Semi-conductors
Properties of Solids
• Electrical (Conducting) properties
of solids:
– Conductors
– Insulators
– Semi-Conductors
• The electrical conductivity at room
temperature is quite different for
each of these three kinds of solids
– Metals and alloys have the
highest conductivities
– followed by semiconductors
– and then by insulators
(Super)conductor / Semiconductor
Superconductor
Wave functions overlap
• When two atoms
approach each other, their
wave functions overlap
• Bonding / Antibonding
depends on relative sign
of the two wave functions
Bonding
Antibonding
The Hydrogen Molecule
Many Atoms
2 hydrogen atoms
• When many atoms approach
each others, more energy states
are formed
Create bands separated by
energy gaps
11 hydrogen atoms
Band Theory of Solids
• The Kronig-Penney Model (1931)
– Interaction between the electrons and the
lattice of atoms
Lattice
Coulomb field
Simplified model
(Kronig/Penney)
Kronig-Penney Model (I)
• Electron:
– essentially free between 0<x<a (and in the
similar region along the lattice)
– Has to tunnel through the barrier regions
Kronig-Penney Model (II)
• Solutions:
– “Free electron” region:
• With:
– Barrier – tunneling:
• With:
• Boundary Conditions:
K, another wave number
Allowed / Forbidden Regions
FORBIDDEN REGIONS
What’s what ?
Band Theory
Electron
No !
• Lower band: valence band
• Upper band: conduction band
(Intrinsic) Semiconductors
Copyright HyperPhysics
•
Energy gap smaller than 1 eV or so.
•
Fermi level ~ in the middle of the gap
•
Thermal excitation electrons can jump to the conduction band
– Two types of charge “carriers”:
• Electrons in the conduction band
• Holes (vacancies) in the valence band
Temperature and Resistivity
• The increased number of electrons in excited states explains the
temperature dependence of the resistivity of semiconductors.
• A useful empirical expression developed by Clement and Quinnell
for the temperature variation of standard carbon resistors is given by
where A, B, and K are constants.
Semi-conductors can be used as thermometers
(Thermoelectric effect. See: Thermocouples p399)
Impurity Semiconductors
electron
•
It is possible to improve very significantly the conduction properties by “doping” the semiconductor.
–
N-type: dopant adds electrons levels close to the conduction band
extra electrons can jump in the conduction band from these donor levels
–
P-type: dopant adds vacancy levels close to the valence band
electrons from the valence band can jump in the acceptor levels leaving holes/vacancies in the valence band
Example: Silicon
• Silicon: 3s23p2
• Arsenic: 4s24p3
One more electron, donor
level
• Indium: 5s25p1
One less electron, acceptor
level
Applications: Diodes
• pn junction
Inverse Bias
No Bias
(p)
(n)
One application: Wheatstone Bridge – a.k.a Bridge Rectifier
Forward Bias
Applications:
Photodiodes / Photovoltaic Cells
• LED (Light Emitting Diode):
• Solar Cell:
Applications: Transistors
Voltage and Current Amplification
Applications: Integrated Circuits
Moore’s law, showing the progress in computing power over a 30-year span, illustrated here with
Intel chip names. The Pentium 4 contains over 50 million transistors. Courtesy of Intel
Corporation. Graph from http://www.intel.com/research/silicon/mooreslaw.htm.