Can bring theory


Theoretical introduction The theory is that the electrons in which the electrons in the crystals are co-cultured in the entire crystal, and the co-culture electron is in the periodic potential of crystal. Movement in the field; the result is obtained: the present guidance wave function of co-cultured electrons is in the form of a Bloch function, and the energy is a number of possible bands composed of quasi-continuous energy.

Theory meaning

The theory of energy belt is the theoretical basis of modern solid electronic technology, which has an inchauble role in the development of microelectronic technology.

can bring an approximate theory of electronic movement in solids. The solid is composed of atoms, and atoms include atomic nuclear and outermost electrons, which are all in a constant movement state. In order to simplify the problem, first assume that the atomic core fixation in the solid is not moved, and according to certain regulations, then further considers that each electronics is in the average potential field of the fixed atomical factor field and other electrons, This simplifies the entire problem into single electronic issues. It is theoretical theory to be the aim of this single electronic approximation. It is first made by F. Brloch and L.-N. Brillun in solving the conductivity of the metal. Specific calculation methods include free electron approximate method, tight buckling approximation, orthogonal plane wavefringing and original method. The first two methods are based on the basis of quantum mechanics, only two extreme situations that are very weak and strong for the atomic real to electronics; the latter two methods are suitable for more general cases, widely used .

Can bring theory


The particles on the solid metal in the solid metal are constituted, which is a metal atom or positive ion, and since the electronization of the metal atom is low, affected by the outside world. The environmental impact (including thermal effect, etc.), valence electron can be detached from atoms, and is not fixed to a ion, while free movement in the lattice, often referred to as free electrons. It is these free electrons to link metal atoms and ions to form a metal. This force is called a metal key. Of course, the solid metal can also be considered as a metal atom (ion) of the equippex sphere to closely deposit into a crystal. At this time, the number of atoms can be up to 8 to 12. There are not much price electrons in metals that are not sufficient to form such a covalent bond. These valences can only be common for the entire metal lattice. Therefore, the metal bond is different from the ion bond; it is also different from the covalent bond (fixed domain bond) of the shared electronics in two atoms. In general, the metal bond belongs to the left domain, that is, a key to sharing the electronic distribution between multiple atoms, but it is a special leaving key, both no direction, and sat.

Qualitative discussion

To clarify the characteristics of the metal bond, the chemist presents the theory of the theory of Mo (Molecular Orbit). It is now only discussed as a metal Li as an example.

Li atom core external electron is 1s2s. Two LIs are close to each other to form a Li2 molecule. According to Mo theory, Li molecules should have four MOs. The energy (σ1s) 2 and (σ1s *) 2 are low, and it is close to LUMO. The more Li atoms participating in the bond, the more different distances have different degrees of force due to different distances of the lattice node, resulting in dividing the electronics level, and the energy level is getting smaller and smaller, the energy level Wrap, eventually forming an energy level that is almost a piece of upper, lower limit, which is to bring. For N Li atom's systems, since the energy difference between 1S and 2S is large, there is two cans without overlapping or overlapping. This band having an unsteaded MO is easily e-to-excitation to an empty Mo, so that Li exhibits good electrical conductivity. This can come to a tape. Any energy level is no longer present between the full belt and the conduction belt is an electronic prohibition area, called a ban. Electronics are not easy to enter the conduction band from full-band pass. Obviously, when the atom is formed, a discrete molecular orbit is formed, and when the atom forms a crystal, the discrete band is formed.

Different metals, due to the different price orbitals and different atomic spacings constituting its atoms, it can bring (empty belt) to partially stacked, which constitutes an unconfilled tape, which is easy to conduct electricity. Rendering a metallicity. From this point of view, as long as there is an unfilled conduction (regardless of whether it is unfilfied, it is formed by the unfilfied band formed by the empty band-full of intercommises). Electron orientation flows to electrically conductive materials. When the temperature is warmed, atomic (ion) vibration on the lattice is intensified, the electron movement is blocked, and the conductive capacity is lowered. The motion of the electron is transmitted in the air-to-domain can cause the metal to have good heat transfer. Sharing the "glue" effect of electrons, so that the metal does not cause fracture when he is being pulled by external force, and exhibits good ductility and plasticity. This is a distinct contrast to the brittleness of the ionic crystals and the fragile cracking. In addition, the exemplary electrons in the metal are easily absorbed and re-emit light, which makes it opaque and has metallic gloss.


The full-air tape in the solid material is referred to as an empty band. When the forbidden bands between the belt and the empty belt are 5 ~ 7eV, the electron is difficult to leap through the forbidden belt, so it is an insulator, such as a disable bandwidth of Diamond to 5.3 eV. However, when the width of the ban belongs in 1 eV (1.602 × 10-19J or 96.48kJ · mol-1), it belongs to the semiconductor material. A typical semiconductor Si is forbidden to 1.12 eV; GE is 0.67 eV.

Isolate atom

Isolated atom's outer electron may take the energy status (energy level), but when the atoms are close to each other, the outer electrons are no longer only protected. The role of the atom is also affected by other atoms, which makes electrons change slightly. When atoms are combined into crystals, the price of the atom's outermost layer is bound to be bound, and it is difficult to distinguish between the original atoms and other atoms. It is difficult to distinguish which atom, which is actually a total of all atoms in the crystal. Co-allocation. When the atomic spacing minimizes, each level of the isolated atom will evolve into a quasi-continuous band consisting of intensive levels. The higher the degree of coexification, the wider the corresponding energy band. Each level of the isolated atom has a belt corresponding to the belt, and all of these can be called allowed. The void between the adjacent two to allow the zone represents the energy state that the crystal cannot occupy, referred to as a ban. When the crystal is composed of n atom (or a few), each band includes N energy, wherein each energy level can be occupied by two spin, so each can accommodate up to 2N. Electronics (see the principle of bubble is incompatible). The energy filled with price electron is called a price band. All quantum states in the price band are covered by electrons, called full belt. Electronics in full belt cannot participate in macroeconomic processes. Can be used as an empty band without any electronics. It is called a guide band that is not covered by electrons. For example, there is a price electron with a price electron, and when n atoms constitute a crystal, only half of the amount of quantum state in the valence band is occupied, and the other is empty. Electronic can participate in the conductive process in the unsuccessful belt, so it is called a conduction.

Solid energy band

The formation of a solid band is achieved by interaction between atoms. When several atoms are close to each other, due to the force of each other, the atomic original energy level is divided by a plurality of strats. Make into a large number of energy levels that can be small, so it can be approximated to continue.

The conductive performance of the solid is determined by its band structure. For a monovalent metal, the price is not full, so it can conduct electricity. For divalent metals, the price is full, but the banned band width is zero, the price band is overlapped with a higher air-zone, and the electrons in the belt can occupy the empty band, and thus can conduct electricity, insulator and semiconductor band. The structure is similar, the price is full, and there is a disabled zone between the price band and the empty band. The disable band width of the semiconductor from 0.1 to 4 electron-volt, the ban on the insulator from 4 to 7 electron volts. At any temperature, due to thermal movement, the electronic general in full belt has some sufficient energy to excite into the empty band, making it a conduction belt. Due to the large width of the insulator, the number of electrons that excited to the empty band is slightly insignificant at room temperature, and the macroscopic manifestation is poor conductivity. The semiconductor has a smaller width, and the electrons in full belt can be excited into the empty band, and the macroscopic appears to have a large conductivity (see semiconductor).


The theory is elucidated to have a significant increase in the motion law of electrons in the lattice, the solid conductive mechanism, the alloy's part of the nature, and the combination of metals. Achievements, but it is an approximate theory, there is a certain limit. For example, the conductivity of certain crystals cannot be used in theoretical interpretation, i.e., electron coexisting model, and single electron approximation is not suitable for these crystals. After the multi-electronic theory is established, the results of single electron can be used often as the starting point of multi-electronic theory, and the two theories are complementary when solving modern complex problems.

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