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

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

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

5. VM Ayres, ECE874, F12

6. z y x Add coordinate axis according to directions:

7. VM Ayres, ECE874, F12 z y x Intercepts1 1/2 No Reciprocals1, 1/ ½ 1/∞ = 0 Whole # Conversion: X 1 1, 2, 0 Miller indexed plane (hkl): (120) Work back wards to get intercepts. Staying in Unit cell is best for answering the how many atoms question..

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

9. VM Ayres, ECE874, F12 z y x Find area of plane in cm 2 : Table 1.5 a = 5.9352 Ang a a

10. VM Ayres, ECE874, F12

11. a = 5.43 Ang

12. VM Ayres, ECE874, F12 (a) Plane passing through points ABC: Intercepts Reciprocals Whole # Conversion: X Miller indexed plane (hkl):

13. VM Ayres, ECE874, F12 (a) Plane passing through points ABC: Interceptsa, a, NO = ∞ Reciprocals1/a, 1/a, 1/ ∞ = 0 Whole # Conversion: X a 1, 1, 0 Miller indexed plane (hkl): (110)

14. VM Ayres, ECE874, F12 Extra: Plane passing through points ABD: start with through D: Intercepts Reciprocals Whole # Conversion: X Miller indexed plane (hkl):

15. VM Ayres, ECE874, F12 Extra: Plane passing through points ABD: Interceptsa, a/2, NO = ∞ Reciprocals1/a, 2/a, 1/∞ = 0 Whole # Conversion: X a 1, 2, 0 Miller indexed plane (hkl): (120)

16. VM Ayres, ECE874, F12 (b) Plane passing through points BCD: Intercepts Reciprocals Whole # Conversion: X a Miller indexed plane (hkl):

17. VM Ayres, ECE874, F12 (b) Plane passing through points BCD: MARK WAS RIGHT, THIS PICTURE IS A DIFFERENT PLANE. Interceptsa, a, ? Reciprocals Whole # Conversion: X a Miller indexed plane (hkl):

18. VM Ayres, ECE874, F12 (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. Interceptsa, a, a Reciprocals1/a, 1/a, 1/a Whole # Conversion: X a 1 1 1 Miller indexed plane (hkl): (111)

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

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

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

22. VM Ayres, ECE874, F12 In Chp. 02 the electrons are described as waves:   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: n = 2d sin . 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.

23. VM Ayres, ECE874, F12 Early experiments showed wavelike electrons and also discreet energies 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

24. VM Ayres, ECE874, F12 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! Power meter Spectral analyzer: 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: E n = nh  nhc , n = 1, 2, 3, …… Sum E n and match the data.

25. VM Ayres, ECE874, F12 Heat hydrogen gas, get atomic hydrogen (not H 2 ) = 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: E n = -13.6 eV/n 2, n = 1, 2, 3, ……

26. VM Ayres, ECE874, F12 Basic explanation is: Angular momentum is quantized: L n = m 0 vr n = nh bar, n = 1, 2, 3, …… Motion: Centripetal force Charge: Coulomb force

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

28. VM Ayres, ECE874, F12 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/ de Broglie’s hypothesis A lucky guess that fits the facts. Wave-particle duality is still not fully explained.