Elementary Particles (the last bit) Review for Final Exam Final Exam: Thursday Dec 18th, 8am to 10am in Physics 203 Steven Weinberg (1933 - )

Particles and Antiparticles  

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)

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 http://quarknet.fnal.gov/run2/standard.html 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.

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

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… http://dvice.com/archives/2012/07/cern-announces.php

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

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

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

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.

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

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

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

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.

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

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

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

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

Total Heat Capacity Electrons + Lattice  

Electrical Conduction  

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