Current–Voltage Characteristics of Long-Channel Nanobundle Thin-Film Transistors: A “Bottom-Up” Perspective

By generalizing the classical linear response theory of “stick” percolation to nonlinear regime, we find that the drain–current of a nanobundle thin-film transistor (NB-TFT) is described under a rather general set of conditions by a universal scaling formula $I_{D} = A/L_{S}\xi(L_{S}/L_{C}, \rho_{S}L_{S}^{2}) \times f(V_{G}, V_{D})$, where $A$ is a technology-specific constant, $\xi$ is a function of geometrical factors such as stick length $L_{S}$, channel length $L_{C}$, and stick density $\rho_{S}$, and $f$ is a function of drain $V_{D}$ and gate $V_{G}$ biasing conditions. This scaling formula implies that the measurement of the full current–voltage characteristics of a “single” NB-TFT is sufficient to predict the performance characteristics of any other transistor with arbitrary geometrical parameters and biasing conditions.