Doping of semiconductors

At the previous video chapter the hybridization, the electron configuration and the crystallization of silicon has been discussed.
To the left of silicon, the element aluminum is placed at the periodic table.
The valence electron configuration at the ground state of a neutral atom is 3s2 3p1.
Like silicon, the aluminum atom forms hybridized orbitals while sharing electrons in a covalent bond.
This special form is called sp2 hybridization, because one s and two components of the p orbital form three unique mixed orbitals.
Not involved in the process is the third component of the p orbital, because it is not occupied by an electron.
The three hybrid orbitals are arranged with the maximum angle between the symmetry axes.
The angle between the grey painted, large drops is 120 degrees and they are arranged in a plane.
The also painted third component of the p-orbital is empty and so it just exists hypothetical.
Like discussed some later, it is very important for the electrical properties, that the outermost shell of the aluminum atom is not completely filled with electrons.
Let's replace the orbital model of aluminum by the ball-and-stick model.
The angle between the orbitals - symbolized by the green sticks - is not a fixed value.
Energy is needed to twist the orbitals, but spending those potential energy is counterbalanced by the higher gain of energy while forming covalent bonds.
The angle between the orbitals of the hybridized aluminum atom is decreasing to 109.5 degrees, which is the tetrahedral angle between the atoms in a silicon crystal.
Let's insert the aluminum atom into the crystal lattice of silicon.
As you can see, all three valence electrons of the aluminum atom form covalent bonds with the silicon atoms next to it.
Because of the fact that silicon atoms have four valence electrons, the bond with the fourth electron of one silicon atom remains unsatisfied.
Those absence of an electron in a covalent bond is called electron hole.
The intentionally introduction of impurities into the crystal lattice is called doping.
Let's remove the top layer of silicon atoms and have a look at the mechanism of moving charges inside of this doped silicon crystal.
The positive terminal of the DC voltage source is at the left side, the negative terminal at the right side of the crystal.
By increasing the voltage output from zero to a certain value, an electric field is generated, which is symbolized by the red field lines pointing from the left to the right.
Negatively charged particles like electrons are pulled to the left inside of this field.
This is pointed out at the used model by shortening the sticks at the right side of the atoms.
Because of the fact that the electrons at the left side of the atoms are also pulled to the positive terminal, those sticks are enlarged.
In doing so, the unsatisfied electron of the silicon atom is moving closer to the aluminum atom.
The formation of a covalent bond is almost done, but an additional electron is still needed.
In reality there are not sticks, but this animation illustrates the fact that there is a force acting from the electron hole to the aluminum atom.
If the strength of the electric field increases, an electron moves from the silicon atom to the aluminum atom.
This process leads to the formation of a negatively charged aluminum ion.
Like noted while talking about the orbitals of the aluminum atom, one component of the p-orbital is empty and so the additional electron can enter this orbital.
Now the aluminum ion can form four identical sp3 hybridized orbitals and so four covalent bonds, resulting in a very beneficial electron configuration.
By adding the electrons shared with the silicon atoms, there are eight valence electrons inside of the electron shell, which is the electron configuration of Argon, the noble gas which is located in the period of aluminum.
Forming four covalent bonds inside of the electric field leads to this stable electron configuration and so to a lower energy level of the whole system.
An additional electric field is created between the negatively charged aluminum ion and the positively charged silicon ion, which is displayed by the additional arrows.
Needless to say that the interaction of two spherical shaped or point charges is resulting in a more complex arrangement of field lines.
Additionally the interaction with the electric field of the voltage source has to be considered.
The exact run of the field lines should not be discussed here. The three arrows simply indicate the direction of the additional electric field.
Between the aluminum and the silicon ion, the field is running contrary to the field of the voltage source, hence the external field is weakened.
To the left and to the right of these two ions, the action of the external field is enforced slightly.
The electron hole is now located between the two silicon atoms to the right of the aluminum ion.
This is the weak point inside of the crystal lattice, now.
An electron is moving from the right silicon atom to the silicon ion, according to the action of the electric field.
The reverse process - meaning the movement of an electron from the left to the right is inhibited by the action of the electric field caused by the voltage source AND the field of the two ions.
Like mentioned before, the electric field of the voltage source is weakened to the left of the positively charged silicon ion and it is enforced to the right of it.
Once more the hole is moving to the right.
This process continues until the negative terminal of the voltage source is reached.
The distance between the negatively charged aluminum ion and the respective positively charged silicon ion is increasing step by step.
The electric field between the ions is getting weaker.
If the distance becomes too big, the hole can also move one step to the left, which inhibits the flow of a current.
There has to be a minimum number of aluminum atoms inside of the crystal lattice, so that the mechanism works from one terminal to the other.
If the hole has reached the negative terminal of the voltage source, one electron is injected into the crystal lattice and simultaneously another one is extracted at the positive terminal.
The balance of charges is kept constant and the hole is jumping from the negative to the positive terminal.
The electric field caused by the two ions is now pointing into the same direction as those of the voltage source, hence the external field is enforced between them.
Nevertheless the electrons still move from the atom at the right side of the hole to the silicon ion at the left side of the hole.
As from now the electron hole is to the left of the negatively charged aluminum ion, which repels the electrons.
The hole is still moving from the left to the right.
As soon as the electron hole and so the positively charged silicon ion has reached the position next to the aluminum ion, the electric field caused by the ions and the external field is at its maximum, hence an electron is moving from the negatively charged aluminum ion to the positively charged silicon ion.
The electron hole has reached it's initial position and there are no ions inside of the crystal lattice.
One electron has been transfered from the negative to the positive terminal of the voltage source and the process starts again.
The electron which exits the crystal lattice at the positive terminal is different from those which entered the crystal at the negative terminal.
During each step of the process another electron is moving into the hole.
Let's now have a look at the process while using the calotte model.
The positively charged silicon ions are marked in red and the negatively charged aluminum ion is painted in blue.
It seems like a positive charge is moving from the left to the right in course of the process, thus from the positive to the negative terminal.
Like discussed, the positively charged silicon ions rest at their position and only the electrons move between close-by atoms from the right to the left, thus from the negative to the positive terminal.
The aluminum atom is negatively charged almost during the whole process.
Only if the electron hole has reached the position left to the aluminum ion, it is handing the additional electron to the close-by silicon ion, while gaining another electron from the atom to the right side immediately.
It seems like the negative charge is resting at the position of the aluminum atom.
This mechanism is called hole conduction or p-type conduction.
Adding atoms of the 13th group of the periodic table into the crystal lattice of silicon is called p-type doping.
P means positive and doping means introducing impurities.
Another possibility to increase the conductance of semiconductors is adding atoms of the 15th group of the periodic table.
Let's use phosphorus as an example.
The electron configuration of a neutral atom at it's ground state is 3s2 3p3.
The 3s orbital is completely occupied with 2 electrons, the 3p-orbital is filled with half the number of electrons possible.
Like silicon, phosphorus can also form sp3 hybridized orbitals.
The four mixed orbitals create four covalent bonds, sharing their electrons with those of the neighboring atoms.
Now those orbitals are occupied by the maximum number of electrons possible, which is the stable configuration of the noble gas argon.
The supernumerous electron is located at the next orbital.
It is the ball socket shaped 4s orbital, drawn translucent.
Let's replace the orbital model by the ball and stick model.
The quasi supernumerous electron is drawn as a small blue sphere, moving somehow around the atom.
To keep the model simple, it is rotating around the atom in a circular orbit. Now we can build a silicon crystal with the phosphorous atom at it's center.
The upper layer of silicon atoms is removed and the bottom layer is connected to the DC voltage source.
Once more an electric field is generated by the voltage source and the electrons are pulled to the left side of the drawing.
Let's observe the unsatisfied electron of the phosphorous atom.
The force acting on the electron is visualized by altering the circular orbit into an elliptical orbit with it's farest point to the left of the atom and the nearest point to the right of the phosphorus.
While increasing the voltage output, the electron is removed completely from the atomic nucleus at a certain field strength.
The electron is just loosely bond to the phosphorous atom. By releasing this electron the phosphorus atom achieves the stable electron configuration of the noble gas argon.
A free electron and a positively charged phosphorous atom is created by this process.
The loosened electron can move about in the crystal lattice relatively freely and it facilitates conduction in the presence of the electric field.
As soon as the electron leaves the crystal lattice at the positive terminal, another electron is entering the crystal at the negative terminal.
An electric current is running through the crystal.
Let's have a look at the process with the help of the calotte model.
The negatively charged electron is moving from the right to the left, thus from the negative to the positive terminal, while the positive charge rests at the phosphorous atom.
Adding atoms of the 15th group of the periodic table into the crystal lattice of silicon is called n-type doping.
N means negative charge is placed in the crystal lattice.
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