Many solids conduct electricity
There are electrons that are not bound but are able to move through the crystal.
Conducting solids fall into two main classes; metals and semiconductors.
 ( RT )metals ;106  108   m
and increases by the addition of small
amounts of impurities (semiconductors do opposite).
In a metal, the conductivity  (1/resistivity )
normally gets smaller (or resistivity
increases) at higher temperatures. Why?
Why smaller?
Impurties have a
big effect on
semiconductors
Why?
Impurities can add states
within the band gap that
makes excitation (and thus
conduction) much more likely
Antimony doped germanium
Doping produces an extrinsic
semiconductor (rather than intrinsic)
• Semiconductors can be easily doped
• Doping is the incorporation of [substitutional]
impurities into a semiconductor in a controlled
manner
• In a doped material, Ne is not equal to Nh
Mott Transition: Impurities wavefunctions
overlap, causing the material to become a metal
f(r)
aB
+
b
+
Donors
• Let’s use Silicon (Si) as an example
– Substitute one Si (Group IV) atom with a
Group V atom (e.g. As or P)
– Si atoms have four valence electrons that
participate in covalent bonding
– When a Group V atom replaces a Si atom, it
will use four of its electrons to form the
covalent bonding
– What happens with the remaining electron?
Donors
• The remaining electron will not be
very tightly bound, and can be easily
ionized at T > 0K
• Ionized electron is free to conduct
– In terms of the band structure, this
electron is now in the conduction band
• Such Group V impurities are called
Donors, since they “donate” electrons
into the Conduction Band
– Semiconductors doped by donors are
called n-type semiconductors (extra
electrons with negative charge)
This crystal has been doped with a pentavalent impurity.
The free electrons in n type silicon support the flow of current.
Hydrogenic Donors
An electron added to an intrinsic semiconductor at T=0
would go into the lowest empty state i.e. at the bottom of
the conduction band.
Conduction
Band
When one adds a donor atom at T=0
the extra electron is bound to the positive
charge on the donor atom (~ hydrogen)
+ve
ion
Ec
ED
-e
The electron bound to the positive
ion is in a state just below the
conduction band, where ED is the
binding energy.
Valence
Band
Ev
Donors: Energy Levels
•
Such impurities create
“shallow” levels - levels within
the band gap, close to the
conduction band
How much is ED?
• The small ionization energy
means a sizable fraction of
donor atoms will be ionized at
room temperature 
Treat Similar to Hydrogen
• Employ the solution for hydrogen atom
– Substitute the effective mass for the electron mass
– The field of the charge representing the impurity
must be reduced by the static dielectric constant
of the semiconductor (dielectric constant for free
space, κ = 1)
me* ~0.15 me and  ~15, ED ~10 meV.
Acceptors
-ve
ion
+e
• Again use example: silicon (Si)
– Substitute one Group III atom (e.g. Al or In)
– Si atoms have 4 electrons for covalent bonding
– When a Group III atom replaces a Si atom, it
cannot complete a tetravalent bond scheme
– A hole is formed.
– If the hole leaves the impurity, the core would be
negatively charged, so the hole created is then
attracted to the negative core, but can migrate
• We can say that this impurity atom accepted an
electron, so called Acceptors (“donate holes”)
• Called p-type semiconductors since they contribute
positive charge carriers
This crystal has been doped with a trivalent impurity.
The holes in p type silicon contribute to the current.
Note that the hole current direction is opposite to electron current
so the electrical current is in the same direction
Acceptor: Energy Levels
– Such impurities create “shallow” levels - levels
that are very close to the valence band
– Energy to “ionize” the atom is still small
– They are similar to “negative” hydrogen atoms
– Such impurities are called hydrogenic acceptors
Examples
Since holes are generally
heavier than electrons, the
acceptor levels are deeper
(larger) than donor levels
Why the range?
me* 1
EDonors ~ 13.6
eV
2
m0 
The valence band has a
complex structure and this
formula is too simplistic to
give accurate values for
acceptor energy levels
Acceptor energy levels
are bigger. Why?
–
–
–
–
–
Ge: 10 meV
Si: 45 – 160 meV
GaAs: 25 – 30 meV
ZnSe: 80 – 114 meV
GaN: 200 – 400 meV
Acceptor and donor
impurity levels are often
called ionization energies
or activation energies
Carrier Concentrations in
Extrinsic Semiconductors
• The carrier densities in extrinsic semiconductors can
be very high
• Depends on doping levels and ionization energy of
the dopants
• Often both types of impurities are present
– If the total concentration of donors (ND) is larger
than the total concentration of acceptors (NA)
have an n-type semiconductor
– In the opposite case have a p-type semiconductor
How can we measure whether
our material is more n or p type?
All solid-state electronic
and opto-electronic
devices are based on
doped semiconductors.
In many devices the doping and hence
the carrier concentrations vary.
In the following section we will consider the p-n junction
which is an important part of many semiconductor
devices and which illustrated a number of key effects
Bringing Two Semiconductors
Together
What
happens?
p-type semiconductor
n-type semiconductor
Electrons
EC
m
EC
m
EV
EV
Holes
Consider bringing into contact p-type and n-type semiconductors.
n-type semiconductor: Chemical potential, m below bottom of
conduction band
p-type semiconductor: Chemical potential, m above top of valence
band.
Electrons diffuse from n-type into p-type filling empty valence states.
Do they fill all of them?
Note: n and p sides are reversed in
this diagram compared to others..
Originally lots of
free carriers of
opposite types in
each material.
Then joined.
Each e- that departs
from the n side leaves
behind a positive ion.
Does this continue
until they cancel out?
The immediate
vincinity of the junction
is depleted of free
carriers.
Electrons enter the
P side and create neg.
ion.
Note: Absence of electrons and holes close to interface
-- This is called the depletion region.
Without applied voltage, an equilibrium is
reached in which a potential difference is
formed across the junction. This potential
difference is called built-in potential.
P-type is connected with positive terminal.
The positive potential applied to the p-type
material repels the holes, while the negative
potential applied to the n-type material repels
the electrons, pushing carriers toward the
junction and reducing the width of the
depletion zone.
With increasing voltage, the depletion zone
eventually becomes thin enough that the
zone's electric field cannot counteract charge
carrier motion across the p–n junction.
Applications of p-n junctions
• Excellent diodes, which can be used for
rectification (converter of AC to DC).
• Light emitting diodes (LEDs)
and lasers: In forward bias one
has an enhanced recombination
current. For direct band gap
semiconductors, light is emitted.
• Solar cells: If photons
with hn>Eg are absorbed
in the depletion region,
get enhanced generation
current. Photon energy
can be converted to
electrical power.
The MOS-FET
•In the MOS device, the gate electrode, gate oxide,
and silicon substrate from a capacitor.
•High capacitance is required to produce high
transistor current.
Cgate = K0A / d
K = dielectric constant, 0 = permittivity of vacuum
A = area of capacitor, d = dielectric oxide thickness
Making Computers Smaller
Cgate = K0A / d
K = dielectric constant, A = area of capacitor, d = oxide thickness
Area
Capacitance
Area
Speed
Capacitance
Thickness
Replacement Oxides
• High dielectric constant
• Low leakage current
• Works well with current Si technology
Many materials have been tried but none are as
cheap and easy to manipulate as existing SiO2.
How can we study potential
replacement materials?
Silicon (p doped)