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Physics


Semiconductors and


Band Theory


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Material





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2

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)


© Learning and Teaching Scotland 2011


The Scottish Qualifications Authority regularly
reviews the arrangements for National
Qualifications. Users of all NQ suppor
t materials,
whether published by Learning and Teaching
Scotland or others, are reminded that it is their
responsibility to check that the support materials
correspond to the requirements of the current
arrangements.
























Acknowledgement

Learning and Teaching Scotland gratefully acknowledges this contribution to the
National Qualifications support programme for
Physics
.


I gratefully acknowledge the kind guidance and advice I have received from Carol
Trager
-
Cowan of the University of Strat
hclyde.


© Learning and Teaching Scotland 2011


This resource may be reproduced in whole or in part for educational purposes by
educational establishments in Scotland provided that no profit accrues at any stage.



SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)

3


© Learning an
d Teaching Scotland 2011





Contents



Electrical
conductivity
an
d
band theory

4


Summary of
band theory

8


Intrinsic
semiconductors

9


Extrinsic
semiconductors

11


Student Activity 1


Thermistor
investigation

13


Summary of
intrinsic
and
extrinsic semiconductors

14


p

n junctions

15


Photovoltaic
cells

17


Student Act
ivity 2


Photovoltaic cell
s

18


Light
emitting diodes

18


Student Activity 3


LED
threshold voltage

20


Why use LEDs?

21


Summary of
p

n junctions
, LEDs and
photovoltaic cells

21


References and
further reading

22



SEMICONDUCTORS AND BAND THEORY

4

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)


© Learning and Teaching Scotland 2011





Semiconductors and band theory


The purpose of this document is to introduce the new approach
that

is being
brought to the Higher Physics course, in teaching about semiconductors from
the perspective of band theory.



El
ectrical conductivity and band theory


All solids can be classified
as conducto
rs, semi
conductors or insulators
according to the availability of conduction electrons in their structures. Band
theory gives an explanation for these differences in electrical properties and
accoun
ts for the availability, or not,

of those condu
ction electrons.


Although individual atoms have certain permitted energy levels for
their
electrons, as defined by quantum theory, when large groups of atoms are

incorporated into a solid mass

those energy levels become reorganised
in
such a way as to res
ult in

bands of
possible energy levels

(
Figure
1)
.

This is
known as the tight binding approximation.





Figure 1

Discrete energy levels within an individual atom (left) and bands of permitted
energy levels within a solid (right
)

Permitted energy levels

Permitted energy bands

SEMICONDUCTORS AND BAND THEORY

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)

5


© Learning an
d Teaching Scotland 2011

There are such enormous numbers of electrons in a solid mass that although
the bands actually consist of very large numbers of closely packed discrete
energy levels, the bands become essentially continuous
.

There may be several
permitted
energy level
ba
nds, but
in
particular

we c
onsider the two uppermost
bands
.

T
hese are known as

the valence band and the conduction band

(Figure
2)
.




Figure 2

Conduction and valence bands in an insulator. These bands contain the only
permitted

energy levels, and since the valence band is full and the conduction band is empty,
no net movement of electrons can occur within the material. Note the gap separating the
bands.


The electrons with lower energy levels are described as
occupying the

valen
ce band.

The innermost electrons in an atom are much less influenced by
neighbouring atoms, and occupy discrete energy levels.

They are sometimes

co
nsidered to be bound
.

At higher levels in the valence band electrons

can
,

in
fact
,

move fr
om atom to atom, b
ut only up to the top of

the valence band.

Since they
are permitted only to

swap places with other valence electrons in
neighbouring atoms, they are

effectively
un
available for conduction.


Electrons fill the valence band from the lowest level to the high
est
.

T
he top
of the valence band
for a material
is the
highest
level
,

which would
,

in
theory,
be filled by all the available electrons
within an atom

of that material
at
a temperature of
0

K
.

In insulators and semic
onductors, the valence band is

completely

fil
led with electrons.

T
he conduction band is empty

(
Figure
2)
.



Conduction band (empty)

Valence band (full)

SEMICONDUCTORS AND BAND THEORY

6

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)


© Learning and Teaching Scotland 2011

The electrons fill energy

levels in order because, as fermions, they must obey
the Pauli exclusion principle and cannot occupy identical energy levels.

T
he
only way that an electron
could

move from one atom to another in an
insulator or
semiconductor would be to occupy a

slightly different energy
level in a neighbouring atom.

However, all those energy levels are already
full.

As discussed above, the electrons

may effectively swap places, bu
t in
order to facilitate conduction, they must leap up to the conduction band.

An
energy level band must have some space within it (some vacant energy levels)
in order for there to be any net movement of electrons within the material.


For a material to

be

able to conduct electricity

it must have electrons

in its

conduction band

or spaces in its valence band
.

There must be spaces for
charges to move into
:

a partially filled band
.


http://phet.
colorado.edu/en/simulation/conductivity

The simulation demonstrates how energy levels differ in conductors,
semiconductors and insulators, and the impact the energy levels have on
conductivity.


A
gain, a
s a result of the wavelike behaviour of electro
ns wi
thin atoms,

materials

may
exhibit

a
certain
range of

forbidden


energy levels

(
Figure
3)
.

I
t is simply not possible for
an electron

to exist with
an energy level

that

would place it in this
range.

This leaves insulators and semiconductors

with a
gap betwe
en the two bands
.




Figure 3
: Conduction bands (blue) and valence bands (yellow) for insulators,
semiconductors and conductors. Note the energy gaps in insulators and semiconductors, and
how in a conductor there is no gap, sim
ply a continuous, partially filled conduction band.


Insulator

Semiconductor

Conductor

Gap

of forbidden energies

SEMICONDUCTORS AND BAND THEORY

SEMICONDUCTORS AND BAND THEORY

(H,
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© Learning an
d Teaching Scotland 2011

In insulators

this zone of forbidden energy levels
is
very
substantial, and
separates the valence band and the conduction band

significantly
.

The
forbidden zone
is of the order of a few electron volts,
and is therefore so
large
that it is not normally practicable for there to be sufficient energy to
move electrons across it from the valence band to the conduction band.

For
example, thermal excitations

and conventional electric circuit voltages

within
a m
aterial provide

energies
that

are

smaller than 1

eV

on an atomic scale
.

It
would be necessary to expose an insulator to electric fields of the order of
1010

V

m

1

in order to give the valence electrons enough energy to jump
across th
e

gap to the conduction

band, since this could provide

energy in the
order of a few electron volts

on
an
atomic scale.

This is what happens when
there is dielectric breakdown.



C
ontrastingly, c
onductors
only
h
ave one

band, and the top of this band is only
partially filled
, perm
itting electrical conduction
.

This means that there
are

plenty of nea
rby energy levels available for electrons to move into.

They can
flow easily from one atom to another when a potential difference is applied
across the conducting material.



Like insulat
ors, s
emiconductors have
a completely full valence band and so
electrons are not able to facilitate conduction at low temperatures.

However,
for semiconductors, the

forbidden energy level
zone between the two bands

is
sufficiently sma
ll to make it much eas
ier
for significant numbers of

electrons
to move across
this gap

and go
from the valence band to the conduction band
.

This can happen if sufficient energy is supplied, for example

if there is some
thermal excitation.

As a result, semiconductors exhibit inc
reased conductivity
with increasing temperatures.

In many semiconductors, a temperature
increase of 10

K will permit a doubling of the numbers of electrons in the
conduction band.


In order to increase the conductivity of semiconductors,

small amount
s

of

d
oping material can
be used.

This
result
s

in

significant increase
s

in
conductivity

as a
result of the narrowing

of the

gap

between
the
conduction
and valence bands
.


SEMICONDUCTORS AND BAND THEORY

8

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)


© Learning and Teaching Scotland 2011

Summary

of
band theory




In

solids, permitted electron energy levels are organised as bands
.



The
valence ba
nd

contains electrons
that

can be considered
to be
bound to
the atom.

In insulators and semiconductors the valence band is full
.



The
conduction band

is a region of permitted energy levels
that

is empty
in insulators and semiconductors, but
partially filled in conductors
.



Only partially filled bands may permit conduction
.



There is a forbidden zone

that

forms an
energy gap

between the valence
and conduction

bands
in insulators and semiconductors
.



That

energy
gap must be jumped if an electron i
s to move to the
conduction band, and this is not normally possible
in insulators because
the

gap is too large
.



In semiconductors, the forbidden

zone is much smaller and electrons can
jump the gap to the conduction zone as a result of thermal excitation
.



D
oping

of semicon
ductors can significantly reduce the

width of the energy
gap
.


For further information on this topic, try this high
-
level simulation:


http://phet.colorado.edu/en/simulation
/band
-
structure


There is also further information from the Hyperphysics website:


http://hyperphysics.phy
-
astr.gsu.edu/hbase/solids/band.html


Many links lead from this, although

i
t should be noted that some (otherwise
very useful) resources describe an overlap between valence and conduction
bands in metals.

This is misleading and should be treated with caution.


SEMICONDUCTORS AND BAND THEORY

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)

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© Learning an
d Teaching Scotland 2011

Intrinsic
semiconductors


Pure, undoped s
ilicon and germanium are tw
o simple examples of intrinsic
semiconductors

(Figure 4)
.

They are both in
Group
IV

of the
Periodic Table
,
and form a tetrahedral crystalline
structure, similar to diamond.

Each atom of
silicon and germanium has four electrons in its outermost electron she
ll, and
each of these electrons is used in a covalent bond with one of the atom’s four
neighbours.






Figure 4

Two
-
dimensional

illustration of a crystal of pure undoped Si. If any individual
atom of silicon is considered, it c
an be seen that each of its four valence electrons
is

used in
maintaining covalent bonds with the atom’s neighbours. These electrons are therefore
unavailable for conduction.


Since all valence electrons are involved in bonding,
pure
silicon and
germanium
may be expected to be good insulators.

However, relatively small
energies are required to move a valence electron across the energy gap to the
conduction band.

This is 1.1

eV for silicon, and only 0.7

eV for germanium.

This means that a significant number
of electrons are available in the
conduction band, even at room temperature

(
Figure
5)
.


SEMICONDUCTORS AND BAND THEORY

10

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)


© Learning and Teaching Scotland 2011




Figure 5

It is possible for significant numbers of electrons to cross the energy gap in
semiconductors.


It must be noted at this stage

that although most thermal excitation involves
energies much less than even 0.7

eV, quantum mechanics clearly shows that
there is a small but significant probability of an electron being able to jump
the energy level gap, even at relatively low temperatur
es.

As previously
discussed, this probability increases rapidly with temperature.


Once an electron jumps up to the conduction band in the crystal lattice, it
leaves behind a

hole


in the covalent bond.

This hole can enable another
neighbouring valence ba
nd electron to move into it.

As such, a hole behaves
rather like a positive charge carrier, even though it is actually a vacancy for
an electron.

A hole can travel through the crystal lattice of the
semiconductor.

A helpful analogy might be to consider a q
ueue of cars on a
road.

If a space appears at the front of the queue, cars may move forward in
turn.

Each time a car moves forward, it leaves a space behind it, into which
the next car may now move.

An observer from above might consider that the
cars are m
oving forwards or that the space is moving backwards.


Some

semiconductors
,

like
pure silicon or

germanium
, are known as intrinsic
semiconductors.

Intrinsic semiconductors

must always contain equal numbers
of conduction

electrons and holes.

If an electron
can move from its place
then
it must leave behind a hole

(Figure 6)
.


Silicon


Germanium

Conduction band

Valence band

El
ectrons
moving
across energy
gap due to
thermal
excitation

SEMICONDUCTORS AND BAND THEORY

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)

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© Learning an
d Teaching Scotland 2011



Figure 6

In intrinsic semiconductors like pure silicon or germanium, every electron that
moves up to the conduction band must leave a hole in the valence b
and. Electrons and holes
exist in equal numbers and both contribute to conduction. There are no majority charge
carriers in intrinsic semiconductors.



Extrinsic
semiconductors


Often, it is more useful to control the properties of a
Group
IV
semiconductor

by deliberately introducing very small propo
rtions of a
Group
III or
Group
V
element.

This is known as doping and results in
what is known as
an extrinsic
semiconductor.

Extrinsic semiconductors have majority charge carriers
that

may be either electrons o
r holes.


Consider

a semiconductor
that

is d
oped with a
Group
III element

(
Figure
7)
.

Each a
t
om

of the doping agent
will
have only three electrons in its outer
shell.

This is insufficient to form the four covalent bonds with i
ts
Group
IV
neighbours and th
erefore

results in a hole.

Countless holes are now built into
the semiconductor’s crystal lattice.

It may be referred to as a p
-
type
semiconductor as the majority charge carriers are positively charged holes.

As a result of the doping process, it will requ
ire much less energy to allow
charge to flow through the semiconductor and so its conductivity is greatly
enhanced.

Unlike metals, a p
-
type semiconductor’s conduction occurs in the
valence band
.

In effect, the doping agent adds an extra energy level just
a
bove the valence band
, sometimes called an acceptor band
.



electrons

holes

SEMICONDUCTORS AND BAND THEORY

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SEMICONDUCTORS AND BAND THEORY

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PHYSICS
)


© Learning and Teaching Scotland 2011




Figure 7

Introducing small quantities of Group III atoms into a silicon lattice (in practice
only around one part in a million) leaves holes built into the valence
band.


T
echnically, t
here will
also
still be a small degree of intrinsic behaviour, as
electrons leave behind holes, but this is not considered to be significant in
comparison with the overwhelming number of majority charge carriers.


A similar process is
involved if a
Group
V element is used for doping.

This
gives an extra electron, surplus to covalent bonding requirements, for each
atom of the doping agent.

These electrons are negatively charged and so an

n
-
type semiconductor has been produced.

In an n
-
t
ype semiconductor, the
majority charge carriers are electrons.

The conductivity has been greatly
enhanced as before
, but this time conduction
occurs in an extra energy level
just below the

conduction band
, which is sometimes called the donor band
.

Therefor
e, in p
-
type and n
-
type semiconductors conduction can occur easily
because there is
effectively
unfilled space within either the valence or the
conduction band
,

respectively.


Semiconductors are crucial to modern life.

According to estimates (Sheffield
Uni
versity) 43% of all semiconductor production goes into computers, 23%
into consumer products, 13% into communication and 12% into
manufacturing.


Electron


Hole



Silicon



Group III

SEMICONDUCTORS AND BAND THEORY

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)

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© Learning an
d Teaching Scotland 2011

In Scotland
,

Silicon Glen

(which is

a large proportion of the central belt
)

has
been pioneering electronics p
roduction since the 1940s, employing around 50
000 people at its peak in 2000.

The name

Silicon Glen


reflects the
importance of semiconductors to this sector of Scottish industry, whilst
making comparisons with California’s Silicon Valley.

One specialist

application for semiconductors is the detection of magnetic
fields using the Hall
effect
.

You may
be lucky enough to
have a Hall
effect
probe in your school.

If not, here are some simulations

of the effect
:


http://www.youtube.com/watch?v=_ATDraCQtpQ&feature=related


http://www.youtube.com/watch?v=FUNnziMmgSQ&feature=related



Student Activity

1


Thermistor
inve
stigation


Thermistors use semiconductors in order to vary resistance as a function of
temperature.

Negative temperature coefficient (NTC) thermistors use thermal
energy to free up more charge carriers, so an increase in temperature results
in a reduction
in resistance.


Students can investigate the resistance variation with te
mperature for an NTC
thermistor:





The thermistor can be immersed in a small beaker of hot water (with a
thermometer) and the meter readings used to calc
ulate resistance at 5
°
C
intervals as it cools.

A plot of resistance versus temperature can then be
produced by the students.

A similar procedure could be used for an L
ight
D
ependent
R
esistor
.


V

A

SEMICONDUCTORS AND BAND THEORY

14

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)


© Learning and Teaching Scotland 2011

Summary of
intrinsic
and
extrinsic semiconductors




Semiconduct
ors allow conduction by means of negative charge carriers,
which are electrons, or positive charge carriers, which are holes.



The energy band gap in semiconductors is small enough that thermal
excitation is sufficient for significant numbers of electrons t
o be able to
move up from the valence to the conduction band.



Intrinsic

semiconductors
,

such as pure silicon
,

will always have equal
numbers of holes and electrons since each conduction electron will leave
behind a hole
.



Semiconductors may be
doped
with im
purities
that

add
either
extra
electrons or holes to the lattice.



These doped semiconductors now have a majority charge carrier present
and are known as
extrinsic
semiconductors.



Group III doping age
nts result in
p
-
type extrinsic semiconductors, which
cont
ain extra holes.



Group V dop
ing age
nts result in
n
-
type extrinsic semiconductors, which
contain extra electrons.



This link gives you a simulation for a semiconductor
that

you can adjust
yourself:


http://phet.colorado.edu/en/simulation/semiconductor


SEMICONDUCTORS AND BAND THEORY

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)

15


© Learning an
d Teaching Scotland 2011

p

n junctions


If a single semiconducting crystal is doped in such a way

that one end is

p
-
type and the other n
-
type, then some very useful properties come into play.

The interface between t
he p
-
type and n
-
type sections is known as a p

n
junction.

In this boundary region, electrons from the n
-
type material may
diffuse across the boundary and
combine with holes from the p
-
type material
,
and vice versa
.

This results in a lack of majority charge

carriers in the
immediate vicinity of the junction and as such the region is known as the
depletion zone.

The p

n junction greatly affects the conductivity of the
semiconductor as a whole.

When electrons from the n
-
type material diffuse
into the p
-
type ma
terial, they form negative ions as they combine with holes.

Positive ions are also left behind in the n
-
type material.

Eventually, this
process results in there being no further diffusion of electrons or holes as a
result of Coulomb attraction and repulsio
n

(
Figures
8a and 8b)
.





Figure 8a

In a p

n junction a depletion zone is formed by the diffusion of electrons from the
n
-
type material into the p
-
type material. As the electrons combine with holes, ions are
formed in the deple
tion zone.


-

-

-

-

-

-

-

-

-

-

-

-

-

-

+ + +

+ + ++

+ + +

p
-
type

n
-
type

Junction

Depletion zone

SEMICONDUCTORS AND BAND THEORY

16

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)


© Learning and Teaching Scotland 2011




Figure 8b

Band theory gives us a model for explaining what happens at a p

n junction.
Holes and electrons diffuse towards the junction in their different bands. At the junction they
combine, producing the depleti
on zone. This p

n junction is forward biased.


The p

n junction may only allow current to flow if it is forward biased.

By
connecting the negative terminal of a power supply to the n
-
type material, the
junction becomes forward biased.

Electrons may be push
ed across the
depletion zone if the supply has a sufficient potential difference to overcome
the Coulomb repulsion discussed above.

This is typically of the order of 0.7

V
.

Once the depletion zone is crossed, conduction is easily facilitated by the
majorit
y charge carriers in each of the semiconducting materials.


If the p

n junction is reverse biased,

ie

the n
-
type material is connected to the
positive terminal of a power supply,

the depletion zone effectively becomes a
greater and greater barrier to condu
ction.

One can imagine the depletion zone
illustrated in
Figures
8a and 8b becoming a higher and higher barrier to
conduction

as e
lectrons are driven further and further back from the depletion
zone.

The junction

can only allow a tiny leakage current
to fl
ow

because of

the intrinsic semiconductor
’s

electrons and holes
.

Since this is usually
undesirable, silicon is preferable to germanium because its leakage current is
so much smaller as a result of it having a larger
energy
gap between i
ts
valence and condu
ction bands (
Figure
5).


Eventually, if the reverse voltage continues to increase, the semiconductor
will break down and may result in damage to the junction.


Conduction

band

Valence band

Depletion zone


p
-
type

n
-
type

SEMICONDUCTORS AND BAND THEORY

SEMICONDUCTORS AND BAND THEORY

(H,
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)

17


© Learning an
d Teaching Scotland 2011

Photovoltaic
cells


A photovoltaic cell consists of a very thin layer of p
-
type semiconductor
t
hat

is in contact with a layer of n
-
type material.

The conduction electrons are
freed through the action of photons of light.

The photons provide sufficient
energy to the electrons to enable them to jump up across the en
ergy gap to the
conduction band, lea
ving behind a hole.

The band gap energy for silicon is of
the order of 1.1

eV, and so only photons with at least 1.1

eV of energy can
cause the release of conduction electrons.

The wafer of semiconductor is very
thin and so there is a good chance that this

process will happen at or very
close to the p

n junction.

The electric field produced by the depletion layer at
this junction forces the electron and hole apart,
creating a potential
difference,
and so a current can flow if the cell is connected to a circ
uit.

The
p
-
type layer must be very thin, perhaps
1


m

thick, to prevent conduction
electrons from being captured and immobilised by holes.


This animation is useful:


http://solarhorizon.com.au/Flash/LightCurrent.html





Figure 9

Simplified photovoltaic cell in cross
-
section.

Photons interact with
electrons close to p

n
junction

p
-
type

n
-
type

Contact
s

SEMICONDUCTORS AND BAND THEORY

18

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)


© Learning and Teaching Scotland 2011

A solar cell must also have a layer of antireflective coating
(not shown in
Figure
9)
to improve efficiency because
a
silicon
crystal
is so shiny that
without this layer many of the photons w
ould be reflected before they could
cause the release of an electron.

Even so, typical efficiencies of solar cells
stand close to 15% and the greatest effic
iencies rarely exceed 25
%.

Finally,
the cell must be coated in glass to reduce damage from the eleme
nts.


A compromise must be reached in the choice of materials used to optimise the
performance of the solar cell.

By reducing the band gap energy in the
semiconducting material, photons with longer wavelengths and lower
frequencies may be harnessed to free

electrons and holes.

Although this may

seem desirable

and will release more charges
, it has the effect of reducing the
strength of the electric field across the junction.

It turns out that a band gap
energy of about 1.4

eV is close to ideal
, maximising th
e current and voltage,
and therefore the power, of the cell
.




Student Activity

2



P
hotovoltaic

c
ell
s


Students can

do

investigation
s

into the voltage produced by a
photovoltaic
cell as a function of one of the following:




Irradiance
.

This investigation
may be better suited to a qualitative rather
than quantitative approach because of difficulties in measuring irradiance
accurately.

One approach

could involve a dimmable light
source, another
could be to vary the distance from source to cell.




A
ngle of inc
idence on the solar cell
.

Us
e

one light source keep the distance
constant at, say, 1.0

m in order to ke
ep the test as fair as possible, then
vary the angle.





F
requency of radiation
.

This could employ

a range of high
-
powered
light
-
emitting diodes

(LEDs)
o
r

filters on a white light source.

Again, distance
and power must be kept constant.


Turning this investigation into a look at the inverse square law is another
possibility.

Best results will be achieved if the laboratory can be

blacked out
for this investi
gation.



L
ight
-
emitting diodes


When a diode is forw
ard biased, electrons from the n
-
type semiconductor may
move across the junction

and combine with holes in the p
-
type material.

The
electrons in the n
-
type semiconductor move within the higher energy

SEMICONDUCTORS AND BAND THEORY

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)

19


© Learning an
d Teaching Scotland 2011

c
onduction band
,

and as they cross the junction they move briefly into the
empty
conduction band of the p
-
type material.

Since the
lower energy
p
-
type
valence band is only partially filled
,

however, the electrons
rapidly fall into
an energy

level within tha
t valence band.

In effect, electrons fall
into holes,
and as this happens

energy is released in the form of emitted
photons

(
Figure
10)
.

For ordinary diodes, these photons have a relatively low frequency and
long wavelength, which means that they fall outs
ide the visible spectrum.

However, in the construction of LEDs the semiconducting materials may be
engineered in such a way as to result in the photons having sufficiently high
frequency
that they

fall within the range of visible light.


The
frequency of t
he
light emitted from LEDs is controlled by

the

size of the
energy gap between the conduction and valence bands.

A bigger gap will
result in a larger energy change and
,

in accordance with the relationship
E

=
hf
, a higher frequency of light will be emitted
.

So, a small energy gap will
result in red light and a much larger energy gap is required for green or blue
light.





Figure 10

In an LED electrons cross the junction from n to p in the conduction band. Once
on the p side of t
he junction, they fall back across the energy gap to the valence band. This
releases photons of light.


n
-
type

p
-
type

Pho
tons emitted as
electrons drop
down to valence
band

Junction

Conduction band

(partially filled)

Valence band

(partially filled)

SEMICONDUCTORS AND BAND THEORY

20

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)


© Learning and Teaching Scotland 2011

Since electrons usually drop from the bottom of the conduction band into the
top of the valence band, light from LEDs tends to be nearly

(although not

completely)

monochromatic, with a narrow emission spectrum.


To alter the energy gap in an LED, different doping agents are used.

They
may typically include indium, gallium and nitrogen to produce blue light,
gallium and phosphorous for green light, and g
allium, phosphorous and
arsenic for red light.

By using combinations of red, green and blue it is
possible to produce any colour of light and this has led to the advent of LED
televisions.

Furthermore, by varying the proportions of the doping agents,
singl
e intermediate colours may also be produced.



Student Activity
3


LED
threshold voltage


There is an approximate correlation between the threshold voltage for an LED
and its
colour, since the energy returned in the form of an emitted photon is
approximat
ely the same as the energy required to raise an electron across the
energy gap of the material.

This can

be investigated in a practical, as
illustrated in
Figure
11.





Figure 11

A practical investigation into the correlation b
etween energy band gaps and
colours of LEDs can be carried out. Different colours of LEDs can be put into the circuit and
the potential difference required to illuminate them noted. A graph of frequency of light
versus potential difference may be plotted.


+ Supply



V

SEMICONDUCTORS AND BAND THEORY

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)

21


© Learning an
d Teaching Scotland 2011

Organic light emitting diodes (OLEDs) use organic polymer layers
sandwiched between two electrodes.

When a voltage is applied across the
layers, electrons and holes are generated
,

which then recombine to emit
photons.

The layers may be put into a composi
te of red
-
, green
-

and blue
-
emitting sections so as to produce full
-
colour displays.

Further information
on this topic can be found here:


http://www.chemistry.wustl.ed
u/~courses/genchem/Tutorials/LED/bands_06.
htm



Why use LEDs?


LEDs have many advantages over oth
er light sources.

An LED typically has
an efficiency of around 80%.

This is far superior even to energy
-
saving
compact lights

because of

the way in which ligh
t is produced.

This clearly
has major implications for reducing carbon dioxide emissions and fuel bills.

Because of

the very low levels of undesirable thermal energy produced, LEDs
may also be expected to have much greater longevity than conventional light

sources.

LED and OLED TVs are expensive but with low power usage and
high reliability

they

are set to become more common in future.


Infrared LEDs are used in remote controls because of their reliability and low
power consumption.

Ultraviolet LEDs can be
used for detecting counterfeit
notes and even for sterilisation procedures.


LEDs have extremely fast switching speeds
,

which mean
s

that they are

particularly useful for applications where light sources

must be

pulsed,
strobed or simply

switched on and off

rapidly

with reliability
.

Additionally,
they work well at low temperatures, are shock resistant and contain fewer
hazardous materials than energy
-
saving light bulbs.



Summary o
f p

n junc
tions
, LEDs and
photovoltaic
c
ells




The interface between p
-
type and

n
-
type material is called the p

n
junction.



Majority charge carriers diffuse towards the junction and electrons
combine with holes
,

forming ions.



This lack of charge carriers results in a depletion zone across the p

n
junction, with positive ions on the n
-
type side and negative ions on the p
-
type side.



If the p
-
type material is connected to the positive terminal of a supply and
the n
-
type to the negative terminal, then the junction is
forward biased
.

SEMICONDUCTORS AND BAND THEORY

22

SEMICONDUCTORS AND BAND THEORY

(H,
PHYSICS
)


© Learning and Teaching Scotland 2011



If the p
otential difference

across the junction is suff
icient to force
electrons to cross the depletion zone, then the junction will conduct.



If the terminals are reversed, the junction is
reverse biased

and cannot
conduct.



LEDs emit photons of light as electrons

fall


from the conduction band of
the n
-
type m
aterial into holes in the valence band of the p
-
type material.



The bigger the energy gap between the bands, the greater the energy, and
therefore the frequency, of the emitted photons.



Photovoltaic
cells use the energy of absorbed photons to separate elect
rons

and holes and thus produce a potential
d
ifference
.



References and
further reading


You will find a great deal of further reading on the internet and in specialist
electronics books
. T
he following sources

are recommended
:


http://www.chemistryexplained.com/Ru
-
Sp/Semiconductors.html


http://hyperphysics.phy
-
astr.gsu.edu/hbase/solids/band.html


http://www.educypedia.be/education/solarcellanimations.htm


and many other linked pages associated with this topic from
Hyperphysics
.


http:/
/en.wikipedia.org/wiki/P
-
n_junction



In addition, for those with a sen
se of humour, the somewhat eccentric


http://britneyspears.ac/physics/basics/basics.htm