ECE 874:Physical Electronics

Prof. Virginia AyresElectrical & Computer EngineeringMichigan State Universityayresv@msu.edu

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Lecture 05, 13 Sep 12

Finish Chp. 01

Start Chp. 02

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VM Ayres, ECE874, F12

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

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VM Ayres, ECE874, F12

z

y

x

Add coordinate axis according to directions:

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z

y

x

Intercepts 1 1/2 No

Reciprocals 1, 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..

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z

y

x

Draw plane through the x-y: 1a, ½ a coordinates.

Locate the Pb atoms:

1/2

1/4

1/4

Therefore: ½ + ¼ + ¼ = 1 equivalent Pb Atom

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z

y

x

Find area of plane in cm2:

Table 1.5a = 5.9352 Ang

aa

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VM Ayres, ECE874, F12

a = 5.43 Ang

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(a) Plane passing through points ABC:

Intercepts

Reciprocals

Whole #

Conversion:

X

Miller indexed plane (hkl):

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(a) Plane passing through points ABC:

Intercepts a, a, NO = ∞

Reciprocals 1/a, 1/a, 1/ ∞ = 0

Whole #

Conversion:

X a

1, 1, 0

Miller indexed plane (hkl):

(110)

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Extra: Plane passing through points ABD: start with through D:

Intercepts

Reciprocals

Whole #

Conversion:

X

Miller indexed plane (hkl):

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Extra: Plane passing through points ABD:

Intercepts a, a/2, NO = ∞

Reciprocals 1/a, 2/a, 1/∞ = 0

Whole #

Conversion:

X a

1, 2, 0

Miller indexed plane (hkl):

(120)

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(b) Plane passing through points BCD:

Intercepts

Reciprocals

Whole #

Conversion:

X a

Miller indexed plane (hkl):

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

Intercepts a, a, ?

Reciprocals

Whole #

Conversion:

X a

Miller indexed plane (hkl):

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(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.

Intercepts a, a, a

Reciprocals 1/a, 1/a, 1/a

Whole #

Conversion:

X a

1 1 1

Miller indexed plane (hkl):

(111)

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Direction O to D: [0, a/2, a/2]

Convert to whole numbers: x 2/a:

Direction [0 1 1]

a/2

a/2

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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

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Principles of Electronic Devices, Streetman and Bannerjee

+ Battery -

Chp. 01: the crystal environment Chp. 02: the electrons that form the current BUT….

Start Chp. 02:

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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.

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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

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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!

Po

wer

met

er

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:

En = nhnhc, n = 1, 2, 3, ……

Sum En and match the data.

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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, ……

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Basic explanation is: Angular momentum is quantized:

Ln = m0vrn = nhbar, n = 1, 2, 3, ……

Motion: Centripetal force Charge: Coulomb force

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Energy due to motion

Energy due to charge

Get v from force balance

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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.