1. Read: Chapter 2 (Section 2.3)
Lecture #3
OUTLINE
Band gap energy
Density of states
Doping
Read: Chapter 2 (Section 2.3)

2. Band Gap and Material Classification=
~9 eV E G c E =
1.12 eV G E E E v v c 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
EE130 Lecture 3, Slide 2

3. Measuring Band Gap EnergyEG
can be determined from the minimum energy (hn) of photons
that are absorbed by the semiconductor.
photon
photon energy: h v
> E G E c
electron
hole
Band gap energies of selected semiconductors
EE130 Lecture 3, Slide 3

4. Density of States gc(E) gv(E)
g(E)dE = number of states per cm3 in the energy range between E and E+dE
Near the band edges:
E  Ec
E  Ev
EE130 Lecture 3, Slide 4

5. Doping Donors: P, As, Sb Acceptors: B, Al, Ga, In
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
EE130 Lecture 3, Slide 5

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.
EE130 Lecture 3, Slide 6

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.
EE130 Lecture 3, Slide 7

8. Donor / Acceptor Levels (Band Model)ED
Donor Level
Donor ionization energy
Acceptor ionization energy
Acceptor Level E A E v
Ionization energy of selected donors and acceptors in silicon
EE130 Lecture 3, Slide 8

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) !
EE130 Lecture 3, Slide 9

10. N-type Material ND >> NA (ND – NA >> ni):
EE130 Lecture 3, Slide 10

11. P-type Material NA >> ND (NA – ND >> ni):
EE130 Lecture 3, Slide 11

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
EE130 Lecture 3, Slide 12

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 (<50 meV)
 ionized at room temperature
Dopant concentrations typically range from 1014 cm-3 to 1020 cm-3
EE130 Lecture 3, Slide 13