Research On Energy Band Structure And Carrier Mobility Of Uniaxial Strained Silicon

Due to high carrier mobility, energy band structure adjusting, and processcompatibility with current silicon process technology, strained silicon technology hasbecome the preferred method to enhance the carriers mobility forhigh-speed/performance semiconductor transistors and integrated circuits. The way tointroduce strain to the channel, including substrate-induced biaxial strain andprocess-induced uniaxial strain. The uniaxial strain have many advantages over thebiaxial strain, such as large hole mobility enhancement at low stress and high verticalelectric field, a small threshold voltage shift, and process easy to implement, whichmake uniaxial strained silicon attracted much attention. The main reason of uniaxialstrained silicon enhancing the carrier mobility, is the modification of the energy bandstructure of silicon under uniaxial stress. Therefore, it is siginificant both in theory andpractice to research the energy band structure and carrier mobility of silicon underdifferent (type, direction, and magnitude) stress configurations.In this dissertation, the effect of uniaxial stress on the energy band structure andhole/electron mobility for silicon are investigated, and extend the research to thegermanium. The primary research work and achievement of the dissertation are asfollows:(1). The conduction band (CB) structure of silicon material under arbitrary uniaxialstress was modeled through degenerate perturbation theory, based on Schrodingerequation. By using the obtained E~k model, the relationship of the CB structure to stressand crystal orientation was elaborated for the commonly used uniaxial stress(along the[100],[110], and [111] crystal orientation) for both compressive and tensile stress. Thecorresponding wave vector k for the CB minimum, the degeneracy of the CB energyvalley, and uniaxial stress induced CB structure change (such as the energy level shift,the splitting energy of CB edge energy level and the warping of CB curves) werequantitative evaluated. The spliting energy of conduction band for silicon under [100],[110] direction uniaxial tensile stress, are consistent with the results of first principlemethod and the electron effective mass for silicon under [110] direction uniaxial tensileshows a good agreement with empirical pseudopotential method calculation. Theobtained quantitative results can lay a foundation for the research of electron mobility ofuniaxial strained silicon.(2). The valence band (VB) structure of silicon material under arbitrary uniaxial stress was modeled by employing the deformation potential theory and a six-bandstress-dependent k·p Hamiltonian, and taking into account spin-orbit coupling. Usingthe obtained E–k relation of valence band, the relationship between VB structure andstress and crystal orientation is clarified—taking [100],[110], and [111] directionuniaxial stresses as example. The shifting, splitting of VB edge energy level and thevariation of effective masses at the gamma point were obtained for different uniaxialstress configurations. The calculated isotropic effective masses in unstressed areconsistent with those reported in the literature. The obtained quantitative results of VBstructures can lay a foundation for the study of hole mobility of uniaxial stained silicon.(3). Using these obtained energy band structure parameters, the models ofdensity-of-states effective mass, conductivity effective mass, as well as density of statesfor electron/hole were established. The major scattering mechanisms, acoustic phononscattering, ionized impurity scattering and intervalley scattering for electron, andacoustic phonon scattering, ionized impurity scattering and non-polar optics-phononscattering for hole were taken into account in the mobility computation. The scatteringrate of electron/hole were presented. Finally, the relationship between electron/holemobility and stress and crystal orientation was clarified. The electron/hole mobility as afunction of doping concentration was analyzed. The direction electron mobility ofsilicon under [100] uniaxial stress, are in good agreement with Monte Carlo simulationmethod. The obtained results can provided valuable references for the study and designof uniaxial strained silicon devices.(4). The impact of uniaxial stress on the CB energy valley (Γ valley, Δ valleys,and L valleys) of germanium was investigated by deformation potential theory. The VBstructure model of germanium in uniaxial stressed was established by using a six-bandk·p model and coupled with deformation potential theory, and the spin-orbit couplingwas included. The variation of valence band edge energy level was analyzed. Theuniaxial stress induced energy band structure change, such as CB splitting energy, VBsplitting energy, band-gap, and hole effetive mass (direction, isotropic, anddensity-of-state effective mass) were obtained. Based on these energy band parameters,the density-of-state for CB/VB, intrinsic carrier concentration, and hole mobility werecalculated for different stress. The obtained quantitative results can provide referencefor the design and modeling simulation of uniaxial strained germanium device.