Semiconductors
Basic Properties
Band Structure
•  Eg = energy gap
•  Silicon ~ 1.17 eV
•  Ge ~ 0.66 eV
1
Intrinsic Semiconductors
•  Pure Si, Ge are intrinsic semiconductors.
•  Some electrons elevated to conduction band
by thermal energy.
Fermi-Dirac Distribution
•  The probability that a particular energy state ε is filled
is just the F-D distribution.
•  For intrinsic conductors at room temperature the
chemical potential, µ, is approximately equal to the
Fermi Energy, EF.
•  The Fermi Energy is in the middle of the band gap.
2
Conduction Electrons
•  If ε - EF >> kT then
•  If we measure ε from the top of the valence band
and remember that EF lies in the middle of the
band gap then
Conduction Electrons
•  A full analysis taking into account the
number of states per energy (density of
states) gives an estimate for the fraction of
electrons in the conduction band of
3
Electrons and Holes
•  When an electron in the valence band is
excited into the conduction band it leaves
behind a hole.
Holes
•  The holes act like positive charge carriers in
the valence band.
Electric Field
4
Holes
•  In terms of energy level electrons tend to
fall into lower energy states which means
that the holes tends to rise to the top of the
valence band.
Photon Excitations
•  Photons can excite electrons into the
conduction band as well as thermal
fluctuations
5
Impurity Semiconductors
•  An impurity is introduced into a
semiconductor (doping) to change its
electronic properties.
•  n-type have impurities with one more
valence electron than the semiconductor.
•  p-type have impurities with one fewer
valence electron than the semiconductor.
Impurities
•  For silicon
§  n-type is pentavalent: As, P
§  p-type is trivalent: Al, Ga, B
6
Impurity Semiconductors
•  n-type
Impurity Semiconductors
•  p-type
7
Band Structure of N-type
Conduction band
Fermi Energy
Donor impurity levels
Valence band
For Si(As):
Econduction - Edonor = 0.049 eV
T = 0K
Band Structure of N-type
Conduction band
Fermi Energy
Donor impurity levels
Valence band
T = 300 K
For Si(As):
Econduction - Edonor = 0.049 eV
Remember kT = 0.025 eV
8
Band Structure of P-type
Conduction band
Acceptor impurity levels
Fermi Energy
Valence band
For Si(Ga):
Eacceptor - Edvalence = 0.065 eV
T=0K
Band Structure of P-type
Conduction band
Acceptor impurity levels
Fermi Energy
Valence band
T = 300 K
For Si(Ga):
Eacceptor - Edvalence = 0.065 eV
Remember kT = 0.025 eV
9
The pn junction
Forming a pn junction
•  p-type and n-type semiconductors are placed in contact.
•  electrons in the conduction band in the n-type diffuse across
the junction into the p-type.
Conduction band
Conduction band
n
p
Valence band
Valence band
10
Forming a pn junction
•  p-type and n-type semiconductors are placed in contact
•  electrons in the conduction band in the n-type diffuse across
the junction into the p-type.
Conduction band
Conduction band
n
p
Valence band
Valence band
Forming a pn junction
once in the p-type they can drop down into the valence
band and to fill up one of the hole states.
•
Conduction band
Conduction band
n
p
Valence band
Valence band
11
Forming a pn junction
once in the p-type they can drop down into the valence
band and to fill up one of the hole states.
•
Conduction band
Conduction band
n
p
Valence band
Valence band
Forming a pn junction
•  Electrons continue to diffuse across the junction.
•  The area of the p-type near the junction becomes more
negative due to the excess electrons while the n-type
becomes more positive due to the excess of holes (or
deficit of electrons).
•  This creates an electric field in the region of the junction
that eventually prevents any further significant diffusion of
electrons.
•  This region is essentially free of mobile charge carriers and
is called the depletion region.
12
Depletion Region
•  The depletion region is free of mobile charge carriers.
•  The typical thickness of the depletion region is about
1 micron or 10-4 cm.
-  - -
+++
-  - -
+++
-  - -
+++
-  - -
+++
Depletion region: Mobile holes and electrons
have combined leaving charged ions.
Formation of the depletion region
1
2
3
4
13
Depletion Region Characteristics
•  The fixed charges in the depletion region create an electric
field that points from the n-type to the p-type. This field
tends to sweep any mobile electrons in the region back to
the n-type and any mobile holes back to the p-type.
Depletion region
= mobile hole
- - - - - - - - - - - - - - - - -
Ed
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
= mobile electron
-
= fixed ionized
donor atom
+
= fixed ionized
acceptor atom
n
p
Energy Diagram for pn junction
•
In equilibrium the Fermi energy must be the same everywhere,
otherwise electrons could reduce the energy of the system by flowing
to unoccupied states in a region of lower Fermi energy.
Electron
Energy
Conduction band
-
EF
+
+
+
+
Valence band
p
n
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Energy Diagram for pn junction
•  The potential energy difference between the two sides of the
junction is given by electric field in the depletion region.
Electron
Energy
Conduction band
-
EF
+
+
+
+
ΔE
Valence band
p
n
d
Equilibrium Currents for pn junction
•  In equilibrium there are still small currents flowing across
the junction though there is no net electron current.
Electron
Energy
Thermal Current
Recombination Current
-
EF
Conduction band
+
+
+
+
Valence band
p
n
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Thermal Current
•
Electrons in the valence band of the p-type can acquire enough thermal
energy to jump into the conduction band. They diffuse into the
depletion region and are swept into n-type by the E-field.
Electron
Energy
Conduction band
-
EF
+
+
+
+
Valence band
n
p
Recombination Current
•
Electrons in the conduction band of the n-type can acquire enough thermal
energy to rise higher in the conduction band. They can then diffuse across the
depletion region to the p-type and drop into the valence band filling a hole.
Electron
Energy
Conduction band
-
EF
+
+
+
+
Valence band
p
n
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Currents in equilibrium pn junctions
•  The thermal current cancels out the recombination
current in the equilibrium state.
•  The thermal current is dependent on the width of
the energy gap in the semiconductor and the
temperature.
•  The recombination current is dependent on ΔE, the
size of energy difference between the p-type and
n-type bands and the temperature.
Biasing pn junctions
•  Apply a voltage across a pn junction:
p
n
p
n
+
+
V
Forward Bias
V
Reverse Bias
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Reverse bias
•  A negative voltage is applied to the p-region. The
energy of the electrons in the p-region will
increase.
•  The potential energy difference between the two
regions will increase by (-e)(-V) = eV
•  This will reduce the recombination current which
depends on the potential difference but leave the
thermal current unchanged.
•  A small net electron current will flow from p to n.
Reverse bias
•  The increase in the potential energy difference reduces the
recombination current.
Electron
Energy
Thermal current
-
EF
Conduction band
Recombination current
+
+
+
+
ΔE + eV
Valence band
p
d
n
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Forward bias
•  A positive voltage is applied to the p-region. The
energy of the electrons in the p-region will
decrease.
•  The potential energy difference between the two
regions will be reduced: (-e)(V) = -eV
•  This will greatly increase the recombination
current which depends on the potential difference
but leave the thermal current unchanged.
•  A large net electron current will flow from n to p.
Forward bias
•  The increase in the potential energy difference greatly
increases the recombination current.
Electron
Energy
Thermal current
Recombination current
Conduction band
-
EF
+
+
+
+
ΔE - eV
Valence band
p
d
n
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Diodes
Diodes
•  The pn junction is used an
electronic circuit element
called the diode or rectifier.
•  The diode is the most basic
electronic component.
•  An ideal diode would have
zero resistance when
forward biased and an
infinite resistance when
reverse biased.
20
Practical Diode Model
•  A somewhat more realistic
model incorporates the turnon voltage or knee voltage.
•  There is a minimum voltage
required across the diode in the
forward direction before it
conducts an appreciable
amount of current.
•  The turn-on voltage is
approximately 0.5 to 0.7 Volts
in Si and about 0.3 volts in Ge.
I
Vturn-on
V
Realistic Model
•  In forward bias the
diode has a resistance
on the order of 10 Ω.
•  In reverse bias the
resistance is on the
order of 108 Ω.
21
Biased pn junction
•  In terms of positive current the current vs.
voltage graph for a biased pn junction:
I = I0 (e+eV /kT − 1)
Breakdown
•  In sufficiently large reverse bias is applied to a diode an
•
•
•
•
avalanche occurs.
At the breakdown voltage charge carriers gain enough
energy (from the reverse bias electric field) between
collisions to break a covalent bond in the lattice and create
another charge carrier.
These two charge carriers are accelerated and create more
charge carriers leading to an avalanche of charge
carriers.
This occurs very sharply at a certain voltage.
Ordinary diodes usually fail in these conditions.
22
The Diode Curve
Real Diodes
•  The schematic symbol for a diode is
•  Diodes come in many shapes, each designed for a
specific set of applications.
23
Diodes and Temperature
•  As temperature
increases, more thermal
energy is available to
electrons enabling them
to escape their binding
atoms more readily. This
causes the knee voltage
(the voltage at which the
diode turns on) to
decrease.
Zener Diodes
•  The p-n junction diode
that operates in the
reverse breakdown region
is usually destroyed by
the excess current and the
heat it produces. The
zener diode is designed
to successfully operate in
this region.
24
Zener Diode
•  The characteristic curve
of the zener operating in
the reverse breakdown
region shows that the
voltage dropped across
the zener diode remains
relatively constant while
current through the zener
current is allowed to
increase dramatically.
Zener Diode
•  When forward biased, the zener has a turn-on voltage of
approximately 0.7 V (like any other silicon diode.) When
reverse biased, the zener can have a zener voltage equal
to whatever amplitude it is designed (and doped) to
possess (from a minimum of approximately 1.8 V to
several hundred volts.)
•  The relatively constant voltage drop across the zener when
it is reverse biased is the reason for to its use as a voltage
regulator. A voltage regulator is a device (or circuit)
designed to maintain a constant output voltage regardless
of any variations in the magnitude of its input voltage or in
the requirements of load current.
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Light-Emitting Diode (LED)
•  LEDs are diodes that emit light when
biased properly.
•  LEDs are available in various colours:
red, green, yellow, orange, blue and
white.
•  Forward knee voltage does vary with
LED color (from approximately 1.2 V
to approximately 4.3 V.)
LEDs
•  LEDs usually have clear
(or semi-clear) cases. The
different colors are
obtained by using
different elements in the
LED's construction.
•  LEDs must be forward
biased to allow current to
pass through them.
•  LEDs will only light up
when current is
sufficiently large.
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LEDs
•  Since LED cases are not labeled, a means of identifying the
anode and cathode must exist.
Laser Diodes
•  Laser diodes are basically LEDs driven at higher
current so that a population inversion is created to
allow stimulated emission of photons.
27
Photovoltaic Diode or Solar Cell
•  A photon is absorbed by a
semiconductor atom promoting
an electron across the energy
gap to the conduction band.
•  The electron is then accelerated
by the electric field in the
depletion region.
•  This produces a reverse current
driven by the incoming photons.
Diode Application:
The Half-wave rectifier
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