Transcript Chapter 29

Chapter 29: Solid State
Electronics
Mike O’Connor
Blake Barber
Nick Keller
Charlie Vana
Nick Dotson
Band Theory
Because energy is quantitized, each atom has a specific
energy level. As these atoms are brought together into solids, the
many, interacting electric fields of the atoms change the energy
levels of the atoms. No two electrons can have the same energy.
The result is many differing energy levels, or energy bands. Energy
bands are regions on a graph where the energy levels of the atoms
in a solid are spread. These bands are separated by forbidden gaps
which are values of energy electrons are not allowed to have.
In insulators, the lowest band is fully filled because it forces
electrons to jump to the next available band in order to move. This
resists electron flow because the electrons must gain more enegry.
In conductors, the lowest band is only partially filled because it
allows electrons to move freely without gaining more energy.
Energy Band of Insulator
Energy Band of Conductor
Example Problem
If a copper atom contributes one electron, how many free electrons exist in a cubic
centimeter of copper? The density of copper is 8.96 g/cm3 and it has an atomic mass
of 63.54 g/mole. Don’t forget Avagadro’s magic number of 6.02E23 atoms/mole.
Given:
Copper
1 free electron per atom
M = 63.54 g/mole
ρ = 8.96 g/cm3
Solution: Dimensional Analysis
(Free e-)/(cm3 Cu) =
((1 Free e-)/(1 atom))x(6.02E23 atoms/1 mole)x((1 mole Cu)/(63.54g Cu))
x(8.96g/1 cm3 Cu)
= 8.49E22 free e- / cm3 Cu
Summary
• In solids, the allowed
energy levels are
spread into broad
bands. The bands are
separated by values
of energies that
electrons may not
have called the
forbidden gap.
What that means
• The levels are spread into broad bands.
• The bands are separated by values of
energy that electrons are not allowed to
have.
• These energies are called forbidden gaps.
• Electrical conduction in solids explained in
terms of these bands, this is called the
band theory.
MORE!
• In conductors,
electrons can move
because the band of
allowed energy levels
is only partially filled.
So…..
• Electricity can be possible because when a
potential difference is placed across a material,
the resulting electric field exerts a force on the
charged particles.
• These accelerate, the field wont work on them,
and they gain energy.
• They can only gain energy if there is a higher
energy level into which they can move, this is
true when the bands are only partly filled.
Example
• Find the fraction of atoms that has free
electrons in silicon. At room temperature,
thermal energy frees 1x 10^13 in pure
silicon. The density of silicon is 2.33
g/m^3 and the atomic mass of silicon is
28.09 g/mol. A. How many silicon atoms
are there in one cubic centimeter? B. What
is the fraction of silicon atoms that have
free electrons? That is, what is the ratio of
free e^-/cm^3 to atoms/cm^3 in silicon?
Given
• Silicon: density, p =
2.33 g/cm^3
• Atomic mass, M=
28.09 g/mol
• Free e^-/cm^3 = 1 x
10^13
• Avogadro's number,
Av = 6.02 x10^23
atoms/mol
Unknowns
• A. Si atoms/Cm^3
• B. Free e^-/atoms Si
Solution- Part A
• A. By dimensional analysis,
• (2.33g/1cm^3)(1 mol/28.09 g
Si)(6.02x10^23 atoms/1 mol)
• = 4.99 x 10^22 atoms/cm^3
Solution-Part B
• Free e^-/ atoms Si =
• (1x10^13 free e^/cm^3)(1cm^3/4.99x1
0^22 atoms Si)
• = 2x 10^-10 Si atoms
with free electrons
Semiconductors Who
Occasionally Enjoy Partying
Chapter 29
Key Points
• Conduction in
semiconductors is usually
the of result doping pure
crystals with small
numbers of impurity
atoms.
• N- type semiconductors
conduct by means of
electrons while in p-type
semiconductors,
conductions is by means
of holes.
Explained
• Conduction in semiconductors
is usually the of result doping
pure crystals with small
numbers of impurity atoms.
• N- type semiconductors
conduct by means of electrons
while in p-type
semiconductors, conductions
is by means of holes.
•
The dispersion of different
atoms within a substance will
effectively determine where
and to what degree they
conduct.
• The electrons within N-types
have free flowing electrons that
can transfer electricity to a
degree. P-type conductors
have positively charged holes
in its valence shell that transfer
electricity by vibrating motion.
History of Semiconductors
• Semiconductors are widely
used in almost all electronic
devices. Most widely used
applications are transistors
used in many electronics. The
transistor was invented by
John Bardeen, William
Shockley, and Walter Brattain
in 1947.
• Semiconductors were
discovered in the 1800’s as
poor conductors that exhibited
photoelectric effects.
Practice Problem
• Silicon is doped with arsenic so that one in every 10^6 Si
atoms is replaced by an As atom. Assume that each As
atoms donates one electron to the conduction band. A.
What is the density of free electrons in this extrinsic
semiconductor?
• Given: As atom density= 1 As atom/ 10^6 Si atoms free e-/
As atom = 1 free e-/ As atom
• Si atom/ cm^3 = 4.99x 10^22 Si atoms/ cm^3 free e-/cm^3
in intrinsic Si= 1x10^13/ cm^3
• Unknowns: As-donated free e-/cm^3
• Solution: a. By dimensional analysis,
Free e-/cm^3= (1 free/1 As atom) x (1 As atom/ 1x10^6 Si
atoms) x ( 4.99x 10^22 Si atoms/ 1 cm^3)= 4.99 x10^3 free
e-/cm^3
Diodes
Diodes are the simplest semiconductor device. A diode
consists of joined regions of p-type and n-type
semiconductors. Holes are on the p-type side and
electrons on the n-type side. The area in between is called
the junction. This is also where the depletion layer occurs.
The depletion layer is created through a loss of holes or
free electrons around
the junction.
A Diode conducts charges in one
direction only and can be used to
produce current that flows in one
direction only.
Voltage Drop V=Vd + IR
Diodes and Circuits
When a diode is connected to a circuit as seen on the bottom
left, the free electrons in the n-type semiconductor and the
holes in the p-type semiconductor are attracted toward the
battery the width of the depletion layer is increased and almost
no current flows through the diode. However if the battery is
connected in the opposite direction like in the bottom right
electrons reach the p-end and fill the holes. The depletion layer
is eliminated and current flows.
Reverse-biased Diode
Forward-biased Diode
Transistors
• A npn transistor consists of n-type
semiconductors surrounding a thin p-type
layer. If the transistor has a n-type in the
center then it is a pnp transistor. The
central layer is called the base and the two
surrounding regions are the emitter and
collector.
Transistors
• Transistors are used as amplifiers in
almost every electronic instrument. The
pn-junctions can be seen as back-to-back
diodes. The base collector diode is
reverse biased so no current flows,
however the base-emitter diode is forward
biased.
Practice Problem
• A diode has a voltage drop of .4V when 12
mA flows through it. If the same 470-Ω
resistor is used, what battery voltage is
needed?
• V=V + IR
• V=.4V + (.012 A)(470 Ω) = 6.0 V
d
Conduction in Solids
Key Points
1. Electrons in metals have a very fast
random motion. A potential difference
across the metal causes a very slow drift
of the electrons.
2. In insulators, electrons are bound to
atoms. More energy is needed to move
them than is available.
Key Points (In simpler terms)
1. The metallic bonds in metals allow the
electrons of the metal atoms to move
throughout the substance when little
potential difference is added.
2. The potential energy needed to break
electrons off insulator molecules is
higher than metals. So insulators need a
lot of energy to transfer a little current.
Example:
A Diode in a Simple Circuit
• A silicon diode, whose I/V characteristics
are shown, is connected to a battery
through a 470Ω resistor. The battery
forward-biases the diode and its voltage is
adjusted until the diode current is 12mA.
• A. Draw a schematic diagram of the circuit
• B. What is the battery voltage?
Solution
• Given: graph of Vd versus I
R=470Ω
• Needed: battery voltage, V
• V= Vd + IR
• When I=12mA, Vd= 0.7V (shown in graph)
• V= Vd + IR
0.7V + (470Ω)(1.2x10-2A)=6.3V
The End