Lecture #3
OUTLINE
• Band gap energy
• Density of states
• Doping
Read: Chapter 2 (Section 2.3)
Band Gap and Material Classification
Ec
Ec
EG = 1.12 eV
Si
EG= ~9 eV
Ev
Ev
SiO2
Ec
metal
• 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
Spring 2007
EE130 Lecture 3, Slide 2
Measuring Band Gap Energy
EG can be determined from the minimum energy (hn) of photons
that are absorbed by the semiconductor.
electron
Ec
photon
photon energy: h v  E G
Ev
hole
Band gap energies of selected semiconductors
Semiconductor
Band gap (eV)
Spring 2007
Ge
0.67
Si GaAs
1.12 1.42
EE130 Lecture 3, Slide 3
Density of States
E
gc(E)
DE
Ec
Ec
Ev
Ev
gv(E)
g(E)dE = number of states per cm3 in the energy range between E and E+dE
Near the band edges:
mn* 2mn* E  Ec )
gc ( E ) 
 2h 3
gv ( E ) 
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m*p 2m*p Ev  E )
 2h 3
E  Ec
E  Ev
EE130 Lecture 3, Slide 4
Doping
By substituting a Si atom with a special impurity atom (Column V
or Column III element), a conduction electron or hole is created.
Donors: P, As, Sb
Spring 2007
Acceptors: B, Al, Ga, In
EE130 Lecture 3, Slide 5
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.
Spring 2007
EE130 Lecture 3, Slide 6
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.
Spring 2007
EE130 Lecture 3, Slide 7
Donor / Acceptor Levels (Band Model)
ED
Donor Level
Ec
Donor ionization energy
Acceptor ionization energy
Acceptor Level
EA
Ev
Ionization energy of selected donors and acceptors in silicon
Donors
Acceptors
Dopant
Ionization energy, E c -E d or E a -E v (meV)
Spring 2007
Sb
39
P
45
EE130 Lecture 3, Slide 8
As
54
B
45
Al
67
In
160
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) !
Spring 2007
EE130 Lecture 3, Slide 9
N-type Material
ND >> NA
(ND – NA >> ni):
Spring 2007
EE130 Lecture 3, Slide 10
P-type Material
NA >> ND
(NA – ND >> ni):
Spring 2007
EE130 Lecture 3, Slide 11
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
Spring 2007
EE130 Lecture 3, Slide 12
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 (<50 meV)
 ionized at room temperature
Dopant concentrations typically range from 1014 cm-3 to 1020 cm-3
Spring 2007
EE130 Lecture 3, Slide 13