PROFESSOR: Hello, everyone.
Today we'll talk about doping, which
is the process of intentionally adding impurities
to a semiconductor in order to change
its electrical properties.
Doping is a critical process in the tech world.
It's used in manufacturing almost all semiconductor
Without doping, the solar industry would not exist,
but even though doping is common today,
the effects of impurities confused semiconductor
physicists in the 1950s, who had trouble reproducing results.
Eventually, they realized that contamination levels,
as low as 1 in a billion, were vastly
changing the electrical properties of their samples.
Today, we'll show you how this works
with a very simple experiment.
We'll be measuring the electrical conductivity
of two silicon slabs using an ohmmeter.
One is doped with impurities, phosphorus in our case,
and the other is ultra-pure, or what we call intrinsic.
Let's go over our experiment.
We'll start with a slab of silicon,
which we attach metal contacts to.
We'll use an ohmmeter, that we connect
to our sample with metal wires to measure the conductivity.
The conductivity describes how well
electricity can flow through the material.
The measured resistance from our ohmmeter
is related to the inverse of the conductivity.
The resistance also varies according to the physical size
and shape of our sample, which adds
a length over area term to our equation, like so.
Rearranging this equation, gives is what we're looking for,
Let's measure our samples, and estimate the conductivity.
Here are two samples, notice that the doped sample looks
identical to the intrinsic one, or undoped sample.
Because we've only added trace impurities,
the optical properties are nearly
identical between the two samples.
Let's hook up the ohmmeter to the intrinsic sample.
We can see that the resistance is 130,000 ohms, which roughly
corresponds to a conductivity of 0.0002 inverse ohm centimeters.
Let's compare this to the doped sample.
We read a resistance of 34 ohms, which
corresponds to roughly 0.6 inverse ohm centimeters.
So we can see that the dope sample is around 3,000 times
But why would adding small amount
of our doping, about one phosphorus
atom for every million silicon atoms,
make our sample 3,000 times more conductive?
On the periodic table, we see that silicon
is in the fourth column, which means
it has four valence electrons.
Phosphorus, which is just to the right in column five,
has five valence electrons, one extra compared to silicon.
I'd also like to point out boron in column three,
with one fewer valence electron than silicon.
Later, I'll explain what happens when you add boron as a dopant.
We'll start with a 2D representation
of a single silicon atom, with the nucleus in the center,
and its four valence electrons in a silicon crystal,
each silicon atom bonds to four other silicon atoms around it.
These rigid covalent bonds, shown here,
keep all of the electrons effectively immobile, and are
therefore, unable to aid in the full electricity.
Our intrinsic silicon, or undoped example,
has this material structure, which
is why it has a very low conductivity.
Let's quantify this relationship between conductivity and mobile
Conductivity is defined as n times mu times e.
n is a number of free or mobile electrons.
Again, in this drawing of intrinsic silicon,
all electrons are covalently bonded so there
are no mobile electrons, and n is 0.
The symbol mu represents the mobility, a material parameter
which you can look up in a textbook, or online,
and it basically describes how well the charge can move around
in the material.
e is simply the amount of charge that each mobile particle
possesses, which in all of our cases,
is simply the charge of an electron.
So let's ask, what happens when we add dopants like phosphorus
and boron to the silicon lattice?
Now, let's dope our material by replacing one of the silicon
atoms with a phosphorus atom.
First, we'll remove a silicon atom,
and for contrast, we'll dim the background silicon lattice
so we can emphasize the dopant atom.
Notice that the inserted phosphorus atom
has five valence electrons, four of which
form four covalent bonds with their neighboring silicon atoms
and are immobile.
The fifth electron is not bonded, and as a result,
is free to move around the lattice.
When the negatively charged electron leaves,
the phosphorus dopant is now positively charged.
So we see that each phosphorus atom that is added
will contribute a single mobile electron.
So basically, in our case, the number of mobile electrons
is roughly equal to the number of phosphorus
atoms in our system.
Now, let's remove our phosphorus atom
and put in an element with three valence electrons,
such as boron.
We see here that boron lacks the necessary valence electrons
to form covalent bonds to its four neighboring silicon atoms.
This missing electron is actually referred to as a hole,
and is represented by an H+ symbol.
This hole acts as a mobile positive charge
because it can swap places with neighboring covalently bonded
electrons and move around the crystal.
When the positively charged hole leaves its nucleus,
the boron atom becomes negatively charged.
So we've demonstrated that introducing
atoms that have one more, or one less, valence electron
than silicon, can add mobile charges
and make the material more conductive.
In our examples, the conductivity of silicon
is proportional with the density of either phosphorus or boron
While phosphorus and boron both affect the conductivity
in a very similar manner, they introduce
mobile and static charges of the opposite sign.
Phosphorus introduces mobile negative charges
and immobile positive charges, while boron
creates mobile positive charges and immobile negative charges.
This subtle difference between phosphorus and boron dopants
will be crucial in our final video
when we discuss solar cell operation.
Today we learned that we can use doping
to control the conductivity of semiconductors
by changing the number of mobile charges in the material.
When we look at the range of conductivities
that silicon possess, it is truly amazing.
Through doping, we have a very powerful way
of varying the conductivity of semiconductors.
This is something that is not possible in other classes
of materials, like metals.
Next time, we'll be discussing how
light can be used to generate mobile charges in silicon,
so watch our next video.
I'm Joe Sullivan, and thanks for watching.