Transcript Full band - Institute of Materials Science

Topic 14: Electronic Properties of
Materials [Chapters 22, 23 & 24]
• For the rest of the course, we will need to
understand the properties of electrons in
materials
– Colors of materials
– Electrical properties (semiconductors, solar cells,
superconductors)
– Optical properties (optical fibers)
– Magnetic properties
• Modern Quantum Mechanics provides a
complete description of electrons
Quantum Mechanics: A historical
perspective
• Scientific theories are developed to understand the
workings of nature
• Galileo, Newton: theories to understand the very large
(planetary motion) [~ 1600]
• Faraday, Maxwell et al: electromagnetism [~ 1800]
• Einstein: theories of the very fast & heavy [ early 1900s]
• Bohr, Heisenberg, Schrodinger et al : theory of the very
small [early 1900s]  Quantum Mechanics
Implications of Quantum Mechanics
• “Energy levels” for electrons (most relevant implication
for practical Materials Science)
• Wave-particle duality
• Measurement affects what is being measured, or “reality
defined by measurement” (Einstein was uncomfortable
with this: tree falling in empty forest)
• Is not consistent with everyday experience!
Wave-particle duality
Particle nature
Wave nature
Source
Double-slit
Screen
• Electrons display both particle and wave nature
• So does light!
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
Light emission from atoms
• When energy is injected into an atom, they jump (quantum leap) to
higher levels
• When they return to their original state, they emit radiation
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
Empty band
Empty band
Gap ( ~ 1 eV)
Empty band
Gap ( > 5 eV)
Full band
Partially full band
Metal
Full band
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
Summary
• In atoms, electrons are arranged in shells of specific energies (not
all energies are allowed)
• Transitions between energy levels result in absorption or emission of
light of the right color (remember: red – violet  1.7 eV – 3.1 eV)
• In solids, discrete energy levels of atoms become energy bands with
gaps in between
• A material with electrons partially filling a band is a metal, and a
material with a fully filled band is an insulator
• Reading assignment: Chapter 23
Electron interactions with light
• 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
Empty band
Empty band
Energy
3.1 eV (violet)
2.4 eV (yellow)
1.7 eV (red)
Partially full band
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
Empty band
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
Full band
Full band
• 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
•
•
•
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
•
•
•
Empty band
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
Empty band
~ 5.5 eV
Acceptor level
1.7 eV (absorption of red)
Full band
Full band
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
Empty band
Absorption of UV
2.1 eV
Full band
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: Europium
impurity in yttrium vanadate (YVO3) for red, silver impurity in zinc
sulphide for blue, and manganese impurity in zinc silicate for green
– 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
Digression: Thin screen displays
Plasma TVs
• A plasma is an ionized gas; electric field when applied to
a gas containing chamber rips apart atoms creating ions
• In plasma TVs, we have a chamber for each sub-pixel
• UV light also created which hit the phosphor coating
generating visible light
Field emission display
Array of electron emitters (metal tips or carbon nanotubes) beneath each pixel !
Summary
•
Electron transitions between energy levels or energy bands result in
absorption or emission of light of the right color (remember: red – violet 
1.7 eV – 3.1 eV; UV higher in energy)
•
Metals are opaque and lustrous because most or part of visible light is
absorbed and re-emitted (reflection); so is Si
•
Insulators with band gaps greater than 3.1 eV are transparent as visible
light cannot excite any electron
•
Impurities cause additional “defect states” in the insulator band gap, and
can result in selective absorption of visible light
•
Luminescence occurs when UV light gets absorbed, and visible light emitted
due to “defect states”
•
Reading assignment: Chapter 24
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)
Si integrated circuits (ICs)
• Scanning electron microscope images of an IC:
Al
Si
(doped)
(d)
45m
0.5mm
• A dot map showing location of Si (a semiconductor):
--Si shows up as light regions.
• A dot map showing location of Al (a conductor):
--Al shows up as light regions.
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”
• Depending on how the rectifier is wired, you have a 0 (if
current does not flow through) or 1 (if current flows)
• We will learn how a rectifier is built using Si
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
Full band
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
Empty band
Empty band
Donor level
1.1 eV
Acceptor level
Full band
Full band
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
Empty band
Empty band
Donor level
1.1 eV
Acceptor level
Full band
n-type semiconductor
(charge carriers are
negatively charged)
Hole
Full band
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
Empty band
Empty band
Donor level
easy
1.1 eV
hard
Acceptor level
Full band
Full band
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