1. Elementary Particles (the last bit)
Review for Final Exam
Final Exam: Thursday Dec 18th, 8am to 10am
in Physics 203
Steven Weinberg ( )

2. Particles and Antiparticles

3. Particles and Antiparticles
Of course “strangeness” and “charmness” also change for antiparticles
containing strange and charm quarks
Basic properties in changing from particle to antiparticle:
Same mass (m)
Same spin (J)
Opposite charge (q) and (-q)

4. The Standard Model
Over the latter half of the 20th century, numerous physicists combined efforts to model the electromagnetic, weak, and strong interactions, which has resulted in The Standard Model.
It is currently widely accepted.
Image from
It is a relatively simple, comprehensive theory that explains hundreds of particles and complex interactions with six quarks, six leptons, and four force-mediating particles.
It’s based on three independent interactions, symmetries and coupling constants.

5. The Higgs Boson What about all the particle masses?
The Standard Model of particle physics proposes that there’s a field called the Higgs field that permeates all of space.
By interacting with this field, particles acquire mass. Particles that interact strongly with the Higgs field have heavy mass; particles that interact weakly have small mass.
The Higgs field requires another boson.
It’s called the Higgs particle (or Higgs boson) after Peter Higgs, who first proposed it.
Detecting and learning more about the Higgs boson is of the highest priority in elementary particle physics.
Wikipedia

6. The Higgs boson was recently detected!
That little bump? That's where CERN has seen a significant number of unusual events at about 125 GeV, which means that something new is going on.
Are we sure it’s the Higgs? Not completely…

7. Review General guidelines: 4 problems, similar to previous exam
No explicit problems on Special Relativity
From the hydrogen atom on is fair game; expect a foundational question
on quantum mechanics (particle in the box, harmonic oscillator,
periodic potential etc.)
Emphasis will be on subjects covered since last exam:
Solids, electronic properties of metals and semiconductors, and
elementary particles

8. Conductors, Insulators, Semiconductors
NaCl is an insulator, with a band gap of 2 eV, which is much larger than the thermal energy atT=300K
Therefore, only a tiny fraction of electrons are
in the conduction band

9. Conductors, Insulators, Semiconductors
Silicon and germanium have band gaps of 1 eV and 0.7 eV, respectively. At room temperature, a small
fraction of the electrons are in the conduction
band. Si and Ge are intrinsic semiconductors

10. Band Diagram: Intrinsic Semiconductor
Conduction band
(Partially Filled) EC EF EV
Valence band
(Partially Empty)
At T = 0, lower valence band is filled with electrons and upper conduction band is empty, leading to zero conductivity.
Fermi energy EF is at midpoint of small energy gap (<1 eV) between conduction and valence bands.

11. Donor Dopant in a Semiconductor
For group IV Si, add a group V element to “donate” an electron and make n-type Si (more negative electrons!).
“Extra” electron is weakly bound, with donor energy level ED just below conduction band EC.
Dopant electrons easily promoted to conduction band, increasing electrical conductivity by increasing carrier density n.
Fermi level EF moves up towards EC. EC EV EF ED
Egap~ 1 eV
n-type Si

12. Band Diagram: Acceptor Dopant in Semiconductor
For Si, add a group III element to “accept” an electron and make p-type Si (more positive “holes”).
“Missing” electron results in an extra “hole”, with an acceptor energy level EA just above the valence band EV.
Holes easily formed in valence band, greatly increasing the electrical conductivity.
Fermi level EF moves down towards EV. EA EC EV EF
p-type Si

13. pn Junction: Band Diagram
pn regions “touch” & free carriers move
Due to diffusion, electrons move from n to p-side and holes from p to n-side.
Causes depletion zone at junction where immobile charged ion cores remain.
Results in a built-in electric field (103 to 105 V/cm), which opposes further diffusion.
Note: EF levels are aligned across pn junction under equilibrium.
n-type
electrons EC EF EF EV
holes
p-type
pn regions in equilibrium – – EC – – + – + – EF + + – – – + + + – – + + – + + + EV
Depletion Zone

14. Forward Bias and Reverse Bias
Forward Bias : Connect positive of the positive end to positive of supply…negative of the junction to negative of supply
Reverse Bias: Connect positive of the junction to negative of supply…negative of junction to positive of supply.

15. PN Junction: Under Bias
Forward Bias: negative voltage on n-side promotes diffusion of electrons by decreasing built-in junction potential  higher current.
Reverse Bias: positive voltage on n-side inhibits diffusion of electrons by increasing built-in junction potential  lower current.
Equilibrium
Forward Bias
Reverse Bias
p-type
n-type
p-type
n-type
p-type
n-type –V +V e– e– e–
Majority Carriers
Minority Carriers

16. pn Junction: IV Characteristics
Current-Voltage Relationship
Forward Bias: current exponentially increases.
Reverse Bias: low leakage current equal to ~Io.
Ability of pn junction to pass current in only one direction is known as “rectifying” behavior.
Forward
Bias
Reverse Bias
Manifestly not a resistor: V=IR
Not Ohm’s law

17. Heat Capacity of Electron Gas
By definition, the heat capacity (at constant
volume) of the electron gas is given by
where U is the total energy of the gas. For a gas
of N electrons, each with average energy <E>,
the total energy is given by

18. Heat Capacity of Electron Gas
Therefore, the total energy can be written as
where a = p2/4

19. Total Heat Capacity Electrons + Lattice

20. Electrical Conduction

21. Temperature dependence
Resistivity
resistivity as a function of n and t
Temperature dependence
Metal: Resistance increases with Temperature.
Why? Temp  t, n same (same # conduction electrons)  r