Semiconductor

The conductivity of an intrinsic (pure) semiconductor depends on its temperature, but its conductivity at room temperature is very low.  In the same fashion, no important electronic device can be developed by those semiconductors.

Therefore, it is necessary to improve their conductivity.  This is done using impurities in those semiconductors.

Doping

When appropriate impurities in a pure semiconductor are added to an extremely small amount such as a few parts per million (ppm), its conductivity increases.

These types of materials are called extrinsic semiconductors or Impurity semiconductors.  Carefully mixing the desired impurities is called doping and the impurities are called nuclear dopants.

This type of material is called a doped semiconductor.  The dopant should be such that it does not distort the lattice of the original semiconductor material.  It should only enclose very few basic semiconductor atomic positions in the crystal. 

An essential condition to achieve this is that the molecules of the dopant and the molecules of the semiconductor material are approximately the same size.

Two types of dopants are used to induct Si or Ge. 
(i) Pentavalent (valency 5)-  Such as arsenic (As), antimony (Sb), phosphorus (P), etc.

(ii) Tri valence (valency 3)-  Such as indium (In), boron (B), aluminum (Al), etc.

Now we will discuss how the number of charge carriers in semiconductors changes by doping due to which the conductivity of that semiconductor changes. 

Si or Ge are members of the fourth group of the periodic table, so we select the nearest third or fifth element for doping, expecting and cautioning that the size of the atom of the element to be dopped.It is almost equal to the Size of an atom of Si or Ge. 

The interesting fact is that the trivalent and pentavalent elements used for sedimentation, after doping, form two completely different semiconductor materials from each other, which are described below. 

n-type semiconductor

Suppose we dopped Si or Ce (valency 4) with a pentavalent (valency 5) element like (figure shown below).

When an element of +5 valence takes its place by replacing one atom of Si, four of its electrons bond to the four Silicon atoms, while the fifth electron is attached to the parent atom by a weak bond.  This is because the four electrons participating in the bond for the fifth electron are parts of the effective core of the atom. 

As a result, the ionization energy required to release this electron is very low and at the normal orbital temperature, it is free to move freely in the lattice of the semiconductor. For example, to free this electron from an atom, it requires ~0.01eV in Germanium and about 0.05 eV in Silicon.

Conversely, energy is required to transfer an electron from the forbidden band (about 0.72eV in germanium and about 1.1 eV in Silicon) to the chamber heat in a rough semiconductor. 

Thus the pentavalent element provides an extra electron for the conductive electromagnet conduction. Hence it is called donor impurity.

The number of electrons provided for the conduction of electromagnetic atoms is strongly dependent on doping.  It does not depend on the surrounding temperature.  In contrast, the number of free electrons (with the same number of holes) generated by the Si atom increases very slightly with heat.

The total number of conductive electrons in a dopped semiconductor is due to the contribution of n_e donors and electrons generated for personal reasons (by heat), and the total number of holes n_h is generated only by the private source.  But the increase in the rate of recombination of the holes is due to the increase in the number of electrons. 

This results in a further reduction in the number of holes. Thus by the appropriate level of doping the number of conducting electrons can be increased compared to the number of holes.

Thus, in a pure semiconductor, electrons become majority charge carriers and hole minor charge carriers when dopped with five-coordinator dopants, hence this type of semiconductor is called an n-type semiconductor.

N_e >> n_h for an n-type semiconductor.

p-type semiconductor

p-type semiconductors are formed when tri-valent impurities to group-III in Si or Ge (tetra-valent);  Such as AL, B, In, etc. are dopped, as shown in Figure below.

Dopants have less of an external electron than Si or Ge and hence this atom can bind to Si atoms on three Sides, but the fourth is not able to form a solid due to the lack of available electrons required to form bonds.

Hence there is a vacancy or hole in the bond between the trivalent atom and the fourth nearest atom which is shown in the figure above.  Because the neighboring Si atom in the lattice seeks an electron in place of the hole, an electron in the outer cell of the nearest atom can fill the junction to fill this vacancy, creating a hole in its own place.  This hole is available for conduction.

It is worth noting that, by sharing the electron with the neighboring Si atom, the trilogy heterogeneous atom is effectively negatively charged, and all its valence bonds are complete. 

Therefore, in ordinary language, the dopped atom of a p-substance with its associated hole is called a negative charge core. 

It is clear that a receptor atom (N_A) gives a hole. This hole is in addition to the doped generated holes, while the source of conduction electrons is only pure generation. 

Thus, for such a substance, the hole is the majority carrier and the electron is the minority carrier.  That’s why triangular conductors that are doped with impurities are called p-type semiconductors. 

The recombination process in p-type semiconductors reduces the number of electrons generated by n_i to n_e.  Hence for p-type semiconductors n_h >> n _e.

It is worth noting that the crystal maintains overall negative damping because the amount of charge on the extra charge carriers is the same and opposite to the amount of charge on the ionized crystals in the lattice. 

Due to the abundance of polymeric stream carriers in nonrenewable semiconductors, there are more opportunities for the minority carriers generated by heating to meet the majority of carriers and thus perish.  Therefore, dopants help in reducing the net concentrations of minority carriers indirectly by adding more types of current carriers, which become the majority carriers. 

The energy band structure of semiconductors is affected by doping.  In the case of external semiconductors, there is also an extra energy state (E_D) due to donor impurities and an additional energy state (E_A) due to receptor impurities.

In the energy band diagram of n-type Si semiconductors, the donor energy level E_D is slightly below the bottom E_C of the conduction band, and some electrons enter the conduction band at very low energy supplies from this level. Most donor atoms are ionized at room temperature, but only very few (~ 10–12) atoms of Si are ionized.

Thus, as shown in Figure below (a), most of the electrons in the conduction band come from donor impurities.  Similarly, in p-type semiconductors, the receiver energy level is slightly above the E_A valence band [see Figure below (b)].

Even with a very low energy supply, an electron from the valence band fills the gap at the level of E_A and makes it negative to the receiver. [Alternatively, we can also say that by supplying very little energy, the hole energy can move from the E_A to the connective band.  On receiving energy, electrons move upwards while holes fall downwards.]

At normal room temperature, most of the receptor atoms get ionized and holes in the valence band are left.  Thus the density of the holes in the connective band at room temperature is mainly due to inaccuracy in the extrinsic semiconductors.  In thermal equilibrium, the concentrations of electrons and holes in semiconductors are expressed as follows. 
      n_en_h = n₁²
     Although the above description is approximate and envisaged as a whole, it is helpful to understand the difference between metals, insulators, and semiconductors (intrinsic and extrinsic) in a Simple way.  The difference in resistances of C, Si, and Ge depends on their conduction and the energy gaps between the connective bands.  The energy gaps for carbon (diamond), Si and Ge are 5.4eV, 1.1eV and 0.7eV respectively.  Sn is also an element of the fourth group but it is metal because the energy gap in its case is 0eV.