Question: Hi, In semimetals the conduction band edge is very slightly lower in energy than the valence band edge. A small overlap in energy of the conduction and valence bands leads to small concentration of holes in the valence band and of electrons in the conduction band. My question is: Why the concentration of holes small in valence band and the electrons concentration in conduction band.
Answer: Firstly, thank you for your question. As we'd already known about semimetal, two distinct energy bands overlap slightly at the Fermi level. So we can say that semimetal is metal but the overlap of two bands at Fermi level is too small. If we are going to talk about holes and electrons concentration of valence band and conduction band respectively, we are talking about only the part that these bands are overlap at Fermi level. Since slightly overlap of two bands at Fermi level, the concentration of holes and electrons is small. But semimetal is just like semiconductors, high temperature can produce more electrons in conduction band and more holes in valence band.
Question: What is difference between real lattic and reciprocal lattic?
Answer: Simply, reciprocal lattice tell diffraction pattern of the crystal, whereas real lattice tell microscope structure of the crystal. If a1, a2, a3 are the axis vectors of the real lattice, and b1, b2, b3 are the axis vectors of the reciprocal lattice, the relationship between these two lattices is followed by these equations…
b1=2π(a2×a3)/(a1∗a2×a3)
b2=2π(a3×a1)/(a1×a2×a3)
b3=2π(a1×a2)/(a1×a2×a3)
Question: What is advantage of point symmetry in Brillouin zone (BZ) for band structure?
Answer: This is very good question. From the point of materials science, brillouin zone can be say primitive cell in reciprocal space. If there is a high symmetry point in BZ, the bands will be touch at that point in the band structure. This touching depend on how high the symmetry of that point. So to get your point, the higher the symmetry of the point in the BZ, the gap will be smaller and the bands will be touched at that point.