The main purpose of the dissertation is to investigate the hole electrical properties of the silicon inversion layer beneath in the presences of both the significant quantum confinement and the complicated mechanical stresses. Based on this main topic, the organization of this dissertation is described below.
First, an introduction to the valence band structures in p-type inversion layer is described in Chapter 1. Then, Chapter 2 of the dissertation is focused on the numerical techniques and physical models of p-NEP. About the numerical technique, the six-band k‧p Schrödinger-Poisson self-consistent method is used to obtain the precise valence subband structures, inversion carrier distribution, and self-consistent potential profile. Concerning the physical models, (i) the phonon scattering rate, surface roughness scattering rate, and Kubo-Greenwood formula are used to achieve the elaborate transport calculation; (ii) the WKB approximation method is used to evaluate hole gate direct tunneling; and (iii) because of the highlighted three dimensional mechanical stresses in the dissertation, the stress-to-strain tensor is included as well. In general, p-NEP is a flexible simulator containing the functions of above calculations with the alternative materials (silicon, germanium, and gallium arsenide), the alternative wafer orientations ((001), (110), and (111)), the alternative temperature conditions (2K to 400K), the alternative stress conditions (GPa-level uniaxial and biaxial stresses), and the alternative substrate doping concentrations (1x1015 to 6x1018 cm-3).
However, according to the algorithm of p-NEP, the computation burden is still
extremely heavy to remain the tolerable computation error. Thus, Chapter 3 presents a novel computational accelerator to intrinsically boost the self-consistent six-band k‧p Schrödinger-Poisson simulation. This accelerator comprises a triangular potential based six-band k‧p simulator, a hole effective mass approximation (EMA) technique, and an electron analogue version of the self-consistent Schrödinger and Poisson’s equations solver. The outcome of the accelerator furnishes the initial solution of the confining electrostatic potential and is likely to be close to the realistic one, valid for different temperatures, substrate doping concentrations, inversion hole densities, and surface orientations. The results on (001) and (110) substrates are supported by those published in the literature. The overall CPU time is reduced down to around 8% of that without the accelerator. The application of the proposed accelerator to more general situations is projected as well.
Secondly, according to three distinct sets of the bulk oriented Luttinger parameters γ1, γ2, and γ3, the validity of the bulk oriented Luttinger parameters in the six-band k‧p Schrödinger-Poisson self-consistent method is confirmed in Chapter 4.
With the bulk oriented Luttinger parameters, the realistic hole subband structures in (110) p-MOSFETs can be well reproduced in comparison with the recent Shubnikov-de Haas (SdH) oscillation experiment by Takahashi, et al.
Thirdly, the hole mobility change for GPa-level uniaxial stresses along each of three crystallographic directions are distinguished into four contributions: (i) the phonon-limited, (ii) the surface-roughness-limited, (iii) the scattering-time-limited, and (iv) the conductivity-effective-mass-limited mobility changes in Chapter 5. In the same chapter, it is also dedicated to three key strain-related material parameters, namely the Bir-Pikus deformation potentials a, b, and d, which are widespread in magnitude. To improve such large discrepancies, we conduct sophisticated
calculations on <110>/(001) and <110>/(110) hole inversion-layer mobility. We find that, to affect the calculated hole mobility enhancement, a is weak, b is moderate, and d is strong, particularly for the uniaxial compressive stress along the <110>
direction. This provides guidelines for an experimental determination of the primary factor, d, and the secondary factor, b, with the commonly used values for a. In Chapter 6, the user interface (UI) and simulation process of p-NEP are demonstrated.
The resulting subbnad structures, threshold voltage, capacitance, and gate direct tunneling current are discussed. Finally, in Chapter 7 we summarize the conclusions of our works.
References
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Fig. 1.1 Constant energy surfaces of heavy-hole, light-hole, and split-off-hole bulk
Fig. 1.2 Comparison of existing algorithms [6]-[11], e.g. the constant effective mass as the conduction band counterpart, the six-band k‧p method, and the pseudopotential method in combination with the Monte Carlo numerical technique, the iterative numerical technique, or the analytical triangular potential technique.
Simulation in p‐type inversion layer
Fig. 1.3 Demonstration of the trade-off of the calculation efficiency and precision