3D Monte Carlo simulation of FinFET and FDSOI devices with accurate quantum correction

Abstract

The performance of FinFET and FDSOI devices is compared by 3D Monte Carlo simulation using an enhanced quantum correction scheme. This scheme has two new features: (i) the quantum correction is extracted from a 2D cross-section of the 3D device and (ii) in addition to using a modified oxide permittivity and a modified work function in subthreshold, the work function is ramped above threshold to a different value in the on-state. This approach improves the accuracy of the quantum-correction for multi-gate devices and is shown to accurately reproduce 3D density-gradient simulation also at short channel lengths. 15 nm FDSOI device performance with thin box and back-gate bias is found to be competitive: compared to a FinFET with (110)/〈110〉 sidewall/channel orientation, the on-current for N-type devices is 25 % higher and the off-current is only increased by a factor of 2.5.

Appendix: On the quantum correction method

In this appendix, we present more details on our quantum correction method. The quantum-mechanical reference in this work is the density-gradient approach. In the context of the quantum correction, the advantage of density-gradient simulation is that it is also possible to simulate the complete 3D device structure which allows to verify the accuracy of the quantum-corrected DD simulations by comparing the corresponding transfer characteristics at different gate lengths as is done in Fig. 4. The parameter of density-gradient simulation is the quantization mass. This mass changes with the crystallographic orientation of the gate interface. In the present work, values for (100), (110) and (111) surface orientations are considered and during device simulation always the value of the nearest surface is used. For example, the electron (hole) quantization masses for (110) and (100) surface orientations are 0.32 (0.91) and 0.92 (0.26) in units of the free electron mass, respectively (for electrons, always the quantization mass of the valley with the largest mass in surface direction is taken since it dominates the electron density).

The new values for effective oxide thickness and workfunction used as a quantum correction are extracted from 2D device simulations on a cross-section of the 3D device which is shown for the FinFET in Fig. 7. The interfacial oxide is divided into different regions for the top side and the two sidewalls and two different values for $\mathrm{\epsilon}_{\mathrm{ox}}$ are used as resulting from the different crystallographic orientations. In the case of the N-type (P-type) FinFETs with (110) sidewall and (001) top side, the effective permittivity values are 2.83 (3.01) and 2.94 (2.68) in units of the vacuum permittivity instead of the original value of 3.9. In case of discrepancies in the sheet densities between density-gradient and quantum correction, a division into more regions could be considered, but the present results as in Fig. 3 suggest that this will probably not be necessary.

Fig. 7

Electron density at a gate voltage of V_GS=0.8 V according to 2D density-gradient simulation. The simulated structure was obtained by a vertical cut through the middle of the FinFET in Fig. 1. The gate stack consists of interfacial oxide, HfO₂, titanium nitride and the gate contact line

When replacing density-gradient simulation by 2D Schrödinger-Poisson solutions on the cross-section in Fig. 7 as the quantum-mechanical reference, 3D MC simulation will still not explicitly use subbands, of course. However, the corresponding correction for threshold voltage and channel charge will accurately be taken into account and the comparison between density-gradient and quantum-corrected DD in Fig. 4 shows that the density profile itself is not important. The crystallographic orientation dependence of the surface mobility is not due to quantization, but originates from the boundary condition in the presence of a gate interface and is therefore captured both in semiclassical transport (via conservation of energy and parallel-momentum) and in quantum transport (via e.g. vanishing wave functions at the gate interface) [4].

Strain changes subband structure and population resulting from Schrödinger-Poisson solutions, but the corresponding change in threshold voltage and channel charge is captured in our quantum correction approach analogously to the unstrained case. Concerning surface mobility, the strain-induced change in the bulk band structure changes the effect of energy and parallel-momentum conservation leading to a similar stress response as subband models (see Fig. 3 of Ref. [4]).