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1 . Lecture #2
OUTLINE
• Energy-band model
• Doping
Read: Chapter 2
Definition of Terms
n = number of electrons/cm3
p = number of holes/cm3
ni = intrinsic carrier concentration
In a pure semiconductor,
n = p = ni
Spring 2003 EE130 Lecture 2, Slide 2
1
2 . Si: From Atom to Crystal
Energy states in Si atom Æ energy bands in Si crystal
• The highest nearly-filled band is the valence band
• The lowest nearly-empty band is the conduction band
Spring 2003 EE130 Lecture 2, Slide 3
Energy Band Diagram
Ec
electron energy
Ev
distance
Simplified version of energy band model, indicating
• bottom edge of the conduction band (Ec)
• top edge of the valence band (Ev)
¾ Ec and Ev are separated by the band gap energy EG
Spring 2003 EE130 Lecture 2, Slide 4
2
3 . Band Gap and Material Classification
Ec
EG= ~9 eV
Ec
EG = 1.12 eV
Ev Ev Ec
Si SiO2 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 2003 EE130 Lecture 2, Slide 5
Measuring Band Gap Energy
• EG can be determined from the minimum energy (hν) 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 Ge Si GaAs
Band gap (eV) 0.67 1.12 1.42
Spring 2003 EE130 Lecture 2, Slide 6
3
4 . Density of States
E
gc(E)
∆Ε
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 ) = E ≥ Ec
π 2h 3
m*p 2m*p (Ev − E )
gv ( E ) = E ≤ Ev
π 2h 3
Spring 2003 EE130 Lecture 2, Slide 7
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 Acceptors: B, Al, Ga, In
Spring 2003 EE130 Lecture 2, Slide 8
4
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 2003 EE130 Lecture 2, Slide 9
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 2003 EE130 Lecture 2, Slide 10
5
6 . Donor / Acceptor Levels (Band Model)
Ec
Donor Level ED
Donor ionization energy
Acceptor ionization energy
Acceptor Level
EA
Ev
Ionization energy of selected donors and acceptors in silicon
Donors Acceptors
Dopant Sb P As B Al In
Ionization energy, E c -E d or E a -E v (meV) 39 45 54 45 67 160
Spring 2003 EE130 Lecture 2, Slide 11
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 2003 EE130 Lecture 2, Slide 12
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7 . N-type Material
ND >> NA
(ND – NA >> ni):
Spring 2003 EE130 Lecture 2, Slide 13
P-type Material
NA >> ND
(NA – ND >> ni):
Spring 2003 EE130 Lecture 2, Slide 14
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8 . 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 2003 EE130 Lecture 2, Slide 15
Summary: Band Model
– Splitting of allowed atomic energy levels
occurs in a crystal
• Separation between energy levels is small, so
we can consider them as bands of continuous
energy levels
– Highest nearly-filled band is the valence band
– Lowest nearly-empty band is the conduction band
Spring 2003 EE130 Lecture 2, Slide 16
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9 . – Energy-band diagram:
• Shows only bottom edge of conduction band Ec
and top edge of valence band Ev
• Ec and Ev are separated by the band-gap
energy EG
• Dopants introduce localized energy levels
within the band gap:
– donor level: slightly below Ec
– acceptor level: slightly above Ev
Spring 2003 EE130 Lecture 2, Slide 17
Summary: Doping
• 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 2003 EE130 Lecture 2, Slide 18
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