Yesterday’s Transistor (1947) Today’s Transistor (2006)

2
– conductivity between conductors and insulators
– Generally crystalline in structure
• In recent years, non-crystalline semiconductors have become commercially very important
Polycrystalline amorphous crystalline
Elements: Si, Ge, C
Binary: GaAs, InSb, SiC, CdSe, etc.
Ternary+: AlGaAs, InGaAs, etc.

Silicon Crystal Structure
• Unit cell of silicon crystal is cubic.
• Each Si atom has 4 nearest
neighbors.
5.43
Å
Silicon Wafers and Crystal Planes
(011) flat z
(100) x
(100) plane y z
(011) x y z
(111) x y
•
The standard notation for crystal planes is based on the cubic unit cell.
Si (111) plane
•
Silicon wafers are usually cut along the
(100) plane with a flat or notch to help orient the wafer during IC fabrication.

Bond Model of Electrons and Holes (Intrinsic Si)
Si Si Si
Si Si Si
•
Silicon crystal in a two-dimensional representation.
Si Si Si
Si Si Si
Si Si Si
Si Si Si
Si Si Si
Si Si Si
Si Si Si
•
When an electron breaks loose and becomes a conduction electron , a hole is also created.
Dopants in Silicon
Si Si Si
Si As Si
Si
Si
Si
B
Si
Si
Si Si Si Si Si Si
N-type Si P-type Si
•
As (Arsenic), a Group V element, introduces conduction electrons and creates
•
N-type silicon, and is called a donor.
B (Boron), a Group III element, introduces holes and creates P-type silicon , and is called an acceptor .
•
Donors and acceptors are known as dopants.

Hole
Electron
Mobile Charge Carriers they contribute to current flow with electric field is applied.
Ionized
Donor
Ionized
Acceptor
Immobile Charges they DO NOT contribute to current flow with electric field is applied.
However, they affect the local electric field
EE143 – Vivek Subramanian Slide 1-9

GaAs, III-V Compound Semiconductors, and Their Dopants
Ga
As
Ga As Ga
As Ga As
Ga As Ga
•
•
GaAs has the same crystal structure as Si.
GaAs, GaP, GaN are III-V compound semiconductors, important for
• optoelectronics.
Which group of elements are candidates for donors? acceptors?
From Atoms to Crystals p s conduction band
Pauli exclusion principle valence band isolated atoms lattice spacing
Decreasing atomic separation
•
•
•
•
Energy states of Si atom (a) expand into energy bands of Si crystal (b).
The lower bands are filled and higher bands are empty in a semiconductor.
The highest filled band is the valence band.
The lowest empty band is the conduction band .

Energy Band Diagram
Conduction band
E c
E g
Band gap
E v
Valence band
•
Energy band diagram shows the bottom edge of conduction band,
E c
•
E c
, and top edge of valence band, E v and E v are separated by the
.
band gap energy, E g
.
Measuring the Band Gap Energy by Light Absorption electron
E c photons photon energy: h v > E g
E g
E v hole
• E g can be determined from the minimum energy ( h photons that are absorbed by the semiconductor.
ν
) of
Bandgap energies of selected semiconductors
Material
E g
(eV)
PbTe Ge Si GaAs
0.31
0.67
1.12
1.42
GaP
2.25
Diamond
6.0

Semiconductors, Insulators, and Conductors
E c
Top of conduction band empty
E c
E g
= 9 eV
E g
= 1.1 eV
E v
E v filled
E c
Si (Semiconductor) SiO
2
(Insulator) Conductor
•
Totally filled bands and totally empty bands do not allow current flow. (Just as there is no motion of liquid in a
•
•
Metal conduction band is half-filled.
Semiconductors have lower doped.
E g
's than insulators and can be
Donor and Acceptor Levels in the Band Model
Conduction Band
Donor Level
E c
E d
Donor ionization energy
Acceptor Level
Acceptor ionization energy
E a
E v
Valence Band
Ionization energy of selected donors and acceptors in silicon
Dopant Sb
Ionization energy , E c
–E d or E a
–E v
(meV) 39
Donors
P
44
As
54
B
Acceptors
Al In
45 57 160
Hydrogen: E ion
= m
0 q 4
8
ε
0
2 h 2
= 13.6 eV

Donors n-type
Acceptors p-type
Dopants and Free Carriers
Dopant ionization energy ~50meV (very low).
General Effects of Doping on n and p
Charge neutrality:
N a
_
N d
+ n
+
N a
_
− p
−
N d
+
: number of ionized acceptors /cm3
: number of ionized donors /cm3
= 0
Assuming total ionization of acceptors and donors: n
+
N a
− p
N a
: number of acceptors /cm3
−
N d
= 0
N d
: number of donors /cm3

E c
E v
Density of States
E g c
ΔΕ
E c g(E)
E v g v g c
( E )
≡ number of states in
Δ
E
Δ
E
⋅ volume
⎛
⎝
⎜ eV
⋅
1 cm
3 ⎠
⎟
⎞ g c
( E )
≡ m n
* g v
( E )
≡ m * p
2 m
* n
π
(
E
2 h 3
−
E c
)
2 m * p
(
E v
π
2 h
3
−
E
)
Thermal Equilibrium

Thermal Equilibrium
An Analogy for Thermal Equilibrium
Sand particles
Dish
Vibrating Table
•
There is a certain probability for the electrons in the conduction band to occupy high-energy states under the agitation of thermal energy (vibrating atoms, etc.)
At E = E
F
, f ( E )=1/2

Effect of T on f(E)
T=0K
Question
• If f ( E ) is the probability of a state being occupied by an electron, what is the probability of a state being occupied by a hole?

N c is called the effective density of states
(of the conduction band) .
N v is called the effective density of states of the valence band.

Intrinsic Semiconductor
• Extremely pure semiconductor sample containing an insignificant amount of impurity atoms.
n = p = n i
E f lies in the middle of the band gap
Material
E g
(eV) n i
(1/cm 3 )
Ge
0.67
2 x 10 13
Si
1.12
1 x 10 10
GaAs
1.42
2 x 10 6