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ECE 874: Physical Electronics

ECE 874: Physical Electronics. Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu. Lecture 05, 13 Sep 12. Finish Chp. 01 Start Chp. 02.

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ECE 874: Physical Electronics

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  1. ECE 874:Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

  2. Lecture 05, 13 Sep 12 Finish Chp. 01 Start Chp. 02 VM Ayres, ECE874, F12

  3. VM Ayres, ECE874, F12

  4. The rocksalt crystal structure (Fig. 1/6 (b)) is formed from two interpenetrating fcc lattices displaced (1/2 a) in any direction, inside a cubic Unit cell VM Ayres, ECE874, F12

  5. VM Ayres, ECE874, F12

  6. z Add coordinate axis according to directions: y x VM Ayres, ECE874, F12

  7. Work back wards to get intercepts. Staying in Unit cell is best for answering the how many atoms question.. z y x VM Ayres, ECE874, F12

  8. Draw plane through the x-y: 1a, ½ a coordinates. Locate the Pb atoms: z 1/4 1/4 1/2 y x VM Ayres, ECE874, F12 Therefore: ½ + ¼ + ¼ = 1 equivalent Pb Atom

  9. Find area of plane in cm2: z Table 1.5 a = 5.9352 Ang a a y x VM Ayres, ECE874, F12

  10. VM Ayres, ECE874, F12

  11. a = 5.43 Ang VM Ayres, ECE874, F12

  12. (a) Plane passing through points ABC: VM Ayres, ECE874, F12

  13. (a) Plane passing through points ABC: VM Ayres, ECE874, F12

  14. Extra: Plane passing through points ABD: start with through D: VM Ayres, ECE874, F12

  15. Extra: Plane passing through points ABD: VM Ayres, ECE874, F12

  16. (b) Plane passing through points BCD: VM Ayres, ECE874, F12

  17. (b) Plane passing through points BCD: MARK WAS RIGHT, THIS PICTURE IS A DIFFERENT PLANE. VM Ayres, ECE874, F12

  18. (b) READ QUESTION: A Plane passing through points BCD. Continue the plane so that it has an intercept on z. Then the rest is easy. VM Ayres, ECE874, F12

  19. Direction O to D: [0, a/2, a/2] Convert to whole numbers: x 2/a: Direction [0 1 1] a/2 a/2 VM Ayres, ECE874, F12

  20. Direction O to E: [3a/4, 3a/4, 3a/4] Convert to whole numbers: x 4/3a Direction: [1 1 1] 3a/4 3a/4 3a/4 VM Ayres, ECE874, F12

  21. Start Chp. 02: Chp. 01: the crystal environment Chp. 02: the electrons that form the current BUT…. + Battery - Principles of Electronic Devices, Streetman and Bannerjee VM Ayres, ECE874, F12

  22. In Chp. 02 the electrons are described as waves: y e-. Why: because electrons moving between crystal layers that are only Ang apart often act like waves. Electrons have a wavelength (de Broglie wavelength) and a phase; those are both wave properties.Two electrons put together can show constructive and destructive interference. Constructive and destructive interference is a wave property. Selected area diffraction in a TEM is another example in which electrons in a beam behave just like x-rays when the beam interacts with crystal layers: nl = 2d sinq. In a micron-scale crystal, electrons have some wave and some particle like properties (wave-particle duality means that an electron can act as either depending on its circumstances). Scattering is a particle-like property. In really small structures like carbon natures, electron transport is like waves forming modes in a waveguide. Consequence: no scattering at really nano level = no heating = really good for devices. In Chp. 02, we consider electrons in circumstances that make them act like waves. VM Ayres, ECE874, F12

  23. The ultraviolet catastrophe and its resolution: data behaving badly Atomic spectra: data behaving badly and also being weird Electrons have a wavelength: was a lucky guess at the time Blackbody radiation The Bohr atom Wave-particle duality Early experiments showed wavelike electrons and also discreet energies VM Ayres, ECE874, F12

  24. In solids, bonds stretch and relax, quite a bit a room temp and above. When bonds relax, they get rid of energy in the form of photons, so all solids emit photons all the time. The dotted line is from a bond stretching (harmonic oscillator) model. It only matches 50% of the data! What was missing: Lattice vibrations are quantized. (simple model: atomic oscillator: consider just two bonded Si atoms vibrating). Therefore a solid can only radiate or absorb energy in discreet packets: En = nhn = nhc/l, n = 1, 2, 3, …… Sum En and match the data. Power meter VM Ayres, ECE874, F12 Spectral analyzer: l

  25. Heat hydrogen gas, get atomic hydrogen (not H2) = 1 proton + 1 electron. You also observe only certain wavelengths of light emitted. No explanation for wavelengths of light that were seen and especially for wavelengths of light that were not seen. What was missing: Atoms have atomic energy levels. Therefore atomic hydrogen can only radiate or absorb energy in discreet packets: En = -13.6 eV/n2, n = 1, 2, 3, …… VM Ayres, ECE874, F12

  26. Basic explanation is: Angular momentum is quantized: Ln = m0vrn = nhbar, n = 1, 2, 3, …… Charge: Coulomb force Motion: Centripetal force VM Ayres, ECE874, F12

  27. Energy due to motion Get v from force balance Energy due to charge VM Ayres, ECE874, F12

  28. Electrons have momentum which is a particle like property, e.g. conservation of momentum in scattering. Electrons have a wavelength, which is a wavelike property. You see it when you put two of them together and observe constructive and destructive interference, e.g., electron diffraction. The connection is: p = h/l de Broglie’s hypothesis A lucky guess that fits the facts. Wave-particle duality is still not fully explained. VM Ayres, ECE874, F12

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