Energy-band Structure In Strained Germanium:High-order K·p Method

As device scaling reaches its outermost limits, using high-mobility channel materials has emerged as an effective method for dramatic improvements in the performance of metal-oxide-semiconductor field-effect transistors(MOSFETs) and for the continuation of Moore's Law. Germanium(Ge) Complementary Metal Oxide Semiconductor(CMOS) is promising for much higher intrinsic mobility for both n- and p-type carriers compared to Si. In addition, as a group ? element, Ge has similar physical and chemical properties to Si, and is fully compatible with the traditional CMOS process. Ge channel MOSFETs have been identified as one of the possible directions for channel engineering. Ge has garnered much attention not only for its high mobility of holes and electrons but also for its unique optical property. The band structure determines several important characteristics, in particular its electronic and optical properties. However, most researchers focus on material preparation and device structure designs, there are few reports about systematical research on the band structure of strained Ge.The basic physical definitions are introduced in Chapter 2, such as the strain and stress tensors and how they are related in cubic semiconductors. Using group-theoretic methods, special focus is put on the consequence of the strain-induced reduction of symmetry for band structure calculations and of the effect of strain on the first Brillouin zone, which is great helpful for the understanding of energy level splitting under strain. Based on the Schrodinger equation and k·p perturbation theory, Chapter 3 give a detailed introduction on 30 k·p method, and the energy bands of Ge, throughout the entire Brillouin zone, have been obtained by diagonalizing a k·p Hamiltonian referred to 15 basis states at k=0. Based on the local-density approximation of density-functional theory, including a GW correction and the relativistic effects, the electronic energy band structure of strained and unstrained Ge is examined using a first-principles-optimized full-zone k·p analysis. In Chapter 4, we systemically investigate the effect on the energy-band structure of biaxially strained(parallel to the(001),(110) and(111) planes) and uniaxially strained(along the [001], [110] and [111] directions) Ge, from which the bandgaps at L, ? and X symmetry points and carrier effective masses are extracted. The calculation results shows that biaxial tension parallel to(001) is the most efficient way to transform Ge into a direct bandgap material among all tensile strains considered, and the transition occurs for an in-plane strain of 1.6% with the bandgap about 0.56 e V. [111]-tension is the best choice among all uniaxial approaches for an indirect- to direct-bandgap transition of Ge. The heavy hole effective mass of biaxially compressive strained Ge is nearly 2/3 lighter than that of unstrained Ge when the Ge fraction is less than 0.7. Our research works on band structure, energy level splitting and carrier effective mass, are essential to prepare for the calculations for carrier mobility and density of states, as well as high-mobility device design.