A Comparison between a Fully-3D Real-Space Versus Coupled Mode-Space NEGF in the Study of Variability in Gate-All-Around Si Nanowire MOSFET

In this work a comparison between the fully-3D (F3D) real-space approach and the Couple Mode Space (CMS) approach in solving the Non-Equilibrium Green Function (NEGF) quantum transport equations is carried out. The CMS approach, as with every mode decomposition technique, is inherently an approximate method, because of the finite number of modes used. This method, due to its quasi-1D nature, is less computationally expensive compared to the fully 3D one. In the simulation of devices, the correct magnitude of the electron current and its electrostatic self-consistency are important issues. We use the current as an indicator for the accuracy of different CMS implementations. The F3D and the CMS approach are compared in the simulation of thin gate-all-around Si Nanowire transistor. The comparison is carried out for devices with different types of non-uniformities including: (i) smooth SiO₂ interfaces and continuous doping as a reference, (ii) discrete charge in the channel (iii) random discrete dopants in the S/D and (iv) surface roughness. The focus is on the performance and accuracy of the CMS simulations as a function of the number of coupled modes in comparison with the F3D simulation results for the current. Because the CMS approach separates the confinement in the transversal directions from the propagation longitudinal direction, this simplifies the dissection of the underlying transport physics. The transmission dependence on energy can be explained as the interaction between different modes. Also, the sub-band energies allow us to visualise the resonances, when superimposed on the LDOS.