In the previous video, we explained that semiconductors
do not conduct electricity very well.Meme it
One way to manipulate electrical conductivity
in semiconductors is to manipulate the concentrationMeme it
of electrically charged carriers.
We can do this by using doping.Meme it
In this video, we will first introduce what
doping is.Meme it
Then we will discuss how doping changes important
material properties in semiconductors.Meme it
The concentration of charge carriers in a
semiconductor can be manipulated by dopingMeme it
Doping means that we add impurities in a controlledMeme it
way to the material.
Let’s take the example of silicon.Meme it
Silicon has four valence electrons.
In a silicon lattice, each atom is bonded,Meme it
covalently, to four other silicon atoms.
We can take that silicon lattice and substituteMeme it
a small amount of silicon atoms with different
This is commonly done with atoms of two different
elements: Boron and Phosphorus.Meme it
Boron atom has three valence electrons, while
phosphorus atom has five valence electrons.Meme it
When Boron is used as a dopant, the resulting
material is called p-type.Meme it
When phosphorus is used, we call that material
So what actually happens when we substitute
silicon atoms with these impurities?Meme it
Here you can see a schematic representation
of the bonding between Silicon and Boron atoms.Meme it
Boron atom is in the middle of this diagram
bonded to four silicon atoms.Meme it
You can see that three of the silicon atoms
have covalent bonds with the Boron atom.Meme it
However, one of the silicon atoms has a funny
looking bond with the Boron atom.Meme it
This is because Boron atom shares only one
valence electron.Meme it
This bond is missing one electron.
This missing electron is denoted as a hole.Meme it
On the right side of this slide we can see
the situation with a phosphorus atom.Meme it
Four valence electrons of the phosphorus atom
form four covalent bonds with neighbouringMeme it
Because phosphorus atom has five valence electrons,Meme it
there is an extra electron floating around
and not being involved in a bond.Meme it
What we just explained can be better visualized
with the help of the two-dimensional bondingMeme it
Let’s start comparing intrinsic and dopedMeme it
semiconductors at zero Kelvin.
We can see that in the lattice of an n-typeMeme it
semiconductor, there are “extra” electrons
carried by phosphorous atoms.Meme it
Similarly, the p-type lattice contains extra
holes carried by boron atoms.Meme it
If the temperature increases, some silicon-silicon
bonds can break and electrons are liberatedMeme it
from the bonds.
The missing electrons in the bonds representMeme it
virtual particles that we call holes.
So, breaking the bonds results in the formationMeme it
of electron-hole pairs.
These electrons and holes are mobile and canMeme it
move through the material.
The same process of breaking bonds also occursMeme it
if the material is doped.
However, in doped material thermal excitationMeme it
also affects the dopant atoms.
In n-type materials, the extra phosphorus’Meme it
electron needs a very small amount of thermal
energy to get loose from the phosphorus atomMeme it
and become mobile.
Hence, we say that the phosphorus atom “donates”Meme it
a free mobile electron into the silicon lattice.
For this reason, phosphorous is also calledMeme it
to be a “donor”.
If this mobile electron leaves the phosphorusMeme it
atom, the phosphorus atom becomes positively
This is because it has more protons than electrons
In p-type materials, electrons can be readily
accepted by Boron atoms to fill the holesMeme it
and complete the covalent bond with silicon
We call dopants like Boron “acceptors”.
The Boron atom becomes negatively chargedMeme it
since it now has accepted an extra electron.
We say that boron atoms are negatively ionized.Meme it
Ionization of dopant atoms can affect locally
the charge neutrality of the lattice itself.Meme it
This happens when mobile carriers deplete
the region with fixed ionized dopant atomsMeme it
As a consequence, the lattice will become
locally positively charged in the n-type,Meme it
while in the p-type it will become negatively
Nevertheless, the charge neutrality of the
whole material is still maintained.Meme it
In the previous videos we stressed out the
relationship between electron’s energy andMeme it
material’s composition and structure.
Moreover, we also introduced the Fermi energyMeme it
level and showed that its position depends
on the effective density of states in theMeme it
conduction and valence bands.
We can therefore expect that, when insertingMeme it
donor and acceptor atoms, these properties
will be affected.Meme it
Let’s see how.
Let’s start by looking at the band diagramsMeme it
of our three materials.
In previous videos I showed you the band diagramMeme it
of an intrinsic semiconductor.
The position of the Fermi level which I haveMeme it
labeled E_Fi is here of major importance.
E_Fi stands for the Fermi level of an intrinsicMeme it
In the band diagram of the n-type material,Meme it
the energy level denoted as E D represents
energy of the “extra” electrons of phosphorusMeme it
atoms that are not involved in bonds.
The energy level of this weakly bonded electronMeme it
lies close to the conduction band.
Once liberated from the atom, it will gainMeme it
energy and occupy an energy level in the conduction
Since by doping we increase number of electrons
with energies in the conduction band the averageMeme it
energy of electrons will increase.
This will result in a shift of the Fermi levelMeme it
towards the conduction band.
I have drawn the intrinsic Fermi level forMeme it
reference, but the real Fermi Level E_F is
drawn here in red.Meme it
You can see that it is between the intrinsic
Fermi level and the conduction band and theMeme it
more we dope the material, the closer the
Fermi level will be to the conduction band.Meme it
If we look at a p-type material we can see
a similar, but opposite effect.Meme it
Now we have an energy level, denoted as E_A,
which is occupied by electrons that are acceptedMeme it
to form covalent bonds.
Since in this case most of the electrons occupyMeme it
energy levels in or close to the valence band
the average energy of electrons will decrease.Meme it
The Fermi level is shifted towards the valence
Again, the higher the doping with acceptor
atoms, the closer the Fermi level will beMeme it
to the valence band.
Before we move forward with some calculationsMeme it
to determine the concentration of mobile charge
carriers, it is important to understand someMeme it
In semiconductors we often distinguish betweenMeme it
majority and minority charge carriers.
As you already understand we deal with twoMeme it
types of charge carriers in semiconductors.
Negatively charged electrons and positivelyMeme it
In an intrinsic semiconductor we have theMeme it
same number of electrons and holes.
However with doping we manipulate the concentrationMeme it
of only one type of the charge carriers.
We call the carriers whose concentration isMeme it
much larger than that of the other type majority
These are holes in p-type materials and electrons
in n-type materials.Meme it
Minority charge carriers are the carriers
with much lower concentration than the majorityMeme it
These are electrons in in p-type materialsMeme it
and holes in n-type materials.
The dopant concentration can be selectivelyMeme it
chosen according to the application.
For crystalline Silicon we may have threeMeme it
levels of doping, low, moderate and heavy,
whose ranges can be seen in this picture.Meme it
For illustration when we take a moderate doping
of 10 to power of 16 dopant atoms per cubicMeme it
centimeter this means that we have substituted
just ONE silicon atom out of 1 million siliconMeme it
For solar cell applications, we generallyMeme it
use layers with moderate to high dopant concentrations.
In this video we looked at how doping affectsMeme it
some of the semiconductor properties qualitatively.
In the next video we will learn how to calculateMeme it
the carrier concentrations and the position
of Fermi levels of semiconductors dependingMeme it
on their doping concentration.Meme it