Transcript Full band

Quiz 3: Chapters 22-25, 28 & 29
• Need to understand the properties of
electrons in materials
– Colors of materials
– Electrical properties (semiconductors, solar
cells)
• Optical properties & optical fibers
Nature of electrons in atoms
Large body (satellite)
Electron
Energy E2
Energy E1
Acceleration from E1 to E2 through
all intermediate energies
Intuitive!
•
•
Abrupt transition from E1 to E2
Intermediate energies not allowed
Not intuitive!
Electron energy levels are quantized
Energy for transition can be thermal or light (electromagnetic), both of which
are quantized resulting in “quantum leap”
Electron energy levels in atoms
• Electrons arranged in shells around the nucleus
• Each shell can contain 2n2 electrons, where n is
the number of the shell
• Electrons try to achieve 8 electrons in the
outermost shell (octet)
• Within each shell there are sub-shells
3rd shell: 18 electrons
2nd shell: 8 electrons
3d
Sub-shells
3p
1st shell: 2 electrons
3s
Units of energy
• Most common unit is calorie: energy
needed to heat 1 gram of water by 1
degree
• 1 food calorie = 1000 calorie
• Appropriate unit for electrons = electron
volt (eV)
• 1 calorie = 2.6 x 1019 eV
Typical magnitudes of energy
• Energy difference between electron shells in an atom ranges
from a fraction of electron volt (eV) to several eV
• White light consists of VIBGYOR, and comes in small
“packets” of energy
• Violet …. Red
3.1 eV …. 1.7 eV
Typical magnitudes of energy
Sodium (Na) atom has 1 electron in 3rd shell (atomic number 11)
3rd shell: 18 electrons
3d
2nd shell: 8 electrons
3p
2.1 eV
1st shell: 2 electrons
3s
Emitted as visible light
• Violet …. Red
3.1 eV …. 1.7 eV
• 2.1 eV corresponds to yellow  sodium vapor lamps
Atoms  solids
• When atoms come together to form
materials, discrete energy levels change to
bands of allowed energies
Energy
Energy gap
Energy gap
Band diagrams & electron filling
Energy
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Empty band
Gap ( ~ 1 eV)
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Gap ( > 5 eV)
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Partially full band
Metal
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Semiconductor
Insulator
• Electrons filled from low to high energies till we
run out of electrons
Energy quantization
• All forms of energy are “quantized”, meaning they come
in small packets (Planck, Einstein)
• Forms of energy: thermal (heat), light (visible & invisible),
electrical
• Even if we dump a lot of energy into a material,
remember that they come in numerous identical tiny
packets
• Each packet of energy has to be large enough to excite
electrons to higher levels
• Example: 1 packet of violet light = 3.1 eV;
1 packet of red light = 1.7 eV
Electron interactions with light: color
• The energy differences between allowed
electron levels is of the order of electron volts
(eV)
• Packets of visible light are 1.7-3.1 eV
• Ultraviolet light has higher energy, and infrared
light has lower energy
• All forms of light are electromagnetic radiation
Electromagnetic spectrum
• All electromagnetic radiation are waves
• Type of waves is determined by its frequency or wavelength
Decreasing energy
Nature of light
• When light hits a material, it gets reflected and/or
transmitted
• Some of the spectral colors may be selectively absorbed
or scattered by the material, so that light which is
transmitted or reflected into our eyes may be missing
some colors (e.g., VisionsWare)
• We should be careful to distinguish between
transmitted and emitted light
• Reflection is really light absorbed and re-emitted
Nature of light (contd.)
Reflected light
(some colors absorbed
& re-emitted)
Incident light
(contains various
colors)
Absorbed light
Transmitted light
(some colors missing)
• Why are some colors absorbed?
• Why are some colors transmitted?
The color of metals
Silver
Gold
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Energy
3.1 eV (violet)
2.4 eV (yellow)
1.7 eV (red)
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All colors absorbed and
immediately re-emitted;
this is why silver is
white (or silvery)
> 3.1 eV
3.1 eV (violet)
2.4 eV (yellow)
1.7 eV (red)
Partially full band
Only colors up to yellow
absorbed and immediately
re-emitted; blue end of
spectrum goes through,
and gets “lost”
The color of pure insulators &
semiconductors
Silicon
Diamond
Energy
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3.1 eV (violet)
3.1 eV (violet)
2.4 eV (yellow)
1.7 eV (red)
~ 5.5 eV
2.4 eV (yellow)
1.7 eV (red)
~ 1.1 eV
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• Insulators: Diamond & glass (SiO2, band gap ~ 9 eV) are
transparent as all visible light goes through
• Semiconductors: Silicon is opaque and silvery as all colors
absorbed and re-emitted
Insulators with impurities
• Impurities generally result in energy levels
(“defect states”) in the band gap
• Two types of impurities:
– Donor impurities have more electrons than
the atom they replace
– Acceptor impurities have fewer electrons than
the atom they replace
Impurities in diamond
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Nitrogen has 5 valence electrons (one
more than carbon)
Thus, nitrogen in diamond produces a
donor level with an electron available
for excitation to the empty band
As the violet end of the spectrum is
absorbed during electron excitation, the
transmitted spectrum looks yellowish
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•
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3.1 eV (absorption
of violet)
Donor level
Boron has 3 valence electrons (one
less than carbon)
Thus, boron in diamond produces an
acceptor level to which an electron from
the full band be transferred
As the red end of the spectrum is
absorbed during electron excitation, the
transmitted spectrum looks bluish
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~ 5.5 eV
Acceptor level
1.7 eV (absorption of red)
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In both cases, color is due to the transmitted light
Luminescence: fluorescence
• Light is emitted from a material in an interesting manner
• Ultraviolet (UV) light has higher energy than visible light,
and can cause electrons to get excited across large
band gaps
• Electrons can then return via impurity states, resulting in
emission of visible light
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Absorption of UV
2.1 eV
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Emission of
yellow light
4.5 eV
Fluorescent lights
• Tubes that contain mercury and are coated inside with a
fluorescent material (e.g., cadmium phosphate, zinc
silicate, magnesium tungstate, etc.)
• Electricity acts on mercury vapor in the tube causing it to
emit the yellow/green light we usually associate with
mercury vapor lamps, but it also emits a lot of UV light
• The UV light hits the fluorescent coating, and we can get
light in a variety of colors depending on the coating and
impurities
Phosphorescence
• Occurs when the impurity levels are “sticky”, that is, if the electron
tends to stay in the impurity level for a little time before jumping to its
original state
• Visible light emission continues for maybe a few seconds or minutes
after the UV source has been turned off
• Results in an after glow, for instance, in TV screens
– Screen coated with material for the three basic colors
– Electron beam scans 525 horizontal lines on a screen at a rate of 60
times per second (new picture is formed every 0.017 seconds)
– Emission needs to last long enough to bridge the time gap between
successive images
– Choosing the right set of phosphorescent (or phosphor) material that
gives the right color, with the right intensity and for the right length of
time is very important
Semiconductor microelectronic
devices
• In a computer, information is represented in binary code (as 0s and
1s)
– Example: 0  000
1  001
2  010
5  101
• We thus need devices to represent 0s and 1s, and the operations
between them
• Till about 60-70 years ago, these were done using vacuum tubes
which were huge; a complex contraption as large as a classroom
was used to perform the operations of today’s calculators!
• With the discovery and understanding of semiconductor materials,
computing “chips” have become much smaller progressively
Moore’s Law
•
Number of transistors (or semiconductor devices) per unit area has doubled every 18 months over
the last 40 years!
•
Cost has also gone down exponentially as the entire chip (containing millions of little devices) is
fabricated using an integrated process, resulting in an integrated circuit (IC)
Semiconductor devices
• Today, most of semiconductor devices are based
on silicon (Si), and some on gallium arsenide
(GaAs)
• These devices help represent 0s and 1s and
also perform operations with 0s and 1s
• Basic device is what is called a semiconductor
transistor, which is made of a rectifier or diode
• A rectifier allows current to flow along one
direction but not along the opposite direction:
some sort of a “valve”
Pure Si
• Band gap of Si small enough (1.1 eV) for visible
light (1.7-3.1 eV) to excite electrons
• Thus visible light will make Si a conductor! So Si
is not exposed to light in devices; it is packaged
3.1 eV (violet)
2.4 eV (yellow)
1.7 eV (red)
~ 1.1 eV
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Impurities in Si
• Impurities are added to Si in a
controlled manner (by a
process called “doping”) to
create donor and acceptor
levels [What does an impurity
do to the band diagram?]
B
C
N
Al
Si
P
Ga
Ge
As
3 valence
electrons
4 valence
electrons
5 valence
electrons
Phosphorous impurity
Aluminum impurity
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Donor level
1.1 eV
Acceptor level
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Both impurities result in levels that are about 0.03 eV from the main band; thus room
temperature thermal energy is sufficient to excite electrons to and from these levels
Impurities in Si: physical picture
Phosphorus atom
Aluminum atom
4+ 4+ 4+ 4+
4+ 4+ 4+ 4+
4+ 5+ 4+ 4+
4+ 3+ 4+ 4+
4+ 4+ 4+ 4+
no applied
electric field
Free electron
valence
electron
Si atom
“Hole”
4+ 4+ 4+ 4+
no applied
electric field
• A “hole” is a missing electron, just like a vacancy is a missing atom
in an atomic lattice
• A hole has the properties of an electron but has an effective
positive charge !
Impurities in Si: band picture
Phosphorous impurity
Aluminum impurity
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Donor level
1.1 eV
Acceptor level
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n-type semiconductor
(charge carriers are
negatively charged)
Hole
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p-type semiconductor
(charge carriers are
positively charged)
Response to electric field
• Say we have two pieces of Si, one is doped with phosphorous (ntype Si), and the other doped with aluminum (p-type Si)
• At room temperature, the first Si piece has a lot of free electrons,
and the second one has free holes
• When an electric field is applied, the two types of charge carriers
move in opposite directions, as they are oppositely charged
n-type Si
p-type Si
Free electrons (negative charge)
Free holes (positive charge)
Bound electrons (negative charge)
The p-n junction rectifier
• When a p-type and a n-type Si are joined
together, we have a p-n junction
• A p-n junction has high electron conductivity
along one direction, but almost no conductivity
along the other! Why?
• Electrons can cross the p-n junction from the ntype Si side easily as it can jump into the holes
• However, along the other direction, electrons
have to surmount a ~ 1.1 eV barrier (which is
impossible at room temperature in the dark)
p-n junction operation
p-type Si
n-type Si
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Donor level
easy
1.1 eV
hard
Acceptor level
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Hole
• This results in a 1-way traffic of electrons, and is a
miniature diode that can be used to represent 0s and 1s
The rectifier
• Rectification is the process of converting
alternating current (AC) to direct current (DC)
• Used in portable electronic equipment that need
to be powered using a wall outlet
n-type
Si
AC
p-type
Si
DC
Case Study: Solar cells
• Uses the principle of the photoelectric effect
(Einstein: Nobel prize, 1919): light hitting on a
material creates current
Sun light
Solar cell
current
current
Silicon based Solar cells
• Band gap of Si small enough (1.1 eV) for visible light (1.7-3.1 eV) to
excite electrons
Exposure to light
3.1 eV (violet)
2.4 eV (yellow)
1.7 eV (red)
Electron-hole
pair
~ 1.1 eV
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•
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In solar cells, Si is exposed to light to create electron hole pairs
However, electron-hole pairs created will annihilate themselves, as electron will fall
back into the hole re-emitting light again
So, a p-n junction is used which will prevent the re-emission process, and will result in
a net current
p-n junction solar cell
n-type Si
p-type Si
neutral
neutral
Some holes
neutralized by
electrons
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Positively
charged
Negatively
charged
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Electric current generated !!
Exposure to light
creates electron-hole
pairs
Basic solar cell
• Anti-reflective coating prevents reflection at top surface to increase
efficiency
• Top and bottom contacts help collect the electron and hole currents
generating electricity in an external circuit
Prospects of solar cells
• Today, only 0.1% of all energy produced come from solar
energy; maximum demonstrated efficiency is 30 %
• We want large pieces of crystalline Si to make solar cells
 counter to the trend of miniaturization, and difficult to
produce large crystalline Si
• Although large, high efficiency amorphous Si solar cells
have been demonstrated, production of these is slow
• Lack of sunshine in some parts of the world, and
unpredictability in others
• Solar cells produce DC, but AC current required for
transmission to large distances
• At present, the most promising applications are in rural
and remote areas
• However, this is a very “clean” source of energy, and
research is continuing …
Sources of Energy (US)
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Oil
Natural gas
Coal
Nuclear
Hydroelectric
Biomass
Geothermal
Solar
Wind
FUEL CELLS
38.8 %
23.2 %
22.9 %
7.6 %
3.8 %
3.2 %
0.3 %
0.07 %
0.04 %
???
Camera photocells & night vision
goggles
• Photocells work due to the fact that Si is an
insulator in darkness, but is a conductor when
exposed to light
• Night vision goggles are of 2 types: active and
passive
– Passive: uses the low intensity light in dark situations,
and will not work in total darkness
• This uses the reverse of the solar cell principle: light creates
electrons, electrons hit other electrons, and create more
electrons, which are all accelerated towards a phosphor
screen
– Active: uses infrared radiation
Light in materials
• When light enters a transparent medium, it loses
some energy by moving electrons
• As a result, light slows down!
• And so, light bends! Why?
Incident light
Reflected light
AIR
GLASS
Refracted light
AIR
Transmitted light
Bending of light
• You are on land, and your friend is in trouble in water
• You can run faster than you can swim
• What is the path you would take to get to your friend as
quickly as possible?
land
water
Bending of light
• The difference in the speed of light in different materials
causes it to bend
Refractive index of material =
speed of light in vacuum
speed of light in material
Total internal reflection
• Consider light that goes from glass to air
• Critical angle is the angle at which the refracted light
goes along the surface
• A light ray with greater angles will get totally reflected
back into the glass
• This is the principle used in optical fibers
AIR
GLASS
Critical angles
• Critical angle for water/air is 48 degrees, for diamond/air
is 24.5 degrees, and in optical fibers is 75 degrees
Optical fiber
Protective cladding
Critical angles & Mirages
Rainbows
Optical fibers
Optical fibers for internet &
telephone communication
•
Information is “digitized” (converted to 0s and
1s); 0 = no light pulse, 1 = light pulse
•
Advantages:
– Clarity of signal: copper wires & electricity can
lead to “cross-talk”, as electric current in one
wire results in magnetic field which causes a
small current in a neighboring wire; “cross-talk”
does not occur in optical fibers
– High information density: Two optical fibers can
transmit the equivalent of 30,000 telephone calls
simultaneously (in 1956, the 1st transatlantic
cable could handle only 52 simultaneous
conversations)
– Low weight & volume: It requires 30,000 kg of
Cu wire to transmit the same amount of
information as 0.1 kg of optical fibers
– Transmission at light speed (instead of at drift
velocity in the case of Cu wires)
– Long transmission distance: very low intensity
attenuation in fibers
Properties of optical fibers
• Fiber has to have two important properties:
– Total internal reflection, so that light is contained
within fiber
– Low attenuation, so that light can be carried over long
distances with minimal loss
• Structure
– Inner core glass: high refractive index (contains light)
– Cladding glass: lower refractive index
– Outer polymer coating: adds strength & protects fiber
Properties of optical fibers
• Light ray must enter the fiber within a certain acceptance angle. If
not, light will get refracted out as condition for total internal reflection
will be violated; this becomes important when a fiber bends
• The way to avoid losing light is to make fibers with small diameters;
thinner fibers also better from a flexibility and weight point of view
Manufacture of optical fibers
• The core glass needs
– To be super-pure (to ensure extremely small absorption)
– A smooth defect-free surface
– Small diameter (~ 10 microns)
• Base material for both core glass and cladding glass is SiO2, made
using chemical vapor deposition (CVD):
– SiCl4 + O2 === SiO2 + 2Cl2
• Since core glass need to have a higher refractive index (i.e., it has to
be denser) Germanium (Ge) is added. Ge has 4 valence electrons
like Si, but is much heavier. This is another example of “doping” as
Ge is an intentional impurity, which substitutes for some of the Si
atoms.
Manufacture of optical fibers
(contd.)
• The next step of the
process is to increase the
temperature of the furnace
so that the glass softens
and the tube collapses to
form a solid rod
• The rod is then placed in a
high temperature furnace
and drawn to form a thin
fiber
• Finally, a thin protective
plastic layer is placed on
the surface to complete
the manufacturing process
Purity of optical fibers
• This technology is made
possible by breakthroughs in
the glass manufacturing
process
• In 1970, only 1% of light
entering a 1 km long fiber made
it to the other end; but today
almost 100% of it is transmitted
• 2 Co atoms for every billion Si
atoms can cause only 1%
transmission; so can 20 iron
atoms or 50 copper atoms!
Quiz 3 (April 19)
Chapters 22-25, 28 & 29
• Need to understand the properties of
electrons in materials
– Colors of materials
– Electrical properties (semiconductors, solar
cells)
• Optical properties & optical fibers
• GOOD LUCK!