Impact of the Substrate Material on the RF Performance of Carbon-Nanotube Transistors

Abstract

We examine the effect of the substrate material on the radio-frequency (RF) behavior of carbon-nanotube transistors by considering the impact of substrate polar phonons (SPPs). We consider SPP scattering from AlN, SiO <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$_{2}$</tex></formula> , HfO <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$_{2}$</tex></formula> , and ZrO <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$_{2}$</tex></formula> substrates within a semiclassical approach by solving the time-dependent Boltzmann transport equation self-consistently with the Poisson equation. Various RF figures of merit, such as the unity-current gain frequency <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$f_T $</tex></formula> , the unity-power-gain frequency <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$f_{{\rm max}} $</tex></formula> , the transconductance <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$g_m $</tex></formula> , and the two-port <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$y$</tex></formula> -parameters, are determined in order to characterize the impact of SPP scattering. We first consider the impact of SPP scattering on the RF behavior of an intrinsic single-tube carbon nanotube field-effect transistor (CNFET). These single-tube results are then combined with the external parasitic elements to analyze the pitch-dependent, RF behavior of an extrinsic array-based CNFET. It is shown that AlN substrates have the least impact in degrading the RF performance of a CNFET, while the more polar substrates (HfO <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$_{2}$</tex></formula> or ZrO <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$_{2}$</tex> </formula> ) have a greater impact. This varying behavior can be attributed to the SPP energies, which are higher in AlN compared to the other materials, making CNFETs with AlN substrates less susceptible to SPP scattering even at room temperature. Our results suggest that substrate engineering will become an important component in the design process of emerging devices to achieve an optimized RF performance.