ece 474: principles of electronic devices · 2011. 1. 31. · wavelength of light to get rid of the...

ECE 474:Principles of Electronic Devices

Prof. Virginia AyresElectrical & Computer EngineeringMichigan State [email protected]

V.M. Ayres, ECE474, Spring 2011

Lecture 09:

Why it matters

Discreet energy levels and the hydrogen atom

“Are electrons waves?” ???!!Davisson-Germer experimente- wavelength

Examples of each

Chp. 02: What quantization is and why it matters. Several game-changing ideas.


Why it matters:

Increase in e-/current speedReduction in device physical sizeReduction in scattering heat

Ubër-VLSI}


Why it matters:Moore’s Law: (Wikipedia)Moore's law describes a long-term trend in the history of computing hardware. The number of transistors that can be placed inexpensively on an integrated circuit has doubled approximately every two years. The trend has continued for more than half a century and is not expected to stop until 2015 or later.

The end of the road


What the problem is in Chp. 02:

Electrons have both particle-like and wavelike properties- particle-like in micron-sized structures- wavelike in nanometer-sized structures


Electrons have both particle-like and wavelike properties:Consequence:

Particle-like electrons in micron-sized transistors means you can make a good OFF

Wavelike electrons in nanometer-sized transistors means that you CANNOT make a good OFF due to quantum tunnelling. This is known as the End of the Road: 2015.


Lecture 09:

Why it matters



Examples of each



http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger2.html


Atoms: Hydrogen atomElectron travels around proton in a spherical orbit at the Bohr radius.This orbit is the lowest energy level for the electron,called the ground state.

Proton +

Electron -


Atoms: Hydrogen atom

If the electron is given extra energy from an electrical discharge or a laser, it can travel around in a higher energy/bigger orbit, called an excited state , for a while.

The electron will eventually drop back down to the ground state energy/orbit, giving off a precise wavelength of light to get rid of the difference in energy when it does. It can do some intermediate drops too.


Atoms: Hydrogen atom


λhcEE groundexcited =−

Know: energy levels are discreet. Why: light emitted in transitions are always the same set of wavelengths.


Ask some questions:Why an orbit at all, instead of +/- charges just combining?

Proton +

Electron --

+


λhcEE groundexcited =−

Ask some questions:Why do the energy levels have fixed values (in eV or J)?(“discreet energy levels”)


Ask some questions;Why are the radii of the orbits fixed distances?


linear


Game changing idea


Why the radii of the orbits fixed values:


Why the energy levels have fixed values (in eV or J)(“discreet energy levels”):

Game changing idea


λhcEEE groundexcited ==− == 2112

Example: E21 transition:


Lecture 09:

Why it matters



Examples of each



http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger2.html


Davisson and Germer designed and built a vacuum apparatus for the purpose of measuring the energies of electrons scattered from a metal surface. Electrons from a heated filament were accelerated by a voltage and allowed to strike the surface of nickel metal.

The electron beam was directed at the nickel target, which could be rotated to observe angular dependence of the scattered electrons. Their electron detector was mounted on an arc so that it could be rotated to observe electrons at different angles.

It was a great surprise to them to find that at certain angles there was a peak in the intensity of the scattered electron beam. This peak indicated wave behavior for the electrons, and could be interpreted by the Bragg law to give values for the lattice spacing in the nickel crystal.

Bragg law for X-rays:

nλ = 2dsinθBut these were electrons?!

Davisson-Germer Experiment


Quantum explanation

It was a great surprise to find in a scattering experiment that at certain angles there were peaks in the intensity of the scattered electron beam that matched the Bragg law to give values for the inter-plane spacing in the nickel crystal.

nλ = 2dsinθ

The electrons were waves exhibiting constructive and destructive interference.The spacing between the atomic planes resulted in a path distance that put them in and out of phase.

Davisson, C. J., "Are Electrons Waves?," Franklin Institute Journal 205, 597 (1928)Davisson-Germer Experiment


=> Constructive interference

2 (dsinθ) = nλn= 1,2,3..

Bragg equation

Wilkipedia

For x-rays which are EM waves, this is diffraction and this is perfectly normal:

But these were electrons. Shooting particle-like electrons at the nickel target should have been like bouncing balls off a tabletop.


Low angle bounce

Anything in between

High angle bounce

Anything in between

What to expect from bouncing a ball:


High angle bounce

Anything in between

How weird would this be?


Quantum explanation

It was a great surprise to find in a scattering experiment that at certain angles there were peaks in the intensity of the scattered electron beam that matched the Bragg law to give values for the inter-plane spacing in the nickel crystal.

nλ = 2dsinθ

The electrons were waves exhibiting constructive and destructive interference.The spacing between the atomic planes resulted in a path distance that put them in and out of phase.

Davisson, C. J., "Are Electrons Waves?," Franklin Institute Journal 205, 597 (1928)Davisson-Germer Experiment


Historical note:Davission and Germer did this experiment and originally they thought they got the expected bouncing ball result. To bounce electrons, you have to do it in a vacuum. The vacuum system developed a leak. When that happens you plug the leak, then “bake out” the system at high temp to make the air that got inside evaporate and get pumped out. D&G did so, leaving their nickel target inside.

When they came back and repeated the exact same experiment they got their surprise and it drove them nuts for a while. Eventually they were forced to discard the electrons-are-particles idea for the electrons-are-waves idea, which was a real game-changer.

What happened was that the nickel target was originally amorphous, so it diffracted electron waves every which way. During the high temp bake out, the nickel became crystalline. The electron waves now exhibited Bragg law diffraction off the crystal planes.

Low angle bounce

High angle bounce

Anything in betweenAnything in between

Anything in between OROR

Anything in between

Anything in between

Anything in between


The wavelength of an electron: deBroglie wavelength λdB:

ph

dB =λ

The electron’s wavelength isn’t a fixed number. The faster the e- moves, the bigger its momentum p and the smaller its wavelength λdB


An e- does have particle-like properties, in addition to wavelike properties. The particle-ness of an electron is mathematically expressed by an envelope called the “modulation”.

mm k

πλ 2=

The deBroglie wave of wavelength λdB is inside the modulation wave packet which has its own periodicity of wavelength λm.

ph

dB =λ

ece 474: principles of electronic devices · 2011. 1. 31. · wavelength of light to get rid of the...

Documents