Announcements Added a final homework assignment on Chapter 44, particle physics and cosmology. Chap 42 Homework note: Binding energy is by convention positive (for molecules and in nuclear physics, next chapter) Preparing Practice Final Exam

Why Some Solids Conduct Current and Others Don’t Conductors, semiconductors, and insulators: Basic idea, Their description is provided in terms of: Energy Bands for electrons in solids The Pauli exclusion principle In order for a material to conduct electricity, it must be possible to get the electrons moving (i.e., give them some energy).

Band gap from PHET University of Colorado Felix Bloch in the 1950’s at Columbia U. Discovered band gaps in 1928 (thesis work in Germany). 1952 Nobel Prize for NMR. https://phet.colorado.edu/en/simulation/band-structure On MACs need Java enabled. Please try it at home too.

Energy bands (Question: why do these arise ?) Metallic sodium is an example, gap is 2.1 eV but even at T=0, conduction electrons. Small band gap e.g. 1.12 eV for Si, 0.67 for germanium Band gap of 5 eV or more

Clicker question on energy bands How would you expect the electric conductivity of a semiconductor to vary with increasing temperature? A. It should increase, because more electrons are thermally excited from the valence band into the conduction band. B. It should increase, because more electrons are removed from their parent atoms and added to the valence band. C. It should decrease, because the added thermal energy breaks apart correlated electron pairs. D. It should decrease, because the atoms in the crystal will vibrate more and thus block the flow of electrons. Answer: A

Clicker question on energy bands How would you expect the electric conductivity of a semiconductor to vary with increasing temperature? A. It should increase, because more electrons are thermally excited from the valence band into the conduction band. B. It should increase, because more electrons are removed from their parent atoms and added to the valence band. C. It should decrease, because the added thermal energy breaks apart correlated electron pairs. D. It should decrease, because the atoms in the crystal will vibrate more and thus block the flow of electrons. Answer: A

Tricky Clicker question on energy bands If you increase the temperature of a block of copper from 300 K to 600 K, what happens to the average kinetic energy of the electrons in the conduction band? (Copper remains a solid at these temperatures.) A. The average kinetic energy increases by a factor of 4. B. The average kinetic energy increases by a factor of 2. C. The average kinetic energy increases by a factor of . D. The average kinetic energy changes by only a small factor. Answer: D

Tricky Clicker question on enegry bands If you increase the temperature of a block of copper from 300 K to 600 K, what happens to the average kinetic energy of the electrons in the conduction band? (Copper remains a solid at these temperatures.) A. The average kinetic energy increases by a factor of 4. B. The average kinetic energy increases by a factor of 2. C. The average kinetic energy increases by a factor of . D. The average kinetic energy changes by only a small factor.

Semiconductors A semiconductor has an electrical resistivity that is intermediate between those of good conductors and good insulators.

Holes A hole is a vacancy in a semiconductor. A hole in the valence band behaves like a positively charged particle. The figure on the right shows the motions of electrons in the conduction band and holes in the valence band with an applied electric field. Question: What is the force on a charged particle in a uniform E field

Doping is the deliberate addition of impurity elements. Impurities Doping is the deliberate addition of impurity elements. In an n-type semiconductor, the conductivity is due mostly to negative charge (electron) motion. In a p-type semiconductor, the conductivity is due mostly to positive charge (hole) motion.

n-type and p-type semiconductors Figure 42.26 (left) shows an n-type semiconductor, and Figure 42.27 (right) shows a p-type semiconductor.

Fermi-Dirac distribution The Fermi-Dirac distribution f(E) is the probability that a state with energy E is occupied by an electron (identical spin ½ particles) Look at the change with temperature There is a different distribution for spin 1 (photons) and spin 0 particles [Bose-Einstein]

Fermi-Dirac distribution example At what energy above the Fermi level is the probability that a particular state is occupied equal to 0.01 ? Note for numeric problems kB=1.3821 x 10-23J/K or 8.61 x 10-5eV/K; kT at room temp ~ 0.0254 eV The probability of occupying a state of energy 4.6kBT is 1%

EF calculation with Fermi-Dirac distributions The density of states dn/dE is given by a function g(E). The number of electrons dN in the range dE around E is given by (integrate up to EF0)

EF calculation with Fermi-Dirac distributions The variable n is the number of free electrons per unit volume. Example: At low temperatures , copper (Cu) has a free–electron concentration of n=8.45 x 1028/m3, what is EF ?

Photocell A photocell is a simple semiconductor device. In a photo-cell an electron in the valence band can jump to the conduction band. The conductivity increases in proportion to the incident light intensity

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

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

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.