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

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> 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 <formula formulatype="inline"><tex>$I_{D} = A/L_{S}\xi(L_{S}/L_{C}, \rho_{S}L_{S}^{2}) \times f(V_{G}, V_{D})$</tex></formula>, where <formula formulatype="inline"><tex>$A$</tex></formula> is a technology-specific constant, <formula formulatype="inline"><tex>$\xi$</tex></formula> is a function of geometrical factors such as stick length <formula formulatype="inline"><tex>$L_{S}$</tex></formula>, channel length <formula formulatype="inline"><tex>$L_{C}$</tex></formula>, and stick density <formula formulatype="inline"><tex>$\rho_{S}$</tex></formula>, and <formula formulatype="inline"><tex>$f$</tex></formula> is a function of drain <formula formulatype="inline"><tex>$V_{D}$</tex></formula> and gate <formula formulatype="inline"><tex>$V_{G}$</tex></formula> 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. </para>