Exam 2 Study Guide
• Emphasizes Homeworks 5 through 9
• Exam covers assigned sections of Chps. 3,4 & 5. Exam will
also assume some basic information from the early part of
the semester. It will assume you know the basic
information from the earlier part of the semester that is
required for this second part of the semesters..
• Covers all class notes, starting with QM of a crystalline
solid and ending with pn junction.
• Do all the reading assignments.
• Read my notes, especially Chps. 5, 6, 7, 8.
• Be able to solve all the homework problems without your
notes.
• Re-do the derivations we did in class on your own.
• Equations given: Download formula sheet
Important Concepts on Energy Bands for Crystalline Solids: Including
Semconductors
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Semiconductors and Metals are crystalline solids.
Electrons exist only in allowed bands of energy.
Bands are composed of many quantum states.
Each band has approximately the same number of states as there are atoms in
crystal.
Bands that are completely filled with electrons cannot conduct electricity
In semiconductors, at T=0oK, all bands are either totally full or totally empty.
The band with highest energy that is totally full is call the valence band (VB).
The next highest band in energy is the conduction band (CB).
In semiconductors there is an energy gap between the valence and conduction
bands
At T > 0oT, some electrons obtain enough energy to jump the gap and exist in
the conduction band.
This process makes the conduction band partially full, and the valence band
partially empty. Therefore, both of these bands can conduct at T > 0oT
Important Concepts on Energy Bands and Conduction for Crystalline
Solids: Including Semconductors
• States in the VB where electrons have left from are now empty. These
empty states are called holes.
• Mathematically, holes act like positively charged electrons and are
treated as such.
• The most popular semiconductor material is Silicon which composes
more than 95% of our chips.
• Pure silicon is also called intrinsic silicon.
• In 1 cubic cm of intrinsic silicon at room temperature there are about
1010 electrons in the conduction band and 1010 holes in the valence
band.
• In a metal at room temperature the CB is typically ½ full meaning that
there are about 1023 conduction electrons/cm3
• Therefore, the conductivity of a metal is approximately 1013 greater
than that of a semiconductor at 300oK (recall current density: J=qnv).
Important Concepts on Energy Bands and Conduction for Crystalline
Solids: Including Semconductors
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We usually want to increase and control the conductivity in semiconductors.
We achieve this with doping.
With doping we substitute impurities for silicon atoms into the lattice that give
rise to mobile electron in the CB or mobile holes in the VB.
In N-type material, the impurities give rise to electrons in the CB
In P-type material, the impurities give rise to holes in the VB.
N-type doping works as follows in Si: Silicon has 4 valence electrons.
Phosphorous, which has 5 valence electrons, is substituted for a Si atom,
leaving one of the 5 electrons essentially unbound. This electron enters the CB
and can now be conducting.
P-type dopants have 3 valence electrons. They accept electrons from the VB,
leaving mobile holes in VB, which can now be conducting.
Doping levels in semiconductors typically range from 1014 to 1019/cm3
Adding 1017 phosphorous atoms to Si will make it 107 times more conductive
than intrinsic Si.
Doped semiconductors are called extrinsic semiconductors.
The fact that we can dope semiconductors to selectively control their
conductivity allows for microelectronics to exist as we know it.
Important Concepts on Energy Bands and Conduction for Crystalline
Solids: Including Semconductors
• By studying the band structure (QM states) we understand the doping
and conduction possibilities of a semiconductors.
• The band structure also tells us the instantaneous (group) velocity of
an electron (by the slope Vg=(1/hbar)(dE/dk)
• Band structure tells us effective mass , 1/m* = (1/hbar)2(d2E/d2k), by
the curvature of the band near the minium.
• The effective mass and group velocity help to account for the quantum
effects of crystal without having to solve the Schrodinger equation for
every application.
• Mobility is another very important concept in semiconductors. It tells
you the average velocity of a conduction electron (or hole) in the
presence of an electric field. Vavg= mobility x field (mobility = μ=
qτ/m*)
• The mean free time between collisions is τ, which is also obtained
using the band structure.
Exam Study Guide
• General Topics
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Generation and Recombination
Drift Current
Diffusion Current
Built-in potential due to non-uniform doping: KNOW HOW TO
EXPLAIN HOW BUILT IN POTENTIAL ARISES.
PN Junction in equilibrium, reverse bias and forward bias
Current components in PN junction
Qualitative and quantitative understanding of built in potential and
balance of drift and diffusion.
Junction Capacitance and Diffusion Capacitance for a PN junction.
Depletion approximation and calculation of internal electric field
and potential as a function of position.
Continuity equation
Derivation of carrier concentrations and current density as function
of position in PN junction.
Know difference between minority and majority carriers.
PN Junction
• A PN junction is a contact between an
N-type material and a P-type material.
• PN junction allows current to flow in
one direction and not the other.
• The 2-terminal device that is made of a
single PN junction is a diode.
• The PN junction structure is found in
almost every electronic device (BJTs,
MOSFETs, etc.)
• A PN junction has a built in potential
barrier that arises due to non-uniform
doping. (which is usually the same
thing as saying different Fermi levels).
PN Junction
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To forward bias a PN junction
apply a positive voltage on the Pside and the negative voltage
(relatively speaking) on the N-side.
When you forward bias a PN
junction it reduces the potential
barrier (and the built in electric
field) and allows mobile electrons
and holes to have a net current that
is due to diffusion.