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$\Omega$ -gated negative capacitance (NC) FinFETs, CMOS inverters and SRAM are fabricated and analyzed. Forming gas annealing (FGA) is performed and found to not only enhance ferroelectricity (FE) but also the NCFET electrostatics, in terms of higher $\mathrm{I}_{\mathrm{ON}}$ , smaller hysteresis and subthreshold slop (SS). The SS is less than 60 mV/dec for both N-FinFET and P-FinFET in this work. Moreover, the CMOS inverter shows more symmetric and larger voltage gain after FGA.

Theoretically, confined heterostructure p(-n)-i-n (n(-p)-i-p) TFETs are promising candidates for future low-power applications, with n-TFET outperforming p-TFET. An optimal body thickness of about 10nm is predicted for Ga 0.5 As 0.5 Sb-In 0.53 Ga 0.47 As n-TFET with I 60 =20µA/µm. For p-TFETs, stronger confinement may be required to avoid tunneling to the heavy-hole band. An unexploited domain is the insertion of thin heterostructure slabs offering a locally reduced dielectric constant, enhancing both SS and I on .

Unlike MOSFETs, tunnel-FETs (TFETs) are not limited by a 60 mV/dec subthreshold swing and therefore scaling the supply voltage beyond the MOSFET's 1 V plateau becomes feasible. Supply voltage scaling is a necessary condition for reducing the power consumption per transistor, which enables further size scaling of the FETs. Designing a successful FET is however challenging, because it is not sufficient for the TFET to realize a sub-60 mV/dec subthreshold swing at one particular voltage. The next-generation FET must realize an average sub-60 mV/dec subthreshold swing over the whole supply voltage window, such that on-currents of about I on = 100 µA/μm are achieved with I on /I off ratios of about 106 for sub 0.5 V supply voltages. Silicon-based TFETs are the most attractive because they allow for a full re-use of the existing expertise in fabricating silicon MOSFETs. However, the large bandgap of silicon (Si) results in low on-currents for the all-Si TFET and both input and output characteristics are inferior to the ones of all-Si MOSFETs.

In numerical computations, unstructured grids can be used easily to fit computational domains involving complex geometries. The method of space-time conservation element and solution element (CE/SE method)[1,2] can be used in conjunction with unstructured grids. In this paper, the procedure of developing a non-splitting unstructured-triangular-mesh Euler solver based on the CE/SE method is described. Numerical examples involving complex features of shock waves are presented to show that the CE/SE method works very well even for unstructured triangular grids.

SUMMARY The reduction-to-periodicity method using the pseudospectral fast Fourier transform (FFT) technique is applied to the solution of non-periodic problems, including the two-dimensional incompressible Navier-Stokes equations. The accuracy of the method is explored by calculating the derivatives of given functions, one- and two-dimensional convective4iffusive problems, and by comparing the relative errors due to the FFT method with a second-order finite difference (FD) method. Finally, the two-dimensional Navier-Stokes equations are solved by a fractional step procedure using both the FFT and the FD methods for the driven cavity flow and the backward-facing step problems. Comparisons of these solutions provide a realistic assessment of the FFT method. In this paper we discuss a numerical technique for solving partial differential equations in nonperiodic domains by the use of the pseudospectral method. This work was motivated by the need to develop a time-dependent incompressible Navier-Stokes solver with non-periodic inflow/outflow boundary conditions involving wave propagation problems. In such problems the use of Chebyshev expansions along the streamwise direction provides an accurate solution procedure at the cost of imposing very stiff viscous time step restrictions. Note that along the streamwise direction, time-explicit methods can be efficiently used owing to the absence of any sharp gradients at inflow/outflow boundaries. In flows bounded by solid walls, however, it is expected that the spectral Chebychev method will be superior for the same number of grid points and the same operation count. The goal of this paper is to provide a direct comparison of the reduction-toperiodicity method with a widely used second-order finite difference method in an effort to isolate the advantages/shortcomings of the reduction-to-periodicity method. In periodic domains the use of the pseudospectral fast Fourier transform technique was instigated by the work of Or~zag,'-~ and since then the method has been extensively used in solving multidimensional fluid dynamics problems with periodic boundary conditions. The article by Orszag and Israeli4 provides other references and an introduction to the subject. The idea of polynomial subtraction for the purpose of satisfying non-periodic boundary constraints was introduced by Lanczos5 and later developed by Gottlieb and Orszag.6 In one-dimensional mode1 problems the well known Gibbs phenomenon that appears at the boundaries when such methods are used with non-periodic boundary conditions has been shown to be suppressed by the use of simple polynomials.'* * In Reference 8 the accuracy of the reduction-to-periodicity method is

The reduction-to-periodicity method using the pseudo-spectral Fast Fourier Transform (FFT) technique is applied to the solution of nonperiodic problems including the two-dimensional Navier-Stokes equations. The accuracy of the method is demonstrated by calculating derivatives of given functions, one- and two-dimensional convective-diffusive problems, and by comparing the relative errors due to the FFT method with seocnd order Finite Difference Methods (FDM). Finally, the two-dimensional Navier-Stokes equations are solved by a fractional step procedure using both the FFT and the FDM methods for the driven cavity flow and the backward facing step problems. Comparisons of these solutions provide a realistic assessment of the FFT method indicating its range of applicability.