  Two-dimensional materials-based field-effect transistors (2DM-FETs) exhibit
both ambipolar and unipolar transport types. To physically and compactly cover
both cases, we put forward a quasi-Fermi-level phase space (QFLPS) approach to
model the ambipolar effect in our previous work. This work aims to further
improve the QFLPS model's numerical aspect so that the model can be implanted
into the standard circuit simulator. We first rigorously derive the
integral-free formula for the drain-source current to achieve this goal. It is
more friendly to computation than the integral form. Besides, it explicitly
gives the correlation terms between the electron and hole components. Secondly,
to work out the boundary values required by the new expressions, we develop a
fast evaluation algorithm for the surface electrostatic potential based on the
zero-temperature limit property of the 2DM-FET system. By calibrating the model
with the realistic device data of black phosphorus (BP) and monolayer
molybdenum disulfide (ML-MoS2) FETs, the completed algorithm is tested against
practical cases. The results show a typical superiority to the benchmark
algorithm by two orders of magnitude in time consumption can be achieved while
keeping a high accuracy with 7 to 9 significant digits.
