Semiconductors

As its name implies, a semiconductor is a material that conducts current, but

only partly. The conductivity of a semiconductor is somewhere between that of
an insulator, which has no conductivity, and a conductor, which has full
conductivity. Most semiconductors are crystals and in this section, we will
focus on silicon as an example of a semiconductor.

To understand how silicon acts as a semiconductor, we turn to how electrons

are organized in an atom. The electrons in the atom are organized in layers
called shells. The outermost shell is called the valence shell. When the atoms
bonds with neighboring atoms, the electrons in valence shell are the ones that
form covalent bonds. Silicon has four electrons in its valence shell making it
possible for each silicon atom to bind with the valence electrons from four
other silicon atoms forming a lattice structure. In figure 1, a two-dimensional
description of the lattice structure is shown.
The electrons in the covalent bonds formed between each atom in the
crystal structure are held in place by these bonds and hence they are
localized to the region surrounding each atom. These bonded electrons
cannot move or change energy, and thus are not considered free. They
cannot participate in current flow, absorption, or other physical processes of
interest in solar cells. However, the situation where all electrons are stuck in
this way is only true at a temperature of absolute zero. At elevated
temperatures, electrons can gain enough energy to escape from their bonds.
When this happens, the electrons are free to move about the crystal lattice
and participate in conduction. At room temperature, a semiconductor has
enough free electrons to allow it to conduct current. At or close to absolute
zero a semiconductor behaves like an insulator.
Bandgap
For an individual atom, there are defined discrete energy levels for the
electrons to occupy. Electrons in atoms (and molecules) can change energy
levels by emitting or absorbing a photon, with energy exactly equal to the
energy difference between the two levels.

When we bring two atoms together a mutual coupling of the atoms occurs.
Thus, the energy conditions change and each energy level is divided into two
individual levels. In the case of three coupled atoms we get three levels and
so on, see figure 2. When we look at our silicon crystal lattice from before we
practically get an infinite number of atoms coupled together, and thus a
continuum of energy levels. We call these energy bands, where each band is
an energy state permitted for an electron.
• The existence of the energy bands explains the conduction behavior of the
semiconductor (remember the semiconductor is an insulator at low
temperatures, and a conductor at high temperatures). The reason being that the
highest occupied energy band is filled with electrons, while the lowest
unoccupied energy band has no electrons, see figure 3. We call these bands
the valence band (highest occupied band) and the conduction band (lowest
unoccupied band) respectively. If the electrons remain in the valence band they
are bound and the semiconductor behaves as an insulator, which is the case at
zero-degree kelvin (-273.15 °C). When the temperature is increased, individual
electrons can loosen from their bonds and become available in the crystal as free
electrons, see figure 3. In the band model this corresponds to the case where the
electrons transitions from the valence band to the conduction band. These free
electrons increase the conductivity of the crystal, making it a conductor at
elevated temperatures. The width of the gap between the valence band and the
conduction band is called the bandgap and in the case of silicon its value is Eg =
1.12 eV.
Insulators, semiconductors, and conductors
To round out the introduction to semiconductors, we will look at how the
energy band applies to the two other classes of materials,
namely insulators and conductors. In the case of insulators, the bandgap is
very large (typically greater than 3 eV), meaning that almost no free
electrons will be available even at high temperatures. In the case of metals (a
conductor), we see a special case, namely that the valence band and the
conduction band overlap. In this case numerous electrons are available as
free electrons and therefore metals possess high conductivity even at very
low temperatures.
Conductivity and doping
When an electron is released from its bond, figure 1 left, a gap is left in
the crystal structure, which we call a hole. This process is
called electron-hole pair generation. The reverse process, where a free
electron falls back into a hole is called electron-hole pair
recombination, and is depicted in figure 1 right. We use the term
“hole” to describe the lack of an electron at a position where one could
exist in an atom or atomic lattice because we can model the hole as a
positively charged particle in the semiconductor.
If an electric voltage is applied across a semiconductor an electric field
is established. This means that the negatively charged electrons will be
accelerated in the direction of the positive pole of the voltage source,
and the holes are accelerated in the direction of the negative pole. In
this way the semiconductor acts as a conductor of current.
We use the notion of a hole as a way to conceptualize the interactions of the
electrons within a nearly full system, which is missing just a few electrons.
The movement of a single hole is conceptually simpler to work with, than
monitoring every electron in the valance band. To more simply explain the
concept of hole mobility, you can imagine a row of people seated in an
auditorium, where there are no spare chairs. Someone in the middle of the
row wants to leave, and climbs over the back of the seat into an empty row,
and walks out. The empty row is the conduction band in this analogy,
while the person leaving is a free electron. Now someone else comes by and
wants to sit down in the crowded row (the valence band). To create space, a
person in the crowded row moves into the empty seat the first person left
behind and the empty seat moves one spot closer to the edge. As every
person follows suit and moves into the empty seat, the empty seat
effectively moves towards the edge of the row. Once the empty seat reaches
the edge, the new person can sit down.
Like we described the movement of an empty seat, hole mobility is actually
the movement of many separate electrons in the valance band.
Doping
As a starting point semiconductors (intrinsic semiconductors) are poor
electrical conductors, since the electrical conductivity relies on thermal
electron excitation. Further the number of electrons in the conduction band
is equal to the number of holes in the valence band. However, we can
change this situation by introducing foreign atoms to the semiconductor
crystal; this process is referred to as doping. The addition of a small
percentage of foreign atoms in the regular crystal lattice produces dramatic
changes to their electrical properties and we can therefore produce n-type
and p-type semiconductors, where there is an abundance of free electrons
or holes.
If for instance we introduce a phosphorus atom into a silicon crystal lattice,
see figure 2, we create a free electron, since phosphorus has one additional
valence electron as compared to silicon. This fifth valence electron finds no
open bonds, and is instead only weakly connected to the crystal lattice,
meaning it is available as a free electron at room temperature. We can
illustrate this in the band diagram as the doping atom generates an
additional energy level just below the conduction band. This means that only
very low energy (far less than room temperature) is required to lift the
electron into the conduction band. We call the foreign atom (phosphorus in
this case) a donor atom, as the donor atom “gives” a free electron to the
crystal lattice. The resulting semiconductor material is said to be n-doped,
since the concentration of free electron rises drastically and there is
therefore a majority of negative charge carriers.
It is likewise possible to do p-doping of a semiconductor by introducing
foreign atoms with less valence electrons (e.g. boron) than the silicon
semiconductor, see figure 3. In the p-doped material hole conductance
becomes possible. The boron atom is in this case referred to as
an acceptor atom. In any case, doping densities are very low, e.g. only
1 in 100,000 silicon atoms are replaced. Yet the effect of doping can
increase the conductivity of the material by orders of magnitude