# 1-1. Energy band diagram

Free electrons in a material allow a free flow of electricity. Although being part of atoms, free electrons are so loosely bound to atoms in a material, they can move about freely.
In classical physics, the Bohr model is a physical model that consists of a small atomic nucleus of protons and neutrons around which electrons travel in multiple orbits. Each element has a fixed number of electrons, which are placed from the orbit closest to the nucleus. For example, silicon (Si), a semiconductor, has 14 electrons. Figure 1-3 shows the Bohr model of silicon.

Since electrons have a wave nature, they are stable only on an orbital with a radius that is an integer multiple of their wavelength. Therefore, electrons move in discrete orbitals as represented by the Bohr model.
The electron orbital in a single isolated atom has an extremely narrow energy band. However, according to the Pauli exclusion principle, two or more electrons cannot occupy the same orbital. Therefore, as the state of matter changes from a single atom to a molecule to a crystal,　their electron orbitals come to form a continuous band structure of energy levels
The closer the electrons are to the nucleus, the more tightly bound they are to the nucleus. The most loosely bound electrons in the outermost shell are called valence electrons. This outermost shell is called the valence band. The area beyond the outermost shell is called the conduction band. Since electrons have a wave nature as described above, there is an energy gap between the valence and conduction bands where electrons cannot exist. This energy gap is called a forbidden band.
Electrons in a valence band cannot move freely since they are bound to the nucleus. For these electrons to move freely between atoms, they have to absorb enough heat or light energy to be excited from the valence band to the conduction band (e.g., from the M shell to the N shell). The minimum amount of energy required for this electron excitation is the band gap.

Figure 1-4 shows the energy bands of insulators, semiconductors, and metals.
In the case of insulators and semiconductors, the outermost shell occupied by electrons is called the valence band, and the shell that is not populated by any electrons is called the conduction band. In the case of metals, not all the orbitals in the outermost conduction band are populated by electrons. Because metals have empty orbitals, electrons are free to move in metals.
The valence and conduction bands are separated by a forbidden band where electrons cannot exist in a stable state. The energy width of the forbidden band is called a band gap. Semiconductors have a narrower forbidden band (i.e., smaller band gap) than insulators.
Insulators and semiconductors have a Fermi level between the conduction and valence bands. The Fermi level of metals lies inside the conduction band. Although the Fermi level is defined as the energy level at which an orbital has a 50% probability of being occupied by electrons at any given time, the Fermi level of insulators and semiconductors falls in the forbidden band where no electrons exist.