OUTLINE

1
Lecture 3

• OUTLINE
• Band gap energy
• Density of states
• Doping
• Read Chapter 2 (Section 2.3)

2
Band Gap and Material Classification

E
c

E
9 eV
G

E
c

E
1.12 eV
G
E

E
E
v
v
c
metal
SiO2
Si

• Filled bands and empty bands do not allow current
  flow
• Insulators have large EG
• Semiconductors have small EG
• Metals have no band gap
• conduction band is partially filled

3
Measuring Band Gap Energy

EG
can be determined from the minimum energy (hn)
of photons
that are absorbed by the semiconductor.
Band gap energies of selected
semiconductors
4
Density of States
E

gc(E)
DE
E
E
c
c
E
E
v
v
gv(E)
g(E)dE number of states per cm3 in the energy
range between E and EdE Near the band edges
E ? Ec
E ? Ev
5
Doping
By substituting a Si atom with a special impurity
atom (Column V or Column III element), a
conduction electron or hole is created.
6
Doping Silicon with Donors
Example Add arsenic (As) atom to the Si crystal
The loosely bound 5th valence electron of the As
atom breaks free and becomes a mobile electron
for current conduction.
7
Doping Silicon with Acceptors
Example Add boron (B) atom to the Si crystal
The B atom accepts an electron from a neighboring
Si atom, resulting in a missing bonding electron,
or hole. The hole is free to roam around the
Si lattice, carrying current as a positive charge.
8
Donor / Acceptor Levels (Band Model)
E
c
ED
Donor Level
Donor ionization energy
Acceptor ionization energy
Acceptor Level
E
A
E
v
Ionization energy of selected donors and
acceptors in silicon
9
Charge-Carrier Concentrations
ND ionized donor concentration (cm-3) NA
ionized acceptor concentration (cm-3) Charge
neutrality condition ND p NA n At thermal
equilibrium, np ni2 (Law of Mass Action)
Note Carrier concentrations depend on net dopant
concentration (ND - NA) !
10
N-type Material
ND gtgt NA (ND NA gtgt ni)
11
P-type Material
NA gtgt ND (NA ND gtgt ni)
12
Terminology
donor impurity atom that increases n acceptor
impurity atom that increases p n-type material
contains more electrons than holes p-type
material contains more holes than
electrons majority carrier the most abundant
carrier minority carrier the least abundant
carrier intrinsic semiconductor n p
ni extrinsic semiconductor doped semiconductor
13
Summary

• The band gap energy is the energy required to
  free an electron from a covalent bond.
• EG for Si at 300K 1.12eV
• Insulators have large EG semiconductors have
  small EG
• Dopants in Si
• Reside on lattice sites (substituting for Si)
• Group-V elements contribute conduction electrons,
  and are called donors
• Group-III elements contribute holes, and are
  called acceptors
• Very low ionization energies (lt50 meV)
• ? ionized at room temperature

Dopant concentrations typically range from 1014
cm-3 to 1020 cm-3