1. Announcements Start reading Chapter 43 (Nuclear Physics)
New terminology and applications of quantum mechanics and special relativity.
Today: p-n junctions, transistors and superconductivity

2. QM/Solid State Physics conceptual question
Question: An isolated zinc atom has a ground state electron configuration of filled 1s, 2s, 2p, 3s, 3p and 4s subshells.
Z=30, 1s22s22p63s23p64s23d10
How can zinc be a conductor if its valence subshell is full ?
Ans: Band gaps form with large number of interacting zinc atoms in a lattice – electronic properties are modified by the Pauli principle with a large number of electrons.

3. Origin of energy bands and band gaps

4. QM/Solid State Physics conceptual question
Question: Speeds of molecules in a gas vary with temperature whereas speeds of electrons in the conduction band of a metal are nearly independent of temperature ? Why ?
Ans: In a gas, molecules move freely with energy 3/2kT = ½ mv2. However, the energy of electrons in the conduction band depends on the Fermi energy and depends only weakly on temperature (see figure).

5. The p-n junction University of Colorado simulation of p-n junction at
Here IS is the saturation current, V is the voltage, T is the temperature and k is Boltzmann’s constant.
Note that V increases, the current goes up exponentially.
For reverse bias, the voltage is negative, the current IS

6. The p-n junction
A p-n junction is the boundary in a semiconductor between a region containing p-type impurities and another region containing n-type impurities.
Very important: Many devices including transistors, integrated circuits and diodes use p-n junctions

7. More on the p-n junction
A p-n junction is the boundary in a semiconductor between a region containing p-type impurities and another region containing n-type impurities.
Reverse biased, big energy gapno current flows across the junction except by tunneling. “Depletion region” forms
Question: What happens when the p-n junction is biased as shown ? - + p n

8. More on the p-n junction
A p-n junction is the boundary in a semiconductor between a region containing p-type impurities and another region containing n-type impurities.
Question: What happens when the p-n junction is biased as shown ? + - p n
Electrons or holes now flow easily.

9. Currents through a p-n junction
Figure below shows a p-n junction in equilibrium.

10. Applications of a p-n junction
LED (Light Emitting Diode) is an example of a technological application of a p-n junction.
Question: How does this work ? Is an LED monochromatic ?
Ans: N.B. the junction is forward biased. When electrons and hole recombine, they emit photons. Yes,the photon energy corresponds to the band gap.

11. Comments
A modern white LED lightbulb converts more than 50 percent of the electricity it uses into light. Compare to the 4 percent conversion rate for incandescent bulbs.
The 2014 Nobel Prize in Physics was for the invention of the blue LED.
Shuji Nakamura (University of California at Santa Barbara),
Hiroshi Amano (Nagoya),
Isamu Akasaki (Nagoya)

12. Applications of a p-n junction
A photovoltaic cell is an example of a technological application of a p-n junction.
Question: How does this work ? Do the incoming photons have to be monochromatic ?
Ans: The incoming photon can dislodge an electron and (and create a hole). No. The electron are in continuous energy bands so the incoming light need not be monochromatic.

13. The transistor invented at Bell Labs, NJ in 1947
William Shockley, John Bardeen* and Walter Brattain. (1956 Nobel Prize in Physics)
*John Bardeen will crop up again in this chapter.

14. Transistors (p-n-p sandwiches)
The figure shows a p-n-p transistor in a circuit.
VC>>VE so the power dissipated in the resistor may be much larger than the power supplied to the emitter by VE.
“Voltage amplifier”

15. Transistors (p-n-p sandwiches)
The figure (right) shows a common-emitter circuit.
A large current IC controlled by a small current Ib
A “current amplifier”

16. MOSFET (Metal Oxide Semiconductor Field Effect Transistor)
The figure shows a field-effect transistor (Current from source to drain controlled by the potential difference between the source and an drain and by the charge on the gate).
Without charge on the gate, one of the junctions is reverse biased and no current flows.

17. MOSFET
Question: Suppose a negative charge is placed on the gate of the MOSFET, will a substantial current flow between the source and the drain ?
Ans: No, the gate will repel electrons

18. MOSFET
Question: Why does QM tunneling limit the miniaturization of MOSFETs ?
Ans: If the barrier between the source and drain becomes too small, it will become easy for electrons to tunnel from the source to the drain. The device will leak current even when turned off. (QM limits electronics miniaturization)

19. Integrated circuit
An integrated circuit can contain millions of transistors

20. Superconductivity

21. Superconductivity: History
Bardeen**, Cooper and Schrieffer explained it in 1956
1911: Kamerlingh-Onnes discovered that some metals at low temperature become perfect conductors. The resistance was lower than could be measured (still true today!).
1933: Meissner discovered that superconductors expel a magnetic field. They can be levitated by the magnetic repulsion.
Temperature
Resistivity
Zero!
This does not happen in a superconductor.
DEMO: Hi Tc levitation

22. How to avoid the Pauli exclusion principle
Pauli and two unidentified men
No two electrons can be in the same quantum mechanical state.
Yet in a superconductor, all the electrons are in the lowest energy state.
Question: What gives ? How do we explain this ?
Ans: Due to the interaction of electrons with nearby positive ions in the lattice. Pairs of electrons with opposite spins can form “Cooper pairs”, which have spin zero and are not subjected to the Pauli exclusion principle.

23. Bardeen, Cooper and Schrieffer explained all this in 1956
Superconductivity
Bardeen, Cooper and Schrieffer explained all this in 1956
Temperature
Resistivity
Zero!
The BCS physics in a (small) nutshell:
At low temperatures, the electrons in superconductors bind into pairs that have zero spin – the pairs are “composite bosons.” They love being in the same state and they condense into it.
A boson condensate can flow without scattering, it’s a charged “superfluid.”
Meanwhile a gap (not a band gap) opens up and there are no single-electron states left to accelerate and experience scattering.  Zero Resistance!
This does not happen in a superconductor.
DEMO: Hi Tc levitation
Demo

24. 1972 Nobel Prize in Physics