a) shows $I_{\mathrm{DS}}$ versus $V_G$ taken at $V_{\mathrm{DS}}=3\mathrm{V}$; (b) shows $\sqrt{I_{\mathrm{DS}}}$ versus $V_G$ taken at $V_{\mathrm{DS}}=13\mathrm{V}$.

Figure 6

(a) Linear FET mobility taken at $V_{\mathrm{DS}}=3\mathrm{V}$, (b) saturation FET mobility taken at $V_{\mathrm{DS}}=13\mathrm{V}$, (c) threshold voltage taken at $V_{\mathrm{DS}}=3\mathrm{V}$, (d) threshold voltage taken at $V_{\mathrm{DS}}=13\mathrm{V}$ as a function of the NC FET film thickness. All data points are average values of raw data within a thickness range of 100 nm.

Figure 7

$\sigma /(e\mu )$ calculated using (a) $e{\mu }_{\mathrm{lin}}$ and (b) $e{\mu }_{\mathrm{sat}}$. The dashed line is a fit to all data (a) and (b) using Eq. (9) and $A=9\times {10}^{16}{\mathrm{cm}}^{-3}$, ${\xi }_c=0.2$, $D=3.1\times {10}^3$, $\nu =1.08$.

Figure 8

$I_{\mathrm{off}}$ taken at (a) $V_{\mathrm{DS}}=3\mathrm{V}$ (b) and $V_{\mathrm{DS}}=13\mathrm{V}$. $I_{\mathrm{on}}-I_{\mathrm{off}}$ taken at (c) $V_{\mathrm{DS}}=3\mathrm{V}$ and (d) $V_{\mathrm{DS}}=13\mathrm{V}$. Ratio of $I_{\mathrm{off}}$: $V_{\mathrm{DS}}$ to the conductance $G$ taken at (e) $V_{\mathrm{DS}}=3\mathrm{V}$ and (f) $V_{\mathrm{DS}}=13\mathrm{V}$. Ratio of ($I_{\mathrm{on}}-I_{\mathrm{off}}$): $I_{\mathrm{off}}$ taken at (g) $V_{\mathrm{DS}}=3\mathrm{V}$ and (h) $V_{\mathrm{DS}}=13\mathrm{V}$ as well as a fit to the data using Eq. (10) (dashed line). The solid line represents an inverse linear dependence with $L$. Data points in these graphs are average values of the raw data within a thickness range of 100 nm.

Figure 9

Schematic illustration true to scale of our NC FETs with an applied voltage of $V_{\mathrm{DS}}=13\mathrm{V}$ and a positive $V_G$ applied. The red arrows symbolize the current flowing in the FET channel of $I_{\mathrm{on}}-I_{\mathrm{off}}={10}^{-6}\mathrm{A}$. $I_{\mathrm{off}}$ is depicted from the data in Fig. 8.