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Links between Atoms :

In this lesson, we will begin to deal with semiconductors, materials that have made important devices (diodes, transistors, integrated circuits ...) able to perform multiple and complex functions.

To fully understand the operation of semiconductor devices, it is necessary to have a good knowledge of the structure of the materials used in their manufacture.

We will begin with a quick review of the internal structure of the crystals.

Throughout this development, we will often use figures to represent in an analog way the phenomena that occur in semiconductors. The use of these figures is very useful whenever it is not possible to directly visualize the phenomenon to be studied. Even if this representation is always approximate and does not faithfully reproduce the phenomenon, it can nevertheless, in a certain way and for a given time, represent as much as possible the known phenomena.


All experiments in chemistry show that the atoms of different bodies attract or repel each other when they are placed at a small distance from one another.

It should be noted immediately that when it comes to distance between atoms, the angstrom (symbole Å ) equivalent to the ten millionth of a millimeter or the millimicron (symbol mµ) corresponding to one millionth of a millimeter is used as the unit of measurement.

The attraction that manifests itself between the atoms is called VAN DER WAALS attraction ; it is in general relatively weak and begins to be exercised only when the atoms are at a distance of a few angstroms (Figure 1).


At a shorter distance, when the external orbits of the electrons touch each other, a narrower bond may be established, called a chemical bond, or on the contrary a repulsive force may occur.

The attraction of VAN DER WAALS is essentially a phenomenon of electrostatic nature, due to the electric force of attraction, exerted between the electrically positive nucleus and the electrons of the neighboring atom, electrically negative.

The chemical bond and the repulsion are on the contrary due to the constitution of the last layer of electrons, rotating around the nucleus, that is to say the outer layer. In general, the inner layers of electrons are stable and are not affected by chemical and electrical phenomena.

The outer layer, on the other hand, may have some instability, because it can lose or gain electrons or pool them with the electrons of the outer layer of a neighboring atom.

To explain the formation of the chemical bond in some cases and in others repulsion, we must refer to a physical principle, known as the principle of PAULI.

According to this principle, in each electronic orbit placed around the nucleus of an atom, there can only be one electron with a determined energy. However, if we admit that all the electrons are exactly equal to each other and that an electron on its orbit is also turning on itself in one direction or the other, we can modify the previous expression of the principle of PAULI and write: on the orbit of a nucleus, it can not turn more than two electrons and these turning on themselves, must turn in opposite directions from one another (principle of PAULI generalized on which we we will base it in the following explanations).

We will admit this principle without demonstrating it because it requires a very deep knowledge of nuclear physics beyond the scope of this lesson.

Now imagine that two hydrogen atoms are getting closer to each other. The atoms of hydrogen can be represented as in Figure 1 ; they consist of a nucleus and a single electron rotating on the layer K (Figure 2 : uranium atom comprising here, 7 layers on which electrons gravitate, the layer K has 2 electrons in this example).

When the nuclei of the two atoms are at a distance of a few angstroms (approximately 5 Å), the attraction of VAN DER WAALS begins to appear.


If the distance decreases, the electrostatic attraction increases and from 0.75 Å, the chemical bond intervenes. This bond ensures the stable union of the two atoms and thus determines the formation of the hydrogen molecule.

The chemical bond is not only constituted by a strong electrostatic attraction between the nucleus and the electrons, but also by an exchange of energy between the atoms, exchange occurring via the electrons passing successively and indifferently from the orbit from one atom to the orbit of another atom.

During the continuous passage of electrons from one atom to another, it obviously happens that in the orbit of a hydrogen atom there are two electrons instead of one.

This possibility is evoked in the principle of PAULI generalized since in each orbit one can find two electrons.

Let us now consider another case: imagine that two helium atoms have approached each other.

Helium atoms consist of a nucleus and two electrons gravitating on layer K This layer, that is to say the layer closest to the nucleus, consists of a single orbit.

For helium, this layer is complete because it includes two electrons and can not, according to the principle of PAULI to accommodate others.

When the nuclei of the two helium atoms are at a distance of a few angstroms, the attraction of VAN DER WAALS can be manifested ; however, at a lower distance, a strong repulsion takes place instead of the chemical bond. This repulsion between the two helium atoms is due to the interaction of their electrons. Indeed, we know that electrons all have the same charge and that they repel each other. On the other hand, it is impossible to obtain a stable distribution of electrons around the two nuclei as in the case of hydrogen, because according to the principle of PAULI generalized, the orbit of each helium atom is considered as complete.

So far we have only examined single atoms, with only one layer of electrons, the K layer.

In the case of atoms with two or more layers (figure 2), one must not only take into account the principle of PAULI but also the fact that the maximum stability of the electrons is obtained, when the outer layer comprises eight electrons gravitating on four orbits.

The elements having eight electrons on the outer layer are grouped in group IX of the MENDELEYEV table given in Figure 3


On the other hand, if an atom with less than eight electrons in an outer layer, different from the K layer, it will tend to accept the chemical bond with other atoms. This ability of the atom to bind chemically with other atoms is called valence. There is a certain relationship between the valence of an atom and the number of electrons that includes its outer layer.

  • - When the outer layer is complete with eight electrons, it is said that the atom has a zero valence..

  • - When the outer layer comprises only one electron, or seven electrons, it is said that the atom has a one valence or that it is monovalent.

  • - When the outer layer comprises only two electrons or six electrons, it is said that the atom at valence two or even that it is bivalent.

  • - When the outer layer comprises only three electrons or five electrons, it is said that the atom at valence three or that it is trivalent.

  • - Finally, if the outer layer comprises only four electrons, it is said that the atom at valence four or that it is tetravalent.

This criterion for distinguishing valences, however, is not always valid; there are even many exceptions.

For example, antimony, arsenic and phosphorus have only five electrons on their outer layer and can therefore be trivalent according to the above criterion, but may also have a valence of five. In this case, they are called pentavalent.

There are also atoms that can have a valency six (hexavalent) and a valence seven (heptavalent).

It is not necessary to go into the general concept of valence, a concept linked to very complex research coming out of this lesson, but it is useful to highlight the chemical link between the atoms of the same element.

We have previously considered the link between two hydrogen atoms when their respective nuclei are at a distance of 0.75Å. This particular type of chemical bond between atoms of the same species is called covalent bond or homopolar bond.

Let us see how a covalent bond can be established between atoms, having more than two electrons and less than eight in their outer layer.

Take for example a few atoms of a tetravalent element, that is to say an element having four electrons on its peripheral layer.

To simplify the representation, it has been shown in the drawing of Figure 4-a that the nucleus of the atoms and the four peripheral electrons (the electrons of the other layers are not concerned).


Of course, in reality the four peripheral electrons of each atom occupy several orbits, but for the sake of clarity it suffices to represent only one.

Between the peripheral electrons, four holes have also been drawn, which represent the free spaces in which four other electrons could come, so as to complete the outer layer.

The sketch of figure 4-a can represent all the atoms of the tetravalent elements classified in group IV of the table of MENDELEYEV (figure 3), that is to say the carbon, the silicon, the titanium, the germanium, the zirconium, tin, hafnium and lead.

Now imagine that four tetravalent atoms are approaching an atom of the same type. When these atoms are a few angstroms away, the forces of VAN DER WAALS manifest themselves ; but at a shorter distance a covalent bond is established between the atom considered and each of the four atoms which have approached each other.

The four covalent bonds are shown in Figure 4-b by the four dashed rays. This phenomenon is easy to understand. Indeed, in the center we have an unstable atom with four electrons on the outer layer that can either recover or give in.

Near these atoms, four other atoms of the same type came closer until the orbits were in contact with each other.

Naturally the central atom thus fills its four holes (see Figure 4-a) with the unstable electrons of the other four atoms

The central atom thus has its complete outer layer with eight electrons. In reality, these eight electrons do not belong exclusively to the same atom; they are subdivided into four pairs and each pair of electrons clearly belongs to the central atom and a peripheral atom.

The covalent bond existing between the central atom and the four peripheral atoms consists of a repeated exchange of energy due to the passage of electrons from one atom to another.


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