Created it, 05/10/15
Update it, 06/01/13
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SEMICONDUCTORS 2 “3rd PART”
The semiconductors used for the manufacture of the of the same devices name are almost never of the intrinsic type. With the intrinsic semiconductor is generally to add a certain quantity of foreign substances who spread themselves in all the crystal and modify the electric state of the crystalline reticle. For this reason, we will examine the consequences of the presence of foreign atoms, in the crystal lattice of intrinsic semiconductors.
Let us suppose that it is possible to intervene directly in the structure of a tiny very pure and perfect germanium crystal, inside of which there are a number well defined of free electrons and an equal number of holes.
In this crystal and constantly, part of the free electrons returns to the valence band, following losses of energy due to the shocks, but at the same time, other electrons pass from the valence band to that of conduction. If the temperature of the crystal remains constant, the number of the free electrons and the holes remain him also constant.
Let us imagine now that in the space of the crystalline reticle, there are only two free electrons and two holes. While intervening in the structure of the crystal, one replaces three germanium atoms by as many antimony atoms (figure 1).
It is of course an example of which the only goal is to facilitate comprehension. In practice, it never happens that a crystal placed at the normal ambient temperature, has only two free electrons and two holes and even less one number of antimony atoms close to that to the free electrons. Actually, the free electrons and the holes contained in one cubic centimeter (cm3) of crystal are several thousands of billion and the atoms of antimony are about in a ratio of 1 out of 1 000 000 of germanium atoms.
The introduction of impurities (here of antimony) into a semiconductor is called doping. This semiconductor is then doped.
Antimony is an element which belongs to the group V of the classification of MENDELEYEV (see the lesson semiconductor the preceding one). The external layer of its atom comprises five electrons indeed. Four of the latter will contribute to restore the covalent bonds with the close germanium atoms, while the fifth, not finding a place in the covalent bonds, will remain related to its own atom.
The bond between the fifth outer-shell electron of antimony and the corresponding atom is not however as extremely as the covalent bonds. It will thus break easily and the fifth electron will enter very quickly the band of conduction to go in the free electrons of the crystal.
Let us return to the example given previously which consisted in substituting three germanium atoms by three antimony atoms. By this operation, one introduces into the reticle of the crystal, three new free electrons which, added to the two first, change the number of the free electrons to five.
One could think that the reticle thus includes/understands five free electrons and two holes. Actually, certain time after substitution of germanium by antimony (and this when the temperature remains constant), there can be in the crystal only four free electrons and one hole (figure 2).
One explains this phenomenon by the fact that a certain number of free electrons occupy an equal number of holes, which inevitably involves the disappearance of the latter.
Ultimately, the operation of substitution of germanium atoms by antimony atoms involves well an increase in the number of free electrons which does not correspond any more, at a given time, with the sum of the free electrons brought by antimony and those existing already. There is recombination of part of the free electrons and holes to form electrons of valence.
Taking into account what has just been known as, we can already draw the following rule :
For any increase in the free electrons in a semiconductor crystal at constant temperature, there is a reduction in a number of holes, so that the product of the number of free electrons by the number of holes remains constant.
In the example of figure 1, we saw at the beginning two free electrons and two holes.
The product is thus of 2 x 2 = 4
After substitution of the three germanium atoms by three antimony atoms, the number of the free electrons increases, passing from 2 to 4, while the number of holes falls, passing from 2 to 1.
The product remains unchanged, i.e. 4 x 1 = 4.
One obtains a similar situation by replacing the three germanium atoms by three indium atoms (figure 3).
Indium is an element which belongs to group III of the classification of MENDELEYEV (see the lesson semiconductor the preceding one). The external layer of its atom indeed comprises three electrons, i.e. one in less compared to the four required to supplement the covalent bonds with the close germanium atoms. After substitution of the three germanium atoms by three indium atoms, we have inside the crystalline reticle, three covalent bonds weakened by the absence of an electron, therefore formation of the three new holes.
The weakened bonds are represented figure 3 and 4, by, the energy tear lines of the indium atoms to the one of the four surrounding germanium atoms.
The holes which appear with the weakened bonds are represented by small white rounds, as those which were formed in the covalent bonds, following the release of an electron of valence.
If one adds the three holes introduced with the indium atoms to the two other holes existing into intrinsic germanium, should have five free holes and two electrons to us. Actually and always at a constant temperature, one cannot have, after substitution of germanium by indium, that four holes and only one free electron (figure 4).
There still, one explains this phenomenon by the fact that part of the free electrons falls into the holes and there remains.
Ultimately, the operation of substitution of germanium atoms by indium atoms involves well an increase in the number of holes which does not correspond any more, at a given time, with the sum of the holes brought by indium and those existing already. There is recombination of part of the holes and free electrons to form the covalent bonds.
We can still draw the following conclusion from it here :
For any increase in holes in a semiconductor at constant temperature, there is a reduction in free electrons, so that the product of the number of the holes by the free electrons remains constant.
In the example of figures 3 and 4, as in that of figures 1 and 2, the initial product of the holes by the free electrons is equal to 4.
After substitution of the three germanium atoms by the three indium atoms, the number of the holes increases, passing from 2 to 4, while that of the free electrons decreases, passing from 2 to 1.
The product remains quite unchanged : 4 x 1 = 4.
Taking into account what has just been known as, one can already decide between the semiconductors in three distinct categories.
- Intrinsic semiconductors having a number of free electrons equal to that of the holes (figure 5-a).
- The semiconductors N, obtained while introducing into a semiconductor crystal of the atoms of elements belonging to the group V of the table of MENDELEYEV. Here, the number of the free electrons is quite higher than that of the holes (figure 5-b).
- The semiconductors P, obtained while introducing into a semiconductor crystal of the atoms of elements belonging to group III of the table of MENDELEYEV. Here, the number of the holes is quite higher than that of the free electrons (figure 5-c).
The elements of the group V of table MENDELEYEV used to form the semiconductors N are antimony, arsenic and phosphorus ; they are called donors.
The elements of group III used to form the semiconductors P are indium, boron, gallium and aluminum ; they are called acceptors or receivers.
Let us see now how electric conduction in the three types of semiconductors enumerated is carried out above.
The figure 5-a represents a small block of intrinsic germanium crossed by the current which a pile produces. One notices inside the semiconductor, the birth of two flows of electric charges.
First consists of free electrons which go from the end B (negative side of the pile) at end A (positive side of the pile). The second flow consists of holes which while moving from one atom to another inside the crystalline reticle, go in the direction opposed to the precedent, i.e. end A towards the end B. two flows consist of equal quantities of electric charges, since in the intrinsic semiconductors, the number of the free electrons is equal to that of the holes.
The connections placed between the end of the semiconductor and the pile on the contrary are crossed by only one flow only made up by electrons.
Let us announce that the current produced by a pile is continuous and that its intensity is invariable in each section and in any point of the driver. That means that at any moment, the same quantity of electrons enters the discussion thread by end A and leaves by the end B. the same quantity electrons also leaves and enters by the ends of the small block (figure 5-a).
To simplify all that, let us imagine that inside the semiconductor and at any moment, an electron leaves by end A and that another electron enters by the end B. We thus note that the entering number of the electrons is always equal to that of the electrons leaving.
The outgoing electron belongs to the band of conduction, i.e. it is about a free electron. Thus, not having bonds with the crystalline reticle, it can freely leave the semiconductor and move towards the positive one of the pile.
At the other end, the entering electron meets the holes which can move in the reticle and concentrate in the end connected to negative of the pile, but cannot however not leave the reticle. These holes are indeed primarily made up of empty places in the valence band of the atoms of the semiconductor.
When the electron coming from negative from the pile meets the holes, it occupies an empty place in the valence band, thus making disappear a hole.
While summarizing what has just been known as, we can draw the following conclusion :
When an electron leaves and that another enters, there is permanently in the semiconductor the loss of a free electron and the disappearance of a hole.
If this process repeated once as many as there are free electrons or holes, one could expect a certain moment that the semiconductor remains without free electrons and holes. Actually, the number of free electrons and holes present in the reticle depends exclusively on the temperature of material. Indeed, if the temperature of the semiconductor block remains constant, for each couple disappeared electron-positron pair, it is formed in a point of the semiconductor another free electron and another hole.
Thus, two flows, that of the free electrons (which go from the end B at the end A) and that of the holes (which in the same semiconductor circulates in direction reverses) are fed in continuity, as long as the production of current by the pile lasts.
In a block of semiconductor N crossed by the current delivered by a pile (figure 5-b), the phenomena of electric conduction differ from those which have been just described since the number of free electrons is higher than the number of holes. In this case, it is formed inside the semiconductor two flows of electric charges, one being stronger than the other. The free electrons which constitute the higher flow are called carrying majority, while the holes which constitutes lower flow are called carrying minority. There is indeed, in the semiconductor N, much more free electrons than of holes.
One can thus easily understand that most of the electrons coming from the end B, crosses the semiconductor block easily, while always remaining in the band of conduction.
In the semiconductor P (figure 5-c), it is also formed two flows, but this time, the strongest flow consists of holes (carrying majority) and the weakest flow, of free electrons (carrying minority). It is thus not very probable that a free electron can cross all the end-block B to that of A.
The free electrons which leave the semiconductor and the holes which go from one end to the other of this same semiconductor occur in general near face A. From this point, the two loads opposite separate. The electron moves towards the positive pole of the pile through the connection and the hole moves towards the end B of the block, where it will disappear as soon as its place is occupied by an electron coming from negative from the pile.
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