What is the electronic band structure
In the crystal lattice of diamond or sphalerite structure, each atom is surrounded by 4 nearest atoms, each atom provides 4 valence electrons, and forms a covalent bond with the valence electrons of the nearest atom, so each covalent bond contains one For electrons [Figure 1.1(a)]. At low temperatures, valence electrons are trapped between atoms and cannot move freely, so they cannot conduct electricity. But at high temperature, thermal vibration will excite the bound valence electrons into free electrons, which can participate in the conduction of electric current. While the valence electrons are excited to become free electrons, the original bonding electron pair loses one valence electron, forming a vacancy [Figure 1.1(b)] This vacancy may be filled by neighboring valence electrons, resulting in a movement equivalent to the vacancy. Phenomenon, here we must pay special attention to fill the vacancy must be bound valence electrons to form a vacancy movement, if it is filled with free electrons, the vacancy will disappear instead of moving, called recombination (recombintion). Therefore, the vacancy can be recombined. Imagine an electron-like particle with a positive charge (because the vacancy moves in the electric field in the opposite direction to that of the electron), which is called a hole (Figure 1.1(c)).
Figure 1.1 (a) In a semiconductor material, each atom is surrounded by 4 nearest atoms, each of which provides 4 valence electrons to form a covalent bond with the valence electrons of the nearest atom;
(b) The valence electron in the A valence bond absorbs enough energy, and the excitation becomes a free electron. Before it returns to the vacant valence bond position, it can move between the lattices, so it is called a conductive electron. The bond electron pair loses a valence electron, forming a vacancy, called a hole;
(c) The valence electron of the B valence bond runs to fill the vacancy of the A valence bond, causing the vacancy to move from the A valence bond to the B valence bond position, which can be regarded as the movement of hole.
From the Bohr hydrogen atom model, we know that in an isolated atomic system, the electron energy can only allow discontinuous energy levels to exist. The energy level state can be represented by the principal quantum number (n) and angular momentum quantum number (l). When two atoms are far enough apart, their electronic system does not undergo any quantum interaction (Pauli exclusion principle), so the electrons in the two atomic systems have the same energy state, which is called double simple The doubly degenerate state. But when two atoms are close enough to interact, the originally degenerate electron energy level will be divided into two. The energy level with lower energy is called bonding orbital, and the energy is higher. The energy level of is called antibonding orbital, as shown in Figure 1.2. When N atoms gather to form a solid, the principle of the relationship between the inner electrons (core electrons) of the atoms and the inner electrons of the surrounding atoms The above will not interact with each other, and still maintain the same discrete energy state as the isolated atomic system. The outer electrons of the atom will overlap and interact. At this time, the energy levels are split into N separate but very close energy levels. When N is large, a continuous energy band will be formed. Therefore, when discussing the electronic properties of solid materials, valence electrons play a major role.
Figure 1.2 (a) Hydrogen molecular orbital; (b) Energy band formation; (c) Semiconductor electric band and valence band formation
Figure 1.3 (a) Diamond structure and (b) corresponding insulator characteristic molecular orbital energy state diagram; (c) Graphite structure and (d) corresponding metal property molecular orbital energy state diagram
Figure 1.3 takes a carbon atom as an example to illustrate that when the valence electrons of the carbon atom are bonded by sp3 hybrid orbitals, because the sp3 hybrid orbital bonding configuration has a tetrahedral structure, it will finally be stacked to form a diamond structure solid. Material, the formed band structure shows that there is a forbidden gap with an energy difference of about 6 eV (electron volts) between the molecular orbital that is completely filled with electrons (molecular orbital) and the molecular orbital that is completely unoccupied by electrons, which is Band gap (or energy gap, energy gap), showing the properties of an insulator. But when the valence electrons of carbon atoms are bonded by sp2 hybrid orbitals, because the valence structure of sp2 hybrid orbitals has a planar triangular configuration, it will finally be stacked to form a graphite layered structure solid material, between the atomic layer and the layer. The valence bond is relatively weak, and the formed energy band structure shows the nature of the molecular orbital completely filled with electrons and the molecular orbital completely occupied by no electrons, showing the characteristics of metal.
The actual energy band splitting in semiconductors is more complicated. When the distance between atoms is shortened, the quantum energy states (such as s and p) will interact and overlap. In the equilibrium state, the atomic distance and energy band will split again (figure) 1.2(c)]. The lower energy has 4N quantum states, and the higher energy band has 4N quantum states. Because each atom has 4 valence electrons, there are 4N valence electrons in total. At absolute zero, electrons will start to occupy the lowest energy state, so the lower energy band (namely the valence band) is just completely filled, while the energy state of the higher energy band (namely the conduction band) is not occupied by any electrons. There is no energy state between the top of the valence band and the bottom of the conduction band. Naturally, there will be no electrons distributed in this energy range, which belongs to the forbidden energy region. Therefore, the energy difference between the top of the valence band and the bottom of the conduction band is called Energy gap. Physically, the energy gap value represents the minimum energy required to ionize the valence electrons of the semiconductor material from the valence bonds into free electrons.
Note: The electrons at the top of the valence band are excited by heat to transition to the empty energy level at the bottom of the conduction band, leaving holes. The electrons excited to the conduction band and the holes remaining in the valence band are respectively negatively charged and positively charged free charges, resulting in the unique conduction properties of semiconductor materials.
Figure 1.4 Schematic diagram of the relationship between energy and momentum of direct-gap semiconductor materials
It should be noted that the effective mass of each energy band is not constant. In addition, at the top of the valence band, its effective mass is actually negative. The electrons originally filled the entire energy band from bottom to top, but some electrons at the top were affected by thermal vibration and jumped to the conduction band, making the energy state near the top of the valence band empty. These empty energy states show conduction currents as positive charge carriers participate in conduction. The carriers whose effective mass is positive are called hole. Conceptually, it is easier to deal with hole with positive effective mass, which behave like classic positively charged particles. The top of the valence band and the bottom of the conduction band tend to be parabolic in appearance, and the effective mass of the electron near the bottom of the conduction band is constant, just like the effective mass of the hole near the top of the valence band. When the minimum value of the conduction band and the maximum value of the valence band occur at the same crystal momentum at the same time, as shown in Figure 1.4, this semiconductor is a semiconductor with a direct band gap. When they are not on a straight line, the semiconductor is called an indirect band gap semiconductor.
Relative to the momentum of electrons, the momentum of photons is extremely small. Therefore, when the photon interacts with the electrons in the semiconductor material, the momentum that can be exchanged is extremely limited, which leads to the transfer of electrons between energy bands without the participation of other particles. The change is minimal. In other words, valence electrons in indirect band gap semiconductor materials are less likely to transition from the top of the valence band to the bottom of the conduction band by absorbing the energy of a photon; it is also not easy for conductive electrons to radiate a photon energy to transition from the bottom of the conduction band to the valence. With top. In contrast, direct energy band semiconductor materials can more effectively absorb or emit photons through the transition of electrons between energy bands.
Even amorphous solid materials will exhibit a similar band structure (Figure 1.5). The reason is that the amorphous material still has a certain degree of short range order, and in the extremely short range, the atoms still have a certain degree of regular arrangement. Taking amorphous silicon material as an example, its atomic structure still maintains a tetrahedral valence bond configuration, that is, the valence bond between the atoms is still sp3 hybrid orbital covalent bonding, and the average distance between atoms and the average valence bond angle are still similar to Crystalline silicon material. Therefore, the local electronic wave function still needs to comply with the periodic potential energy established by the regular arrangement of atoms, and the entire bulk electronic wave function can be regarded as the superposition of the local wave functions. Simply put, amorphous material can be regarded as a material made up of many tiny molecules connected in a network. The atomic structure of each tiny molecule is not exactly the same, but there are still corresponding energy band characteristics. There are many defects between tiny molecules. Therefore, the energy band characteristics of the whole amorphous material include the superposition of the band structures of many tiny molecules and the combination of local defect states. Because the wave function of electrons in extremely tiny molecules is affected by the periodic potential energy of atoms, their band structure is still similar to that of crystal materials, with valence band and conduction band characteristics. However, unlike crystalline materials, due to the disordered structure, the extended state (extended state) in some crystalline materials will be transformed into a localized state. The extended energy band of the entire bulk material also includes the local state where the electron wave function is limited to a local area; among them, because electrons or hole occupy the local energy state, they cannot move effectively, and the electrons and hole are only in the material. It can move through overlapping and expanding energy bands, so in amorphous materials, the definition of “mobility gap” (mobility gap) is defined to replace the concept of energy gap of crystalline materials, and the valence band is divided into two parts: valence band mobility boundary energy The following energy bands and valence band tail states (va-lence band tail). The conduction band also includes above the conduction band mobility boundary and conduction bandtail. Amorphous materials contain high-density dangling bonds. These dangling bonds have only one electron, which may capture an electron or release an electron, thus forming a defect, which will form a defect state near the Fermi energy and reduce the carrier. Longevity makes material properties worse. Actually, in the application of amorphous materials, it is often necessary to dope a large amount of hydrogen atoms to passivation the dangling bonds, reduce the defect state, and improve the conductivity.
Figure 1.5 Schematic diagram of electronic energy states of amorphous semiconductor materials