Extended Scale Length Theory for Low-Dimensional Field-Effect Transistors

Low-dimensional (low-D) semiconductors such as carbon nanotubes (CNTs) and 2-D materials are promising channel materials for nanoscale field-effect transistors (FETs) due to their superior electrostatic control. However, classical scale length theory (SLT) does not incorporate the effect of channel extensions, which becomes crucial for thin channels (< 10 nm) and short gate lengths. Here, we extend the classical SLT by introducing two boundary coupling parameters, which describe the impact of gate and drain biases on the source- and drain-channel junction potentials. Moreover, we introduce a general expression for the scale length specifically for low-D FETs. This extended SLT accurately describes electrostatic short-channel effects (SCEs) of low-D FETs, with < 5% error in subthreshold slope over a wide range of parameters versus >
$2\times $
error using the classical SLT. The extended SLT is based on three parameters (scale length, gate, and drain boundary coupling parameters) which can be extracted from potential profiles or FET transfer characteristics. In addition, the extended SLT uses analytical closed-form expressions that can be easily included in a compact model to facilitate design-technology co-optimization (DTCO) with low-D FETs to leverage the crucial role of their extensions.