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Electrons at Work
SECTION 2. ELECTRONS AT WORK
2a) Conductors, semi-conductors and insulators
Learning content: State that solids can be categorised into conductors, semi-conductors or insulators by their
ability to conduct electricity. Give examples of each type
Classifying materials
By considering their electrical properties, we can divide materials into three groups:
Materials with many free electrons. These elections can
 Conductors
easily be made to flow through the material. For example, all
metals, semi-metals like graphite, antimony and arsenic.
Materials which are insulators when pure, but will conduct
 Semiconductors
when an impurity is added and/or in response to light, heat,
voltage, etc.
For example, elements like silicon (Si),
germanium (Ge), selenium (Se); compounds like gallium
arsenide (GaAs) and indium antimonide (InSb).
Materials that have very few free electrons, which cannot
 Insulators
move easily. For example, plastic, glass and wood.
The atomic model
Learning Content: State that electrons in a free atom occupy discrete energy levels.
The simple model of the atom contains a positive nucleus surrounded by negative electrons. Each
electron can have an energy determined by the energy levels of the particular atom. The electrons
in an isolated or free atom occupy discrete energy levels. However, when atoms are close to each
other the electrons can also use the energy levels of the neighbouring atoms.
Electrons are constantly in random motion due to the heat energy that they gain from their warm
surroundings. This is called thermal agitation. This thermal energy allows some electrons to
move from a lower energy level to a higher one.
Learning Content: State that when the atoms come together to form solids, the electrons then become
contained in energy bands separated by gaps.
When the atoms are all regularly arranged in what is called the crystal lattice of a solid, the energy
levels become grouped together in a band. This is a continuous range of allowed energies rather
than a single level. There will also be groups of energies that are not allowed, in what is known as a
band gap. Similar to the energy levels of an individual atom, the electrons will fill the lower bands
first. The Fermi level gives a rough idea of which levels electrons will generally fill up to, but there
will always be some electrons with individual energies above this.
When atoms combine to form a solid the electrons align themselves into energy bands. The two
highest energy bands are known as the valence band and the conduction band (see diagrams on
the following pages). The conduction band is the higher of the energy bands.
The electrons are held tightly in the valence band, but are able to move freely in the conduction
band. So if there are electrons in the conduction band the solid will conduct. If there are no
electrons in the conduction band, the solid will not conduct.
Electrons at Work
Energy Band Diagrams
Simple diagrams can be used to explain the difference between the three types of solid.
Conductor
Learning content: State that in metals which are good conductors, the highest occupied band is not
completely full and this allows the electrons to move and therefore conduct. This is the conduction band.
Conduction band
Valence band
In a conductor, the valence band is not full which
means that the conduction band overlaps it.
Thermal agitation of electrons boosts electrons from
the valence band into the conduction band. As a
result, there are many electrons in the conduction
band which are able to move. When an e.m.f. is
applied to the solid, these are the electrons that flow
to produce the current.
Insulator
Learning Content: State that in an insulator the highest occupied band (called the valence band) is full. For
an insulator the gap between the valence band and the conduction band is large and at room temperature
there is not enough energy available to move electrons from the valence band into the conduction band
where they would be able to contribute to conduction.
Conduction band
In an insulator the valence band is full and there is a large
energy gap to the next available energy level in the conduction
band. The gap is so large that even with thermal agitation, the
electrons almost never cross the gap and the solid never
conducts. The electrons remain in the valence band.
Valence band
If the applied voltage is high enough (beyond the breakdown
voltage) sufficient electrons can be lifted to the conduction
band to allow current to flow (e.g. lightning in air). Often this
flow of current causes permanent damage. Within a gas this
voltage is often referred to as the striking voltage. In a
fluorescent lamp, e.g. a neon lamp, this is the voltage at which
the gas will start to conduct and the lamp will light.
Semi-Conductor
Conduction band
Valence band
Learning Content: State that in a semi-conductor the gap between the
valence band and conduction band is smaller and at room
temperature there is sufficient energy available to move some
electrons from the valence band into the conduction band allowing
some conduction to take place.
Semiconductors are like insulators as their valence band is full.
However the gap between the two bands is relatively small and
at room temperature some electrons have enough energy to
jump the gap. The solid will conduct to some extent.
Electrons at Work
The Fermi Level
If an atom is cooled to absolute zero temperature (0 K) the thermal energy available to its electrons
is zero. If all its electrons were removed and replaced one by one, each electron would occupy the
lowest available energy level at the time. Since electrons cannot occupy the same level, the
electrons would fill up the atom from the bottom up. The Fermi Level is the name given to the
highest occupied energy level of the electron in the valence band. This would be occupied by the
last electron to be replaced.
Electron
energy
No overlap
Conduction
band
Fermi
level
Conduction
band
Band
overlap
Valence
band
Conductor
Conduction
band
Band
gap
Valence
band
Valence
band
Semiconductor
Insulator
In a conductor, there is no energy gap between the top Fermi level of the valence band
and the lowest energy level of the conduction band. At normal room temperature, there
is some thermal energy available to the electrons. Effectively this means that the valence
band and the conduction bands overlap. In contrast, for semi-conductor there is a small
energy band gap, and for an insulator there is a large energy band gap.
The Effect of temperature on a semi-conductor
Learning Content: State that an increase in temperature increases the conductivity of a semi-conductor.
Conduction band
Valence band
Thermal agitation of electrons increases with temperature. As
the temperature increases, some electrons in the valence band
gain enough thermal energy to boost them up to the conduction
band. This causes the number of conduction electrons to
increase and so the semiconductor conducts better.
In an insulator, the energy gap is still much greater than the
energy which can be gained from thermal agitation so very few
electrons are available to conduct.
Note: Electron bands also control the optical properties of materials. They explain why a hot solid
can emit a continuous spectrum rather than a discrete spectrum as emitted by a hot gas. In a solid,
the atoms are close enough together to form continuous bands. The exact energies of these bands
determine which frequencies a material will absorb or transmit and therefore what colour it emits.
Electrons at Work
Section 2b) p-n junctions
Manufacturing Semiconductors
The electrical properties of semiconductors make them very important in electronic devices like
transistors, diodes and light-dependent resistors (LDRs). In such devices the electrical properties
are dramatically changed by the addition of very small amounts of impurities. The process of adding
impurities to these semiconductors is known as doping.
The development of doped
semiconductors in the 1950s led to the invention of the transistor and the start of the ‘solid state’
revolution that transformed the whole face of electronics.
Bonding in semiconductors
The most commonly used semiconductors are silicon and germanium. Both these materials have a
valency of four, that is they have four outer electrons available for bonding. In a pure crystal, each
atom is bonded covalently to another four atoms. All of its outer electrons are bonded and
therefore there are few free electrons available to conduct. This makes the resistance very large.
The few electrons that are available come from imperfections in the crystal lattice and thermal
ionisation due to heating. A higher temperature will thus result in more free electrons, increasing
the conductivity and decreasing the resistance, as in a thermistor.
Holes
When an electron leaves its position in the crystal lattice, there is a space left behind that is
positively charged. This lack of an electron is called a positive hole.
This hole may be filled by an electron from a neighbouring atom, which will in turn leave a hole
there. Although it is technically the electron that moves, the effect is the same as if it was the hole
that moved through the crystal lattice. The hole can then be thought of as the charge carrier.
In
an
undoped
semiconductor,
the
number of holes is
equal to the number
of electrons. Current
consists of drifting
electrons
in
one
direction and drifting
holes in the other.
Electrons at Work
Doping
Learning Content: State that the addition of impurity atoms to a pure semiconductor (a process called
doping) decreases its resistance.
If an impurity such as arsenic (As), which has five outer electrons, is present in the crystal lattice,
then four of its electrons will be used in bonding with the silicon. The fifth will be free to move
about and conduct. Since the ability of the crystal to conduct is increased, the resistance of the
semiconductor is therefore reduced. The addition of an impurity like this is called doping.
n-type semiconductors
Learning Content: Explain how doping can form an n-type semiconductor in which the majority of the charge
carriers are negative, or a p-type semiconductor in which the majority of the charge carriers are positive.
This type of semiconductor is called n-type, since most conduction is by the movement of free
electrons, which are, of course, negatively charged.
p-type semiconductors
Learning Content: Explain how doping can form a p-type semiconductor in which the majority of the charge
carriers are positive.
The semiconductor may also be doped with an element like indium (In), which has only three outer
electrons. This produces a hole in the crystal lattice, where an electron is ‘missing’.
An electron from the next atom can move into the hole created as described previously.
Conduction can thus take place by the movement of positive holes. This is called a p-type
semiconductor, as most conduction takes place by the movement of positively charged ‘holes’.
Electrons at Work
Additional Notes on doping

The doping material is not simply added to the semiconductor crystal. It has to be grown
into the lattice when the crystal is made so that it becomes part of the atomic lattice.

The quantity of impurity is extremely small; it may be as low as one atom in a million. If it
were too large it would disturb the regular crystal lattice.

Although p-type and n-type semiconductors have different charge carriers, they are still both
overall neutral (just as metal can conduct but is normally neutral).

In terms of band structure we can represent the electrons as dots in the conduction band,
and holes as circles in the valence band. The majority charge carriers are electrons in n-type
and holes in p-type, respectively.
In an intrinsic semiconductor (one which has not been doped) the creation of an electronhole pair means that every electron which is boosted to the conduction band leaves behind
a hole in the valence band. This is shown below in (a).
Electron
energy
Conduction
band
Conduction
band
Conduction
band
Fermi level increased
Fermi
level
Fermi level decreased
Valence
band
Valence
band
Valence
band
(a) Intrinsic
semiconductor
(b) n-type
semiconductor
(c) p-type
semiconductor
Figure (b) shows an n-type semiconductor. The addition of Group 5 “donor” atoms into
the semiconductor introduces electrons in new energy levels which are just below the
conduction band. This raises the Fermi level. It takes much less energy to boost these
electrons into the conduction band. As these are electrons from group 5 atoms, when they
move into the conduction band, they do not leave a hole behind in the valence band. At
higher temperatures, a few electrons are boosted directly from the valence band up to the
conduction band, creating some holes in the valence band which are free to move. Holes
are the minority charge carriers in an n-type material.
In a p-type semiconductor (c) the addition of Group 3 acceptor atoms lowers the
Fermi level. However, because of the impurities, there are now stable energy levels for
the valence electrons to fill which are much closer than the original conduction band.
Valance electrons can move into this level, leaving behind a hole in the valence band.
This hole is the majority charge carrier and is free to move. As before, at higher
temperatures, some electrons are boosted directly up to the conduction band. These
electrons are free to move and are the minority charge carriers in the p-type material.
Electrons at Work
P-N JUNCTIONS
Learning content: When p-type and n-type material are joined, a layer is formed at the junction. The
electrical properties of this layer are used in a number of devices.
When a semiconductor is grown so that one half is p-type and the other half is n-type, the product
is called a p–n junction and it functions as a diode.
Thermal agitation means that at temperatures other than absolute zero, the electrons in the n-type
material and the holes in the p-type material will constantly diffuse. Diffusion is the spread of any
particle through random motion from high concentration regions to low concentration regions.
Electrons in the n-type material near the junction will be able to diffuse across it.
Electron energy
p-n junction
Conduction
band
Fermi
level
Fermi level flat as electron
drift balances diffusion
-
+
-
+
Filled sites where there is
an excess of charge
eVi
Diffusion
Valence
band
p-type
-
+
Drift
+
n-type
Excess
of
n-type
electrons diffuse across
junction to fill holes on
p-side which becomes –
while n side becomes +.
Any free electrons in
junction drift back to ntype, holes drift back to
p-type.
When an electron meets a hole, they recombine, i.e. the electrons ‘fill in’ the holes. This is shown as
a filled-site in the diagram above. This creates a charge imbalance: excess negative charge in the ptype region and excess positive in the n-type. This creates a slope in the conduction level which acts
as a potential barrier (Vi ≈ 0.7 V for silicon) since it would require work of eVi to be done in order to
get electrons to move against the barrier (e is the electron charge).1
The build up of charge on either side of the junction causes any free electrons/holes in the junction
to drift back across the junction. Once this drift balances the diffusion in the opposite direction,
equilibrium is reached and the Fermi level (where you are likely to find electrons) is flat across the
junction.
When no external voltage is applied to a p–n junction we refer to it as unbiased.
1
Any attempt to use this inbuilt voltage to do electrical work would prove futile, however, since in a complete
circuit the curves in the conduction and valence bands would even out.
Electrons at Work
Biasing the diode
To bias a semiconductor device means to apply a voltage to it. A diode may be biased in two ways.
The forward-based diode
When the p-side is attached to the positive side of a battery (Va = applied voltage) then the electrons
at that side have less potential energy than under no bias. This lowers the Fermi level and the
conduction bands on the p-side from where they were originally. We say it is forward biased.
Electron energy
Conduction
band
Junction
e(Vi – Va) = W
Fermi
level
W = eVa
Valence
band
p-type
n-type
As the applied voltage (Va) approaches the built in voltage (Vi), more electrons will have sufficient
energy to flow up the now smaller barrier and an appreciable current will be detected. Once the
applied voltage reaches the in-built voltage there is no potential barrier and the p–n junction
presents almost no resistance, like a conductor. The holes are similarly able to flow in the opposite
direction across the junction towards the negative side of the battery.
Electrons at Work
The reverse-biased diode
The applied voltage can either act against or with the in-built potential barrier. When the p-side is
attached to the negative side of a battery (Va, the applied voltage is now negative) then the electrons
at that side have more potential energy than previously. This has the effect of raising the bands on
the p-side from where they were originally. We say it is reverse biased.
Electron energy
Conduction
band
p-n
Junction
e(Vi + Va) = W
Fermi
level
W = eVa
Valence
band
p-type
n-type
Almost no conduction can take place since the battery is trying to make electrons flow ‘up the slope’
of the difference in the conduction bands. The holes face a similar problem in flowing in the opposite
direction. The tiny current that does flow is termed reverse leakage current and comes from the
few electrons which have enough energy from thermal ionisation to make it up the barrier.
Electrons at Work
The light-emitting diode
Learning Content: LEDs are p-n junctions which emit photons when a current is passed through the junction.
We have seen that in a forward-biased p-n junction diode, holes and electrons pass through the
junction in opposite directions. Sometimes holes and electrons will meet and recombine. When
this happens, energy is emitted in the form of a photon. For each recombination of electron and
hole, one photon of radiation is emitted. In most semiconductors this takes the form of heat,
resulting in a temperature rise. In some semiconductors such as gallium arsenic phosphide,
however, the energy is emitted as light. If the junction is close to the surface of the material, this
light may be able to escape. This makes what we call a Light Emitting Diode (LED). The colour
of the emitted light (red, yellow, green, blue) depends on the relative quantities of the three
constituent materials. The recombination energy can be calculated using E = hf if the frequency of
the light emitted is measured.
The LED does not work in reverse bias since the charge carriers do not travel across the junction
towards each other so cannot recombine.
The photodiode
A p-n junction in a transparent coating will react to light, producing electronhole pairs. This can be used to generate electricity.
The photovoltaic mode
Learning Content: Solar cells are p-n junctions designed so that a potential difference
is produced when photons enter the layer. This is the photovoltaic effect.
A p–n junction in a transparent coating will react to light in what is called the photovoltaic
effect. Each individual photon that is incident on the junction has its energy absorbed,
assuming the energy is larger than the band gap. In the p -type material this will create
excess electrons in the conduction band and in the n -type it will create excess holes in the
valence band. Some of these charge carriers will then diffuse to the junction and be swept
across the built-in electric field of the junction. The light has supplied energy to the
circuit, enabling a flow of current, ie it provides the emf in the circuit. More intense light
(more photons) will lead to more electron–hole pairs being produced and therefore a
higher current. In fact the current is proportional to the light intensity.
Electrons at Work
Energy Band diagram for the photodiode
The band diagram below shows that


Incoming photons boost electrons from the valence band of the p-type material to
the conduction-band (top-left of the diagram).
holes are created by the removal of electrons from the valence band of the n-type
material (bottom right).
These particles can then drift back across the junction due to the static charge that is
present on either side of the p-n junction (+ on the n-side and – on the p-side!)
Electron
energy
Incident photons
Incident photons
Conduction
band
Electron
drift
Fermi
level
Valence
band
Hole
drift
p-type
n-type
As a result a current flows in the circuit. The p–n junction can supply power to a load, eg a motor.
Many photodiodes connected together form a solar cell.
It is interesting to note that there is no bias applied to a solar cell and the photodiode therefore acts
like an LED in reverse.
END OF ELECTRICITY UNIT NOTES!