Quasi-Fermi-Level Phase Space and its Applications in Ambipolar Two-Dimensional Field-Effect Transistors

Ambipolar field-effect transistors (FETs) based on two-dimensional (2D) channel materials have enabled various applications such as in-memory computing, nonlinear logic, and frequency multipliers, taking advantage of the simultaneous transport of electrons and holes. From a device simulation perspective, it is much harder to handle ambipolar transport than unipolar electron or hole transport, mainly due to the splitting of quasi-Fermi-levels. While setting up a proper recombination model, the problem can be addressed by self-consistently solving the continuity equations, this brings about tremendous computational complexity and model uncertainty. In this work, we introduce the concept of quasi-Fermi-level phase space (QFLPS) that is spanned by the electron and hole quasi-Fermi potentials (Vn and Vp), on which the drain-source current is written as a curve integral within the QFLPS without explicitly involving the spatial message. However, the curve requires the relation between Vn and Vp that is unknown a priori. A promising solution is to search the conditions where the integral is almost path independent, such that the drain current may be evaluated through the simplest path. We convert the problem into inspecting the conservative property of a field defined on QFLPS, the work done by which (i.e., the curve integral) gives the current. A detailed analysis for devices working under normal conditions predicts that the QFLPS can be divided into full-curl and null-curl regions, where within the latter the integral can be regarded as path independent. The exact criteria have been prescribed and the simplest linear path from source to drain is suggested as the path for fast calculation, leading to the so-called quasiequilibrium approximation (QEA). For extensive well-designed examples, the QEA results have been compared with the exact solutions derived from continuity equations. The concept of proper Fermi path has been proposed to connect the approximations and exact solutions. QFLPS is not only a theoretical basis for the fast evaluation of drain current, but it also provides a general platform for analyzing the device behaviors of ambipolar 2D FETs. Actually, it is applicable to unipolar FETs as well. Based on QEA's current formula, typical applications of QFLPS are demonstrated, including recovering the various operational modes of 2D FETs as well as the logic inverter, and an ambipolar-2D-FET-based threshold inverter quantization circuit as the core component of a flash analog-to-digital converter is proposed, which achieves a linearithmic dependence of the chip size with the quantization levels compared with the quadratic dependence offered by the traditional CMOS scheme. The prospect of QFLPS in 2D FET-based circuit design is demonstrated.