6. Summary and Conclusion

TO EFFICIENTLY characterize carrier transport in the inversion layer of deca-nanometer devices, a higher-order transport model for a two-dimensional electron gas based on Subband Monte Carlo tables has been developed. The first six moments of Boltzmann's transport equation are considered and compared to device-Subband Monte Carlo simulations. Fully depleted ultra thin body SOI MOSFETs with several channel lengths are the objects of investigations. As a consistency check, for long channel devices ( $\approx {\mathrm{1000}}{\;}{\mathrm{nm}}$ ) all models converge to the same results. With decreasing channel lengths down to ${\mathrm{100}}{\;}{\mathrm{nm}}$ , the drift-diffusion model underestimates the current compared to the reference Subband Monte Carlo device simulator, while the energy transport and the six moments model can accurately reproduce the reference results. The error of the current of the energy transport model increases rapidly below a channel length of ${\mathrm{80}}{\;}{\mathrm{nm}}$ and becomes even larger than the error of the drift-diffusion model at ${\mathrm{40}}{\;}{\mathrm{nm}}$ . The error of the six moments model is about ${\mathrm{17}}{\;}{\mathrm{\%}}$ for a critical channel length of ${\mathrm{30}}{\;}{\mathrm{nm}}$ , while the errors of the drift-diffusion and the energy transport model are at $-{\mathrm{20}}{\;}{\mathrm{\%}}$ and ${\mathrm{55}}{\;}{\mathrm{\%}}$ , respectively. A comparison of a very sensitive quantity, the transit frequencies of the drift-diffusion, energy transport, and the six moments model has been carried out. The error of the drift-diffusion, energy transport, and the six moments model is at ${\mathrm{-40}}{\;}{\mathrm{\%}}$ , ${\mathrm{40}}{\;}{\mathrm{\%}}$ , and ${\mathrm{18}}{\;}{\mathrm{\%}}$ for a channel length of ${\mathrm{30}}{\;}{\mathrm{nm}}$ , respectively. The inaccuracy of the drift-diffusion model in the transit frequency is twice as large as in the current. The developed six moments model for carrier transport in inversion layers yields very accurate results through the whole scattering dominated regime and outperforms the energy transport and the drift-diffusion model in deca-nanometer channel length devices.

Furthermore, a detailed study concerning the impact of surface roughness scattering and quantization on higher-order transport parameters is given for the homogeneous inversion layer and in a whole device. It has been demonstrated that the influence of surface roughness scattering on the carrier mobility within low fields is higher than for the higher-order mobilities, while the relaxation times are unaffected by surface roughness scattering, due to the elastic nature of the process. The influence of quantization on transport parameters is presented by a comparison between Subband Monte Carlo simulations and three-dimensional bulk Monte Carlo data. Additionally, the behavior of higher-order macroscopic models for a three-dimensional electron gas has been investigated using $\mathrm {n}^+\mathrm {n}\mathrm {n}^+$ test-structures. Here, short channel effects as well as the validity of macroscopic models are studied and benchmarked against the Spherical Harmonics Expansion approach. The increasing error of the models for decreasing channel lengths is demonstrated. Investigations concerning the closure relation of the six moments model are given. It shows that the empirical factor of the closure relation of the three-dimensional electron gas can be used also in a quantized system of a two-dimensional electron gas and in material alloys such as SiGe and GaAs. In order to use higher-order macroscopic transport models in material alloys, higher-order transport parameters are extracted and discussed.