Download 14. Elementary Particles

Elementary Particles (last bit); Start Review for Final
Start Review for Final Exam
Final Exam: Tuesday Dec 15th, 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)
May also have other quantum numbers that change
Review
General guidelines:
4 problems – exam is 2 hours
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
T>0
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
EF
EV
n-type Si
ED
Egap~ 1 eV
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.
EC
EF
EV
EA
p-type Si
pn Junction: Band Diagram
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.
EC
EF
EV
n-type electrons
pn regions
“touch” &
free
carriers
move
EF
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
p-type
n-type
e–
Forward Bias
p-type
n-type
Reverse Bias
–V
e–
Majority Carriers
p-type
n-type
e–
Minority Carriers
+V
pn Junction: IV Characteristics
Current-Voltage Relationship
I  I o [e
eV / kT
 1]
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
dU
CV 
dT
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
UN E
Heat Capacity of Electron Gas
Therefore, the total energy can be written as
 kT 
3
U  NEF     NkT
5
 EF 
where  = p2/4
dU p
T
CV 

Nk
dT
2
TF
2
Total Heat Capacity Electrons + Lattice
Electrical Conduction
Resistivity
resistivity as a function of n and 
FE
ma
E
m
1
e
e
 



2
J
ne vd
ne (a )
n
ne 
Temperature dependence
• Metal: Resistance increases with Temperature.
Why? Temp  , n same (same # conduction electrons)  