- + Some analogies between the flow of current in a conductor, and and the flow of water in a rigid pipe (good to keep in mind for those who are scared by “Volts”, “Amps”, “Ohms”….): - + Battery or generator Stream of electrons Conductor

One more thing to remember: Note: this is also true for any current source. Current not only flows out of a battery – exactly the same amount of charge returns by the other terminal.

Electrical conductivity: let’s begin with metals, which are the relatively simple conductors. Electrons in a metal occupy quantum states. There are many states with different energies. We can imagine such states as “parking sites” in a multi-level parking garage. Two cars cannot occupy the same site. Likewise, two electrons cannot quantum state. So, the electrons occupy available states with the lowest energies, up to certain level – and all states above are “empty” . Note the analogy with H2O molecules in a glass of water:

As we said, all conductors have to obey the rule: “one electron in, one out”. Our “garage” obeys an analogous rule: one car in, one car out. The “garage” is a good “car conductor”, because the cars can move freely at the level that is not occupied:

In semiconductors, the situation is different: Just above the filled levels, there are several levels that are not accessible. It’s an analogy with the famous energy gap in semiconductors. The cars could move freely at the levels above the “forbidden zone” – however, there is no such an elevator that could move them up there.

However, if additional containers with cars are placed In the “forbidden zone” near its top, then the cars can be easily lifted to the “allowed levels” above, and “car traffic” in our garage becomes possible. In real semiconductors, atoms that have one loosely coupled electron may be put near the top of the energy gap, an they may “donate” the electron to levels above the energy gap, where they can move freely. Such atoms are called “donor atoms”, and such semiconductors ale called n-type or n-doped .

However, there is another possible way of enabling the cars to move However, there is another possible way of enabling the cars to move. We can put special “containers” near the bottom of the “forbidden zone” – each container can “capture” a car from the level underneath, leaving a vacant space, a hole. In real semiconductors atoms that can absorb an extra electron are put near the energy gap bottom. Such atoms are called acceptors, and the vacant electron states they create are called holes. Such semiconductors are called p-type or p-doped.

Once a “hole” is created, the cars may start moving Once a “hole” is created, the cars may start moving! One by one, the cars shift to the left by one position, and thus the hole “propagates” to the right, until it reaches the rightmost space – as is shown in this animation: (the animation is repeated five times, and the stops).

Once the hole moved all the way to the right, a car from outside can move into the vacant space. But due to the “one in, one out” rule, the leftmost car has to leave the garage. It creates a new hole which again propagates all the way to the right, and the cycle is repeated. Cars keep moving in and out of the garage!

COCLUSIONS FROM THE LAST SEVERAL SLIDES: Free electrons in metals and n-type semiconductors are negative current carriers. The holes in p-type semiconductors behave as positive current carriers. Now we are almost ready to start talking about p-n junctions, which are the crucial elements of solar cells. But before we start, let’s refresh our memory about the electric potential.

But first a few words about the potential due to Earth gravity: m m mg m m h1 mg h2 U1 = mgh1 U2 = mgh2 Earth surface

Electric charges are sources of electric fields. The electric field can also be described in terms of the potential. The measure of the potential of an electric field is the potential energy of a unit positive charge placed in this field.

A simple-minded theory of a p-n junction Taka a piece of p-type silicon, and a piece of n-type silicon. In each there are mobile carriers -- holes and electrons, respectively. The donor and acceptor atoms are not mobile! They are solidly built in the crystal structure of silicon. But both materials are electrically neutral, because in each the charge of the mobile carriers is compensated by the charge acquired by the donor/acceptor atoms.

When p and n-type semiconductors are combined, they form a p-n junction. Mobile carriers from each side diffuse across the “borderline”…. Extra negative charge Extra positive charge

Consider a large (“semi-infinite”) slab with uniform negative volume charge. A positive point charge Q located outside the slab is always attracted toward it with the same force, regardless of the distance to the slab surface. Uniform negative charge

And what if the charge is inside the slab? Then we can always Divide the slab in our mind into two “sub-slabs”, of which one Pulls the charge to the left, and the other one to the right, with forces proportional to the amount of charge in each imaginary “sub- slab”. Hence, a plot of the force acting on the charge Q as a fun- ction of its position looks as plotted below: F -d/2 d/2 x d

Let’s now take two slabs of the same thickness d and with volume charges of the same density, but opposite signs. - + Force from the negative slab F -d d x Force from the positive slab

F -d d x x 1 1 -1 -2 Force from the negative slab Force from the d x Force from the positive slab -1 Net force from both slabs x -2

Conclusion: we now understand where this graph comes from! The force acting on a positive charge in the “space charge” region is always negative (i.e., to the left) and has the form of a “dip”. Conversely, a negative charge is always driven to the right. To reach the overall conclusion, we have to say a few words about the Photoelectric Effect .