EEE 429: Opto-Electronics(3 Credit)
Dr. MD Shahrukh Adnan Khan
Department of Electrical and Electronic Engineering,
University of Asia Pacific
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EEE 429
An introduction to optoelectronics
• Properties of Light (Historical Sketch)
The ancient Greeks speculated on the nature of light from about 500 BC. The
practical interest at that time centred, inevitably, on using the sun’s light for military
purposes; and the speculations, which were of an abstruse philosophical nature,
were too far removed from the practicalities for either to have much effect on the
other.
The modern scientific method effectively began with Galileo (1564 – 1642), who
raised experimentation to a properly valued position. Newton was born in the year
in which Galileo died, and these two men laid the basis for the scientific method
which was to serve us well for the following three centuries.
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EEE 429
An introduction to optoelectronics
• Properties of Light (Historical Sketch)
Newton believed that light was corpuscular (particle like electron, photon, neutron)
in nature. He reasoned that only a stream of projectiles, of some kind, could
explain satisfactorily the fact that light appeared to travel in straight lines.
Euler, Young and Fresnel began to gain their due prominence. These men
believed that light was a wave motion; they developed an impressive theory which
well explained all the known phenomena of optical interference and diffraction. The
wave theory rapidly gained ground during the late 18th and early 19th centuries.
The final blow in favour of the wave theory is usually considered to have been
struck by Foucault (1819 – 1868) who, in 1850, performed an experiment which
proved that light travels more slowly in water than in air. This result agreed with the
wave theory and contradicted the corpuscular theory.
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EEE 429
An introduction to optoelectronics
• Properties of Light (Historical Sketch)
For the next 50 years the wave theory held sway until, in 1900, Planck (1858 – 1947)
found it mathematically convenient to invoke the idea that light was emitted from a
radiating body in discrete packets, or ‘quanta’, rather than continuously as a wave.
Although Planck was at first of the opinion that this was no more than a mathematical
trick to explain the experimental relation between emitted intensity and wavelength,
Einstein (1879 – 1955) immediately grasped the fundamental importance of the discovery
and used it to explain the photoelectric effect, in which light acts to emit electrons from
matter: the explanation was beautifully simple and convincing. It appeared, then, that
light really did have some corpuscular properties.
In parallel with these developments, there were other worrying concerns for the wave
theory. From early in the 19th century its protagonists had recognized that ‘polarization’
phenomena, such as those observed in crystals of Iceland spar, could be explained if the
light vibrations were transverse to the direction of propagation. Maxwell (1831 – 1879) had
demonstrated brilliantly (in 1864), by means of his famous field equations, that the
oscillating quantities were electric and magnetic fields.
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EEE 429
An introduction to optoelectronics
• Properties of Light (Historical Sketch)
Einstein into an entirely new view of space and time, in his two theories of
relativity: the special theory (1905) and the general theory (1915). Light, which
propagates in space and oscillates in time, plays a crucial role in these theories.
Thus physics arrived (ca. 1920) at the position where light appeared to exhibit both
particle (quantum) and wave aspects, depending on the physical situation. To
compound this duality, it was found (by Davisson and Germer in 1927, after a
suggestion by de Broglie in 1924) that electrons, previously thought quite
unambiguously to be particles, sometimes exhibited a wave character, producing
interference and diffraction patterns in a wave-like way.
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EEE 429
An introduction to optoelectronics
• Wave Nature of Light
In 1864, Clerk Maxwell was able to express the laws of electromagnetism known
at that time in a way which demonstrated the symmetrical interdependence of
electric and magnetic fields.
In order to complete the symmetry he had to add a new idea: that a changing
electric field (even in free space) gives rise to a magnetic field. The fact that a
changing magnetic field gives rise to an electric field was already well known, as
Faraday’s law of induction.
Since each of the fields could now give rise to the other, it was clearly
conceptually possible for the two fields mutually to sustain each other, and thus
to propagate as a wave.
Maxwell’s equations formalized these ideas and allowed the derivation of a wave
equation.
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EEE 429
An introduction to optoelectronics
• Wave Nature of Light
This wave equation permitted free-space solutions which corresponded to
electromagnetic waves with a defined velocity; the velocity depended on the
known electric and magnetic properties of free space, and thus could be
calculated.
The result of the calculation was a value so close to the known velocity of light
as to make it clear that light could be identified with these waves, and was thus
established as an electromagnetic phenomenon.
All the important features of light’s behaviour as a wave motion can be deduced
from a detailed study of Maxwell’s equations. We shall limit ourselves here to a
few of the basic properties.
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EEE 429
An introduction to optoelectronics
• Wave Nature of Light
If we take Cartesian axes Ox, Oy, Oz, we can write a simple sinusoidal solution
of the free-space equations in the form:
The result of the calculation was a value so close to the known velocity of light
as to make it clear that light could be identified with these waves, and was thus
established as an electromagnetic phenomenon. All the important features of
light’s behaviour as a wave motion can be deduced from a detailed study of
Maxwell’s equations. We shall limit ourselves here to a few of the basic
properties.
These two equations describe a wave propagating in the Oz direction with
electric field (Ex) oscillating sinusoidally (with time t and distance z) in the xz
plane and the magnetic field (Hy) oscillating in the yz plane. Note also that the
two fields must oscillate at right angles to the direction of propagation, Oz.
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EEE 429
An introduction to optoelectronics
• Wave Nature of Light
If we take Cartesian axes Ox, Oy, Oz, we can write a simple sinusoidal solution
of the free-space equations in the form. The result of the calculation was a value
so close to the known velocity of light as to make it clear that light could be
identified with these waves, and was thus established as an electromagnetic
phenomenon. All the important features of light’s behaviour as a wave motion
can be deduced from a detailed study of Maxwell’s equations. We shall limit
ourselves here to a few of the basic properties.
These two equations describe a
wave propagating in the Oz direction
with electric field (Ex) oscillating
sinusoidally (with time t and distance
z) in the xz plane and the magnetic
field (Hy) oscillating in the yz plane.
Note also that the two fields must
oscillate at right angles to the
direction of propagation, Oz.
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EEE 429
An introduction to optoelectronics
where v and k are known as the angular frequency and propagation constant,
respectively. it is clear that the velocity of the wave is given by:
The free-space wave equation shows that this velocity should be identified as
follows10
EEE 429
An introduction to optoelectronics
where v and k are known as the angular frequency and propagation constant,
respectively. it is clear that the velocity of the wave is given by:
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An introduction to optoelectronics
The free-space wave equation shows that this velocity should be identified as
follows:
where e0 is a parameter known as the electric permittivity, and µ0 the magnetic
permeability, of free space. Thus Maxwell was able to establish that light in free
space consisted of electromagnetic waves.
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EEE 429
An introduction to optoelectronics
Quantum Numbers and Atomic Orbitals
A wave function for an electron in an atom is called an atomic orbital; this atomic orbital
describes a region of space in which there is a high probability of finding the electron. Energy
changes within an atom are the result of an electron changing from a wave pattern with one
energy to a wave pattern with a different energy (usually accompanied by the absorption or
emission of a photon of light).
Each electron in an atom is described by four different quantum numbers. The first three
(n, l, ml) specify the particular orbital of interest, and the fourth (ms) specifies how many
electrons can occupy that orbital.
Principal Quantum Number (n): n = 1, 2, 3, …, ∞
Specifies the energy of an electron and the size of the orbital (the distance from
the nucleus of the peak in a radial probability distribution plot). All orbitals that
have the same value of n are said to be in the same shell (level). For a hydrogen
atom with n=1, the electron is in its ground state; if the electron is in the n=2
orbital, it is in an excited state. The total number of orbitals for a given n value
is n2.
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An introduction to optoelectronics
1. Principal Quantum Number (n): n = 1, 2, 3, …, ∞
Specifies the energy of an electron and the size of the orbital (the distance from the nucleus of
the peak in a radial probability distribution plot). All orbitals that have the same value of n are
said to be in the same shell (level). For a hydrogen atom with n=1, the electron is in its ground
state; if the electron is in the n=2 orbital, it is in an excited state. The total number of orbitals
for a given n value is n2.
2.Angular Momentum (Secondary, Azimunthal) Quantum Number (l): l = 0, ..., n-1.
Specifies the shape of an orbital with a particular principal quantum number. The secondary
quantum number divides the shells into smaller groups of orbitals
called subshells (sublevels). Usually, a letter code is used to identify l to avoid confusion
with n.
The subshell with n=2 and l=1 is the 2p subshell; if n=3 and l=0, it is the 3s subshell, and
so on. The value of l also has a slight effect on the energy of the subshell; the energy of the
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subshell increases with l (s < p < d < f).
EEE 429
An introduction to optoelectronics
3.Magnetic Quantum Number
(ml): ml = -l, ..., 0, ..., +l.
Specifies the orientation in space of an
orbital of a given energy (n) and shape
(l). This number divides the subshell into
individual orbitals which hold the
electrons; there are 2l+1 orbitals in each
subshell. Thus the s subshell has only
one orbital, the p subshell has three
orbitals, and so on.
4.Spin Quantum Number (ms): ms = +½ or -½.
Specifies the orientation of the spin axis of an electron. An electron can spin in only one of two
directions (sometimes called up and down).
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An introduction to optoelectronics
The Pauli exclusion principle (Wolfgang Pauli, Nobel Prize 1945) states
that no two electrons in the same atom can have identical values for all four of
their quantum numbers. What this means is that no more than two electrons can
occupy the same orbital, and that two electrons in the same orbital must
have opposite spins.
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An introduction to optoelectronics
Electron Spin
An electron spin s = 1/2 is an intrinsic property
of electrons. Electrons have intrinsic angular
momentum characterized by quantum number
1/2. In the pattern of other quantized angular
momenta, this gives total angular momentum
The resulting fine structure which is observed
corresponds to two possibilities for the zcomponent of the angular momentum.
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An introduction to optoelectronics
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An introduction to optoelectronics
Bosons and Fermions
All particles in nature are either bosons or fermions
Every particle -- in addition to the normal properties you know like mass and
electric charge -- has an intrinsic amount of angular momentum to it,
colloquially known as spin.
FermionsParticles with spins that come in half-integer
(e.g., ±1/2, ±3/2, ±5/2, etc.) are known as fermions
multiples
BosonsPparticles with spins in integer multiples (e.g., 0, ±1, ±2, etc.) are bosons.
Their statistical properties are very different: no two fermions can be in the same
state, but there is no such restriction on bosons.
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EEE 429
An introduction to optoelectronics
Bosons and Fermions
All particles in nature are either bosons or fermions
Every particle -- in addition to the normal properties you know like mass and
electric charge -- has an intrinsic amount of angular momentum to it,
colloquially known as spin.
FermionsParticles with spins that come in half-integer
(e.g., ±1/2, ±3/2, ±5/2, etc.) are known as fermions
multiples
BosonsPparticles with spins in integer multiples (e.g., 0, ±1, ±2, etc.) are bosons.
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EEE 429
An introduction to optoelectronics
Bosons and Fermions
An example of a boson is a photon. Two or more bosons (if they are of
the same particle type) are allowed to do the same exact thing. For
example, a laser is a machine for making large numbers of photons do
exactly the same thing, giving a very bright light with a very precise
color heading in a very definite direction. All the photons in that beam
are in lockstep.
You can’t make a laser out of fermions. An example of a fermion is an
electron. Two fermions (of the same particle type) are forbidden from
doing the same exact thing. Because an electron is a fermion, two
electrons cannot orbit an atom in exactly the same way. This is the
underlying reason for the Pauli exclusion principle If electrons were
bosons, chemistry would be unrecognizable!
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EEE 429
An introduction to optoelectronics
Bosons and Fermions
All particles in nature are either bosons or fermions
For reasons we do not fully understand, a consequence of the odd half-integer
spin is that fermions obey the Pauli Exclusion Principle and therefore cannot
co-exist in the same state at same location at the same time.
Their statistical properties are very different: no two fermions can be in the same
state, but there is no such restriction on bosons.
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An introduction to optoelectronics
Fermi Energy
Fermi energy is often defined as the highest occupied energy level of a
material at absolute zero temperature.
Fermi Level
"Fermi level" is the term used to describe the top of the collection of electron energy
levels at absolute zero temperature.
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An introduction to optoelectronics
we can approximate the average energy level at which an electron is present is with
the Fermi-Dirac distribution
where E is the energy level, k is the Boltzmann constant, T is the (absolute)
temperature, and E_F is the Fermi level.
You can calculate the fermi energy state using:
N - number of possible quantum states
V - volume
m - mass of electron
h - planc's constant
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An introduction to optoelectronics
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An introduction to optoelectronics
Fermi level in extrinsic
semiconductor
In extrinsic semiconductor, the number
of electrons in the conduction band and
the number of holes in the valence
band are not equal. Hence, the
probability of occupation of energy
levels in conduction band and valence
band are not equal. Therefore, the
Fermi
level
for
the
extrinsic
semiconductor lies close to the
conduction or valence band.
At room temperature, the number of electrons in the conduction band is greater
than the number of holes in the valence band. Hence, the probability of occupation
of energy levels by the electrons in the conduction band is greater than the
probability of occupation of energy levels by the holes in the valence band. This
probability of occupation of energy levels is represented in terms of Fermi level.
Therefore, the Fermi level in the n-type semiconductor lies close to the conduction
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band.
EEE 429
An introduction to optoelectronics
Fermi level in p-type
semiconductor
In p-type semiconductor trivalent impurity
is added. Each trivalent impurity creates a
hole in the valence band and ready to
accept an electron. The addition of
trivalent impurity creates large number of
holes in the valence band.
At room temperature, the number of holes in the valence band is greater than the
number of electrons in the conduction band. Hence, the probability of occupation
of energy levels by the holes in the valence band is greater than the probability of
occupation of energy levels by the electrons in the conduction band. This
probability of occupation of energy levels is represented in terms of Fermi level.
Therefore, the Fermi level in the p-type semiconductor lies close to the valence
band.
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