Topic 14: Electronic Properties of Materials Chapters 22, 23

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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

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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

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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!

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Wave-particle duality
Particle nature
Wave nature

• Electrons display both particle and wave nature
• So does light!

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Nature of electrons in atoms
Electron
Large body (satellite)
Energy E2
Energy E1
Abrupt transition from E1 to E2 Intermediate
energies not allowed Not intuitive!
Acceleration from E1 to E2 through all
intermediate energies Intuitive!

• Electron energy levels are quantized
• Energy for transition can be thermal or light
  (electromagnetic), both of which are quantized
  resulting in quantum leap

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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
3d
Sub-shells
2nd shell 8 electrons
3p
1st shell 2 electrons
3s
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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

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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

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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

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Typical magnitudes of energy

• Violet . Red
• 3.1 eV . 1.7 eV
• 2.1 eV corresponds to yellow ? sodium vapor lamps

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Atoms ? solids

• When atoms come together to form materials,
  discrete energy levels change to bands of allowed
  energies

Energy gap
Energy gap
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Band diagrams electron filling
Energy
Empty band
Partially full band
Metal

• Electrons filled from low to high energies till
  we run out of electrons

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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

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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

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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

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Electromagnetic spectrum

• All electromagnetic radiation are waves
• Type of waves is determined by its frequency or
  wavelength

Decreasing energy
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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

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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?

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The color of metals
Silver
Energy
Empty band
3.1 eV (violet)
3.1 eV
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)
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The color of pure insulators semiconductors
Silicon
Diamond
Energy
Empty band
3.1 eV (violet)
2.4 eV (yellow)
3.1 eV (violet)
1.7 eV (red)
5.5 eV
1.1 eV
2.4 eV (yellow)
1.7 eV (red)
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

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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

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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

• 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
Empty band
3.1 eV (absorption of violet)
5.5 eV
Acceptor level
Donor level
1.7 eV (absorption of red)
Full band
Full band
In both cases, color is due to the transmitted
light
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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
4.5 eV
Emission of yellow light
2.1 eV
Full band
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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

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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

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Digression Thin screen displays
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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

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Field emission display

• Array of electron emitters (metal tips or carbon
  nanotubes) beneath each pixel !

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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

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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 todays calculators!
• With the discovery and understanding of
  semiconductor materials, computing chips have
  become much smaller progressively

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Moores 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)

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Si integrated circuits (ICs)
Scanning electron microscope images of an IC
(d)
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.
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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

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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
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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?

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
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Impurities in Si physical picture
Phosphorus atom
Aluminum atom

Hole

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3

valence
electron
no applied
no applied
Si atom
electric field
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 !

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Impurities in Si band picture
Phosphorous impurity
Aluminum impurity
Empty band
Empty band
Donor level
1.1 eV
Acceptor level
Full band
Full band
Hole
n-type semiconductor (charge carriers are
negatively charged)
p-type semiconductor (charge carriers are
positively charged)
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Response to electric field

• Say we have two pieces of Si, one is doped with
  phosphorous (n-type 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

p-type Si
n-type Si
Free electrons (negative charge)
Free holes (positive charge)
Bound electrons (negative charge)
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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
  n-type 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)

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p-n junction operation
p-type Si
n-type Si
Empty band
Empty band
Donor level
1.1 eV
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

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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
p-type Si
DC
AC