Almost There!

1
Almost There!

• Interference and Review for 3rd Hour Exam

2
Review

• The probability of finding a particle in a
  particular region within a particular time
  interval is found by integrating the square of
  the wave function
• P (x,t) ? Y(x,t)2 dx ? c(x)2 dx
• c(x)2 dx is called the probability density
  the area under a curve of probability density
  yields the probability the particle is in that
  region
• When a measurement is made, we say the wave
  function collapses to a point, and a particle
  is detected at some particular location

3
Particle in a box

• c(x) B sin (npx/a)

n3
c(x)
c(x)2
n2

• Only 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

4
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
n2
n1
x
5
Quantum wells

• An electron is trapped since no empty energy
  states exist on either side of the well

6
Escaping quantum wells

• Classically, an electron could gain thermal
  energy and escape
• For a deep well, this is not very probable.
  Given by Boltzmann factor.

7
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.

8
Tunneling and Interference

• Can occur when total particle energy is less than
  barrier height.
• Particle can be scattered back even when its
  energy is greater than barrier height.
• What affects tunneling probability?
• T ? e2kL
• k 8p2m(Epot E)½/h

9
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

10
The tunneling transistor

• As the potential difference increases, the energy
  levels on the positive side are lowered toward
  the electrons energy
• Once the energy state in the well equals the
  electrons energy, the electron can go through,
  and the current increases.

11
The tunneling transistor

• The current through the transistor increases as
  each successive energy level reaches the
  electrons energy, then decreases as the energy
  level sinks below the electrons energy

12
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!)
13
Randomness Revisited

• If particle/probabilistic theory correct, half
  the intensity always arrives in top detector,
  half in bottom
• BUT, can move mirror so no light in bottom!

(Color of line is NOT related to actual color of
laser all beams have same wavelength!)
14
Interference effects

• Laser light taking different paths interferes,
  causing zero intensity at bottom detector
• EVEN IF INTENSITY SO LOW THAT ONE PHOTON TRAVELS
  THROUGH AT A TIME
• What happens if I detect path with bomb?

No interference, even if bomb does not detonate!
15
Interpretation

• Wave theory does not explain why bomb detonates
  half the time
• Particle probability theory does not explain why
  changing position of mirrors affects detection
• Neither explains why presence of bomb destroys
  interference
• Quantum theory explains both!
• Amplitudes, not probabilities add - interference
• Measurement yields probability, not amplitude -
  bomb detonates half the time
• Once path determined, wavefunction reflects only
  that possibility - presence of bomb destroys
  interference

16
Quantum Theory meets Bomb

• Four possible paths RR and TT hit upper
  detector, TR and RT hit lower detector
  (Rreflected, Ttransmitted)
• Classically, 4 equally-likely paths, so prob of
  each is 1/4, so prob at each detector is 1/4
  1/4 1/2
• Quantum mechanically, square of amplitudes must
  each be 1/4 (prob for particular path), but
  amplitudes can be imaginary or complex!
• e.g.,

17
Adding amplitudes

• Lower detector
• Upper detector

18
What wave function would give 50 at each
detector?

• Must have a b c d 1/4
• Need a b2 cd2 1/2

19
(No Transcript)
20
(No Transcript)
21
Oriented interconnected nanotube
networksAjayan et al
Focused Ions

• Local modification and Junction formation
• Termination (cutting of structures)

22
DNA and a little moreIvar GiaeverRensselaer
Polytechnic InstituteandApplied BioPhysics,
Inc.Troy, NY 12180andOslo Universitetet
Blindern, Oslo
23
(No Transcript)
24
(No Transcript)
25
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?

26
How does a semiconductor laser work?
27
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
1950s.
28
Biased junction
Negative bias
n-type
depleted region (electric field)
29
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
30
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 the work function
of the metal, the electron can leave if not, it
cant Kmax Eabs F hf - F
crest
trough
31
Bipolar Junction Transistor
Base
Emitter
Collector
increasing electron energy
increasing hole energy
n-type
p-type
n-type
32
Bipolar Junction Transistor
http//hyperphysics.phy-astr.gsu.edu/hbase/solids/
trans.htmlc1
33
NOT Gate - the simplest case

• Put an alternate path (output) before a switch.
• If the switch is off, the current goes through
  the alternate path and is output.
• If the switch is on, no current goes through the
  alternate path.
• So the gate output is on if the switch is off and
  off if the switch is on.

Input
Output
Dump
Switch
34
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
• 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.

Output
Switch
Input
Input
Dump
Switch
Switch