2. Review for Final Monday 5/6, 3:00-6:00pm Sage 4101

3. 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

4. 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

5. 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

6. 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

7. 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!!!

8. 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

9. 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

10. 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

11. 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

12. First Exam

13. What have we learned? Any traveling sinusoidal wave may be described by y = y m sin(kx   t +  ) 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

14. Review (cont.) Any periodic function of frequency f 0 can be expressed as a sum over frequency of sinusoidal waves having frequencies equal to nf 0, 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 f 0  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.

15. What Else Have We Learned? Can represent binary data with pulses in a variety of ways 10110 could look like... Non-return-to-zero (NRZ) Return-to-zero (RZ) Bipolar Coding Notice that the NRZ takes half the time of the others for the same pulse widths Other schemes use tricks to reduce errors and BW requirements.

16. 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

17. 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

18. Interference of Waves  If crests match crests, then waves interfere constructively  Crests will match if waves are one wavelength, two wavelengths, … apart: path difference = m A max 2A max wave 1 wave 2 sum A max

19. Destructive Interference  If crests match troughs (180° out of phase), then waves interfere destructively  Crests will match troughs if waves are one/half wavelength, three/half wavelengths, … apart: path difference = (m+½) wave 1 wave 2 sum A max

20. 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 = E max 2 /(2c  0 )  Constructive interference produces brighter light; destructive interference produces dimmer light.

21. Comparing Interference E max 2E max 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

22. Coherent vs. Incoherent Light “Everyday light” is incoherent Laser light is an example of coherent light Simple wave equation describes coherent waves y = y m sin(kx   t +  )

23. Diffraction Math  The locations of successive minima are given by  tan  = y/D  for small angles, sin  ~  ~ tan  = y/D

24. Diffraction by a circular aperture  A circular aperture of diameter d  Single slit of width a

25. 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)  As before,  approximately y/L

26. Comments on Resolvability  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

27. 2 nd Exam

28. 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:  V=E  x, where  x 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.

29. What Have We Learned About Electrical Storage The electric force F E on a charge q 0 can be considered due to an electric field which is produced by other charges in the area F E = q 0 E If moving a charge between two points requires work (or does work), the charge gains (or loses) potential energy:  V = –  E  dx = (for a constant field) E  x Capacitors store charge Q in proportion to the voltage V between the plates: C = Q/V = C =  0 A/d Capacitors are used in RAM

30. What Have We Learned About Magnetic Storage? Two domains magnetized in same direction is a 0 Two domains magnetized in opposite directions is a 1 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:

31. What Have We Learned About Magnetoresistance? Charges traveling through magnetic field experience magnetic force (provided velocity and field are not aligned): F B = 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

32. 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

33. 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

34. 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=1 n=2 n=3 n=4 Really eight distinct states with closely spaced energies, since two electrons cannot occupy the same state.

35. 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

36. Conductors & Semiconductors In conductors, the valence band is only partially- full, so electrons can easily move from being near one atom to being near anotherconductors In semiconductors and insulators, the valence band is completely full, so electrons must gain extra energy to movesemiconductors In semiconductors, extra electrons (or holes) can be introduced in a “controlled” way.

37. 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

38. 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 cross- sectional area: R =  L/A The constant of proportionality here is called the resistivity. It is a function of material and temperature.

40. p-n junction n-type p-type Energy depleted region (electric field) ++++++ + + ----- - - - VoVo

41. Biased junction n-type p-type depleted region (electric field) Negative bias photon out

42. How does a semiconductor laser work?

43. 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.

44. MOSFET The potential difference between drain and source is continually applied When the gate potential difference is applied, current flows Source Drain n-type p-type n-type Gate (Metal-Oxide-Semiconductor, Field-Effect Transistor)

45. Bipolar Junction Transistor n-type p-typen-type Emitter Base Collector increasing electron energy increasing hole energy

46. Bipolar Junction Transistor http://hyperphysics.phy-astr.gsu.edu/hbase/solids/trans.html#c1

47. 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. Dump Input Switch Output

48. 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?

49. Pictorial Representation of 3D Integration Concept using Wafer Bonding, * Figure adapted from IBM Corporation and used with permission. J. Lu et al

50. Broad band interconnect technology ---high speed data transfer Replacing electrical connection by optics: Modulators/switches: electro-optic, optic-optic Optical waveguides Data compression (software) Modulatorsguide Chip stack switches fiber Or: wireless! light

51. Oriented & interconnected nanotube networks—Ajayan et al –Local modification and Junction formation –Termination (cutting of structures) Focused Ions

53. Einstein to the Rescue Einstein suggested that light was emitted or absorbed in particle-like quanta, called photons, of energy, E = hf crest trough If an electron absorbs one of these photons, it gets the entire hf of energy. If that energy is larger than the work function of the metal, the electron can leave; if not, it can’t: K max = E abs –  = hf - 

54. Particle in a box  (x) = B sin (n  x/a)  (x) |  (x)| 2 n=2 n=3  Only certain wavelengths  = 2a/n are allowed  Only certain momenta p = h/ = hn/2a are allowed  Only certain energies E = p 2 /2m = h 2 n 2 /8ma 2 are allowed - energy is QUANTIZED  Allowed energies depend on well width

55. “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) |  (x)| 2 n=1 n=2 x

56. 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.

57. 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

58. 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.

59. 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

60. 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!)

61. Adding amplitudes Lower detector: Upper detector: