Review for Final
Monday 5/6, 3:00-6:00pm
Sage 4101
How is Light Better?
• FASTER
– nothing can travel faster than light in vacuum
– Extremely high bandwidth
• COOLER (transfer, not nec. processing)
– Less loss from scattering as light travels through fibers
than electrons through wires
• FOURIER TRANSFORMS (clever parallel
processing)
– Light traveling through a lens performs a Fourier
transform automatically
Fabry-Perot Interferometer
• Ends of cavity like open ends of string: wave not
inverted when it is reflected
• Standing wave set up if cavity length integer
number of half-wavelengths
• Can’t just change frequency, since that affects
other devices too
More Fabry-Perot Interferometer
• Index of refraction determines wavelength
• Intensity affects index of refraction
• If intensity inside cavity high enough, wavelength
will change - from destructive to constructive
• This is a resonant process - a large effect occurs
very quickly
• Can amplify a signal by keeping a constant
intensity near the critical value
Advantages of FP
• MULTI-FUNCTION - same device can be
– AND – low constant signal – need both inputs
to produce resonance
– OR – medium constant signal - either input
strong enough to produce resonance
– Amplifier – medium constant signal – small
input leads to resonance
Why Aren’t Fabry Perot Devices
Front Page Now?
• High intensity used to change n also produces heat
- materials (usually) expand when heated - throws
off interference effect
• Can switch on faster than off
• Need wide bandgap to operate at room T
• BIG!!!
Another Option: Excitons
• Hole and electron are attracted, lowering energy in a bound
state
• Photons emitted when hole and electron pair (exciton)
combine has therefore slightly less energy than when hole
and electron are not bound
• Can maximize this effect by forcing electron and hole into
close proximity (quantum well)
• Applying a voltage means energies are closer together, but
might break bond
• Can minimize bond breaking by quantum well
SEEDs
• Self-Electro-optic Effect Device (uses feedback)
• Set stage:
– Shine light of exciton energy on quantum well in
middle of p-n junction
– Light is absorbed and produces excitons
– Apply reverse bias which slightly separates excitons but
“significantly” lowers the energy and reduces
absorption
• If light intensity is increased, absorption increases
slightly
– can produce more excitons and raise their energy
– brings energy back to absorption peak
Pros and Cons of SEEDs
• Needs only low power (FP needs high
power)
• Easier to manufacture – don’t need
fine-tuned cavity length
• Lower operating speed than FP
Problems with
Optical Computers
• Using only part-optical computers (i.e.,
interconnects) requires adapters
• Much research already in semiconductors - hard
for light to beat that
– Light doesn’t interact because it’s not charged
First Exam
What have we learned?
• Any traveling sinusoidal wave may be described by
y = ym sin(kx  wt + f)
• Light always reflects with an angle of reflection equal to
the angle of incidence (angles are measured to the normal).
• When light travels into a denser medium from a rarer
medium, it slows down and bends toward the normal.
• The Fourier spectrum of a wider pulse will be narrower
than that of a narrow pulse, so it has a smaller bandwidth.
• Your bandwidth B must be as large as the rate N at which
you transfer different amplitudes.
• The rise time of each pulse must be no more than 70% of
the duration of the pulse
Review (cont.)
• Any periodic function of frequency f0 can be expressed as a
sum over frequency of sinusoidal waves having frequencies
equal to nf0, where n is an integer. The sum is called the
Fourier series of the function, and a plot of amplitude
(coefficient of each sin/cos term) vs. frequency is called the
Fourier spectrum of the function.
• Any non-periodic function (so frequency f0 0) can be
expressed as an integral over frequency of sinusoidal waves
having frequencies. The integral is called the Fourier
transform of the function, and a plot of amplitude vs.
frequency is called the Fourier spectrum of the function.
• The Fourier spectrum of a wider pulse will be narrower than
that of a narrow pulse, so it has a smaller bandwidth.
What Else Have We Learned?
• Can represent binary data with pulses in a variety of ways
• 10110 could look like . . .
Notice that the NRZ
takes half the time of
the others for the
same pulse widths
Non-return-to-zero
(NRZ)
Return-to-zero
(RZ)
Bipolar Coding
Other schemes use
tricks to reduce
errors and BW
requirements.
Optical Waveguides Summary
• Dispersion means spreading
• Signals in a fiber will have several sources of dispersion:
– Chromatic:
• Material: index of refraction depends on wavelength (prism)
• Waveguide: some of wave travels through cladding with
different index of refraction (primarily single-mode) – leads to
wavelength-dependent effects
– Modal: different modes travel different paths and so
require different amounts of time to travel down fiber
(CUPS)
• Also have attenuation/loss due to scattering/absorption by
fiber material, which depends on wavelength/frequency
Optical Waveguide Summary
(cont.)
• Modes in a fiber are specific field
distributions that are independent of “z”, or
length traveled down the fiber
• Fields of modes look like harmonics of
standing waves
• Can make a single-mode fiber by:
– reducing diameter of fiber so smaller cone of
light enters
– reducing NA of fiber so smaller cone of light is
trapped
Interference of Waves
Amax
 If crests match
crests, then waves
Amax
interfere
constructively
 Crests will match 2Amax
if waves are one
wavelength, two
wavelengths, …
apart: path
difference = ml
wave 1
wave 2
sum
Destructive Interference
 If crests match troughs Amax
(180° out of phase),
then waves interfere
Amax
destructively
 Crests will match
troughs if waves are
one/half wavelength,
three/half wavelengths,
… apart: path
difference = (m+½)l
wave 1
wave 2
sum
What This Means for Light
 Light is electromagnetic radiation
 A light wave is oscillating electric and magnetic
fields
 The amplitude of the oscillation represents the
maximum electric (or magnetic) field and
determines the intensity of light
 Intensity depends on the square of the maximum
electric field: I = Emax2/(2cm0)
 Constructive interference produces brighter light;
destructive interference produces dimmer light.
Comparing Interference
2Emax
Emax
Medium amplitude
of electric field
yields medium
intensity light
Double amplitude
of electric field
yields quadruple
intensity (very
bright) light
Zero amplitude
of electric field
yields zero
intensity (no)
light
Coherent vs. Incoherent Light
• “Everyday light” is incoherent
• Laser light is an example of coherent light
• Simple wave equation describes coherent
waves
y = ym sin(kx  wt + f)
Diffraction Math
 The locations of successive minima are given by
a
1

sin q   m  l (m  0,  1,  2,...)
2
2

a sin q  nl (n  1,  2,  3.....)
 tan q = y/D
 for small angles, sin q ~ q ~ tan q = y/D
Diffraction by a circular aperture
 A circular aperture of diameter d
l
sin q  1.22 (1st minimum)
d
 Single slit of width a
sin q 
l
a
(1st minimum)
Resolvability
 Two objects are just resolved when the central
diffraction maximum of one object is at the first
minimum of the other. (Rayleigh’s criterion)
1.22l 1.22l
  sin

d
d
1
R
 As before, q approximately y/L
Comments on Resolvability
y
1.22 l
 
D
d
R
 If want to resolve objects closer to each
other (smaller y), need smaller wavelength
of light or larger aperature
 This is called the diffraction limit
nd
2
Exam
Charges in Conductors
 Electric fields are created when positive charges
and negative charges are separated
 A uniform electric field existing over a region sets
up a potential difference between points in that
region: DV=EDx, where Dx is the distance along
a field line.
 If I apply a potential difference across a
conducting object (including semiconductors),
charges experience a force, and charge carriers
will flow until the potential difference is removed.
What Have We Learned About
Electrical Storage
• The electric force FE on a charge q0 can be considered due
to an electric field which is produced by other charges in
the area
FE = q0 E
• If moving a charge between two points requires work (or
does work), the charge gains (or loses) potential energy:
DV = –  E  dx = (for a constant field) EDx
• Capacitors store charge Q in proportion to the voltage V
between the plates:
C = Q/V = C = e0 A/d
• Capacitors are used in RAM
What Have We Learned About
Magnetic Storage?
• Two domains magnetized in same direction is a 0
• Two domains magnetized in opposite directions is
a1
• Direction of magnetization changes at start of new
bit.
• Magnetic data is written by running a current
through a loop of wire near the disk
• As magnetic data passes by coil of wire, changing
field induces currents according to Faraday’s Law:
e
d B
dB
 iR  
 A
dt
dt
What Have We Learned About
Magnetoresistance?
• Charges traveling through magnetic field experience
magnetic force (provided velocity and field are not
aligned):
FB = qv x B = (if v perpendicular to B) qvB
• In a current-carrying wire, this force results in more
frequent collisions and thus an increased resistance:
Magnetoresistance
• Electrons traveling through magnetized material undergo
spin-dependent scattering
• When magnetic field is present in magnetic superlattice,
scattering of electrons is cut dramatically, greatly
decreasing resistance: Giant magnetoresistanced
Stuff to remember about GMR
• Electrons (and other elementary “particles”) have
intrinsic magnetic fields, identified by spin
• The scattering of electrons in a ferromagnetic
material depends on the spin of the electrons
• Layers of ferromagnetic material with alternating
directions of magnetization exhibit maximum
resistance
• In presence of magnetic field, all layers align and
resistance is minimized
What Have We Learned About
Spectra?
• ENERGY LEVELS ARE QUANTIZED
• Different elements have different allowed energies (since
different numbers of protons and electrons provide
different structure of attraction
• Light emitted when electrons move from a high energy
level to a lower energy level in an atom will have only
certain, QUANTIZED, allowed energies and wavelengths.
• Those wavelengths depend solely on the element emitting
the light and compose the characteristic emission spectrum
for that element
Our Model of the Atom
• If the atom is in the “ground state” of lowest energy, electrons fill the
states in the lowest available energy levels. The first shell has two
possible states, and the second shell has eight possible states. Higher
shells have more states, but we’ll represent them with the eight states
in the first two sub-shells.
• Electrons in the outermost shell are called “valence” electrons. We’ll
make them green to distinguish from e- in filled shells
E=0 (unbound)
n=4
n=3
n=2
n=1
Really eight distinct states with
closely spaced energies, since two
electrons cannot occupy the same
state.
Electrons in Solids
• The shifted energies in adjacent atoms combine to create a continuous
“band” of allowed energies for each original energy level; each band,
however, has a finite number of states equal to the number in original
atoms
• Electrons can move from the locality of one atom to the next only if an
energy state is available within the same band
Conductors & Semiconductors
• In conductors, the valence band is only partiallyfull, so electrons can easily move from being near
one atom to being near another
• In semiconductors and insulators, the valence
band is completely full, so electrons must gain
extra energy to move
• In semiconductors, extra electrons (or holes) can
be introduced in a “controlled” way.
What Have We Learned About
Solids?
• In conductors, the valence band is only partially-full, so
electrons can easily move
• In semiconductors and insulators, the valence band is
completely full, so electrons must gain extra energy to
move
– semiconductors have smaller band gap, insulators have larger band
gap
• Conductors have a partially-filled valence band
– The primary effect of higher temperature on resistance is to
increase R due to more collisions at higher temperatures
• Semiconductors have a completely-filled valence band
– The primary effect of temperature on resistance is due to this
requirement: the higher the temperature, the more conduction
electrons
What have we learned about
Resistance?
• In many, ohmic, materials, current is proportional
to voltage:
V = iR
• Resistance is proportional to the length of an
object and inversely proportional to crosssectional area:
R = rL/A
• The constant of proportionality here is called the
resistivity. It is a function of material and
temperature.
V EL
i  Anevd  
R
R
eE
vd 
m
Ane 
1/ R 
Lm
2
p-n junction
Energy
+
+
+
+
+
+
+
Vo
+
--
-
-
p-type
n-type
depleted region
(electric field)
-
-
-
-
Biased junction
Negative
bias
photon out
p-type
n-type
depleted region
(electric field)
How does a semiconductor
laser work?
Stimulated vs. Spontaneous
Emission (Cont.)
Derived in 1917 by Einstein. (Required for
thermal equilibrium was it was recognized
that photons were quantized.)
However, a “real” understanding of this was not
achieved until the 1950’s.
MOSFET
(Metal-Oxide-Semiconductor, Field-Effect Transistor)
• The potential difference between drain and source is
continually applied
• When the gate potential difference is applied, current flows
Gate
Drain
Source
n-type
p-type
n-type
Emitter
Bipolar Junction
Transistor
Base
Collector
increasing
electron energy
increasing hole
energy
n-type
p-type
n-type
Bipolar Junction Transistor
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/trans.html#c1
AND - slightly more complicated
AND gate returns a signal only if both of its two
inputs are on.
Use the NAND output as input for NOT
Output
Switch
Input
Switch
Input
Switch
Dump
If both inputs are on, the NOT input is off, so the
AND output is on.
Else the NOT input is on, so the output is off.
Wide Bandgap Semiconductors
What is a wide bandgap semiconductor?
Larger energy gap allows higher power and
temperature operation and the generation of more
energetic (i.e. blue) photons
The III-nitrides (AlN, GaN and InN), SiC have
recently become feasible. Other materials (like
diamond) are being investigated.
What are they good for?
J. Lu et al
Pictorial Representation of 3D Integration Concept
using Wafer Bonding,
Via Bridge
Via Plug
Substrate
Device
Surface
Third Level
(Thinned
Substrate)
Bond
(Face-to-back)
Substrate
Second Level
(Thinned
Substrate)
Device
Surface
Bond
(Face-to-face)
First Level
Device
Surface
Substrate
* Figure adapted from IBM Corporation and used with permission.
Broad band interconnect technology
---high speed data transfer
Or: wireless!
Replacing electrical connection by optics:
•Modulators/switches: electro-optic, optic-optic
•Optical waveguides
•Data compression (software)
Modulators guide
switches
light
fiber
Chip stack
Oriented & interconnected nanotube networks—Ajayan et al
Focused Ions
Catalyst
Junctions
– Local modification and Junction formation
– Termination (cutting of structures)
Einstein to the Rescue
• Einstein suggested that light was emitted or absorbed in
particle-like quanta, called photons, of energy, E = hf
If that energy is larger than
an electron
absorbs
theIfwork
function
of the one
of these
photons,can
it gets
metal,
the electron
leave;
if not,hf
it of
can’t:
the entire
energy.
Kmax = Eabs –  = hf - 
Particle in a box
c(x) = B sin (npx/a)
n=3
c(x)
n=2
|c(x)|2
certain wavelengths l = 2a/n are allowed
 Only certain momenta p = h/l = hn/2a are allowed
 Only certain energies E = p2/2m = h2n2/8ma2 are
allowed - energy is QUANTIZED
 Allowed energies depend on well width
 Only
“Real-World” Wells
• Solution has non-trivial form, but only certain
states (integer n) are solutions
• Each state has one allowed energy, so energy is
again quantized
• Energy depends on well width a (confinement
width)
|c(x)|2
n=2
n=1
x
Escaping quantum wells
• Thanks to quantum mechanics, an electron has a non-zero
probability of appearing outside of the well
• This happens much more often than thermal escape if the
wells are close together.
A tunnel diode
• According to quantum physics, electrons could tunnel
through to holes on the other side of the junction with
comparable energy to the electron
• This happens fairly often
• Applying a bias moves the
electrons out of the p-side
so more can tunnel in
The tunneling transistor
• As the potential difference increases, the energy levels on the
positive side are lowered toward the electron’s energy
• Once the energy state in the well equals the electron’s energy,
the electron can go through, and the current increases.
The tunneling transistor
• The current through the transistor increases as each successive
energy level reaches the electron’s energy, then decreases as the
energy level sinks below the electron’s energy
Quantum Entanglement
(Quantum Computing)
• Consider photons going through beam splitters
• NO way to predict whether photon will be
reflected or transmitted!
(Color of line is
NOT related to
actual color of
laser; all beams
have same
wavelength!)
Adding amplitudes
1
1
1 i
1 i
  TR 
RT 
RR 
TT
2
2
2 2
2 2
1 1
  
0
2 2
2
• Lower detector:
2
1 i 1 i
2  2i
• Upper detector:  


1
2 2 2 2
2 2
2
2
2