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

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

are quantized resulting in “quantum leap”

Energy E2

Energy E1

Large body (satellite)

Acceleration from E1 to E2 through all intermediate energiesIntuitive!

Electron

Abrupt transition from E1 to E2Intermediate energies not allowedNot intuitive!

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

1st shell: 2 electrons

2nd shell: 8 electrons

3rd shell: 18 electrons

3s

3p

3dSub-shells

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 …. Red3.1 eV …. 1.7 eV

Typical magnitudes of energy

2nd shell: 8 electrons

3rd shell: 18 electrons

3s

3p

3d

Sodium (Na) atom has 1 electron in 3rd shell (atomic number 11)

2.1 eV1st shell: 2 electrons

Emitted as visible light

• Violet …. Red3.1 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

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

Empty band

Energy

Partially full band

Metal

Empty band

Full band

Gap ( ~ 1 eV)

Semiconductor

Empty band

Full band

Gap ( > 5 eV)

Insulator

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.)

• Why are some colors absorbed?

• Why are some colors transmitted?

Incident light(contains various colors) Transmitted light

(some colors missing)

Absorbed light

Reflected light(some colors absorbed & re-emitted)

The color of metals

Empty band

Energy

Partially full band

> 3.1 eV3.1 eV (violet)

1.7 eV (red)2.4 eV (yellow)

Silver

All colors absorbed and immediately re-emitted; this is why silver is white (or silvery)

Empty band

Partially full band

3.1 eV (violet)

1.7 eV (red)2.4 eV (yellow)

Gold

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

• 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

Empty band

Energy

Full band

~ 5.5 eV3.1 eV (violet)

1.7 eV (red)2.4 eV (yellow)

Diamond

Full band

~ 1.1 eV

3.1 eV (violet)

1.7 eV (red)2.4 eV (yellow)

Silicon

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

Full band

~ 5.5 eV

3.1 eV (absorptionof 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

Full band

1.7 eV (absorption of red)

Acceptor level

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

Full band

4.5 eV

Absorption of UV

Emission of yellow light2.1 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 0012 0105 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

Full band

~ 1.1 eV

3.1 eV (violet)

1.7 eV (red)2.4 eV (yellow)

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 As3 valence electrons

4 valence electrons

5 valence electrons

Empty band

Full band

1.1 eV

Donor level

Empty band

Full band

Acceptor level

Phosphorous impurity Aluminum impurity

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

• 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 !

no applied electric field

5+

4+ 4+ 4+ 4+

4+

4+4+4+4+

4+ 4+

Phosphorus atom

no applied electric field

Aluminum atom

valence electron

Si atom

3+

4+ 4+ 4+ 4+

4+

4+4+4+4+

4+ 4+

Free electron

“Hole”

Impurities in Si: band picture

Empty band

Full band

1.1 eV

Donor level

Empty band

Full band

Acceptor level

Phosphorous impurity Aluminum impurity

Hole

n-type semiconductor(charge carriers are negatively charged)

p-type semiconductor(charge carriers are positively charged)

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

Free electrons (negative charge) Free holes (positive charge)

Bound electrons (negative charge)

n-type Si p-type Si

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)

p-n junction operation

• This results in a 1-way traffic of electrons, and is a miniature diode that can be used to represent 0s and 1s

Empty band

Full band

1.1 eV

Donor level

Empty band

Full band

Acceptor level

n-type Si p-type Si

Hole

easy hard

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-typeSi

p-typeSi

ACDC

Case Study: Solar cells• Uses the principle of the photoelectric effect

(Einstein: Nobel prize, 1919): light hitting on a material creates current

current

Solar cell

Sun light

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

Full band

~ 1.1 eV

3.1 eV (violet)

1.7 eV (red)2.4 eV (yellow)

Full band

Exposure to light

Electron-hole pair

• 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 cellp-type Sin-type Si

neutral neutral

Full band

Positively charged

Negatively charged

Full band Exposure to light creates electron-hole pairs

Electric current generated !!

Some holes neutralized by electrons

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)

• Oil 38.8 %• Natural gas 23.2 %• Coal 22.9 %• Nuclear 7.6 %• Hydroelectric 3.8 %• Biomass 3.2 %• Geothermal 0.3 %• Solar 0.07 %• Wind 0.04 %• FUEL CELLS ???

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

Refracted light

Transmitted light

AIR

AIR

GLASS

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 material

speed of light in vacuum

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

GLASS

AIR

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!