TABLE OF CONTENTS In Fig. 2.10 we have shown the electronic band structure of Si. It has been calculated with a sophisticated method known as the pseudopotential technique, which will be discussed in this section. Comparing these results with the nearly free electron band structure in Fig. 2.9 we notice that there are many similarities between the two. The nearly free electron band structure is basically a parabola redrawn in the reduced zone scheme. In the other case the band structure is computed by large-scale numerical calculations using supercomputers. The question is now: why do the two band structures, obtained by completely different methods, look so similar qualitatively? The answer to this question lies in the concept of pseudopotentials.
The electronic configuration of a Si atom is 1 s 22 s 22 p 63 s 23 p 2. When Si atoms form a crystal we can divide their electrons into core electrons and valence electrons as pointed out in Sect. 2.1. In crystalline Si the 1 s, 2 s, and 2 p orbitals are completely occupied and form the core shells. The outer 3 s and 3 p shells are only partially filled. Electrons in these shells are called valence electrons because they are involved in bonding with neighboring Si atoms. The crystal structure of Si at ambient pressure is similar to that of diamond. The tetrahedral arrangement of bonds between a Si atom and...
