Two-dimensional quantum effects in “ultimate” nanoscale metal-oxide-semiconductor field-effect transistors

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We have carried out a thorough analysis of quantum effects in sub-10-nm silicon double-gate field-effect transistors with ultrathin undoped channels connecting highly doped bulk electrodes, using a self-consistent solution of the two-dimensional (2D) Schrödinger and Poisson equations in a mixed momentum-space representation. The results are compared with the earlier solution of the same problem using the one-dimensional (1D) Schrödinger equation. The 2D theory confirms the basic qualitative conclusions of the 1D theory, but shows that at large values of source-drain voltage, the 1D approximation underestimates the electron backscattering into the source. As a result, the drain current saturates better than the 1D approximation predicts. Our results indicate also that the on/off current performance expectations in an influential industrial forecast are way too optimistic, regardless of the possible gate insulation material improvement.