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Characteristics of Semiconductor Materials
Chapter 2 : Semiconductor Manufacturing Technology by M. Quirk and J. Serda
Chapter 3.1 and 3.2 : Semiconductor Science by Tudor E. Jenkins
Saroj Kumar Patra,
Department of Electronics and Telecommunication,
Norwegian University of Science and Technology ( NTNU )
TFE4180 Semiconductor Manufacturing Technology, Characteristics of Semiconductor Materials
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Electron Shells in Atoms
Q=2
P = 10
O = 32
N = 32
M = 18
L=8
K=2
Figure 2.2 Quirk & Serda
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Elementary Model of Carbon Atom
Proton
(positive charge)
-
Electron
(negative charge)
Atomic number
(number of protons)
Nucleus (center of atom;
contains protons and neutrons)
C 6
Orbital shell
-
Neutron
(neutral charge)
+ N
+
N +N +
N N
+
N
+
-
-
Valence electron
Valence shell
(outer shell of atom)
Carbon atom: The nucleus contains
an equal number of protons (+) and
neutrons (6 each). Six electrons (-)
orbit around the nucleus.
Figure 2.1 Quirk & Serda
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Group IV A Elemental
semiconductors
Semiconductors
Group IVA
C, Carbon
6
Si, Silicon
14
Ge, Germanium
32
Sn, Tin
50
Pb, Lead
82
Figure 2.18 Quirk & Serda
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Covalent Bonding of Pure Silicon
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Silicon atoms share valence electrons
to form insulator-like bonds.
Figure 2.19 Quirk & Serda
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Crystal Structure of Si and GaAs
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Crystal Structure
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Classifying Materials
• Conductors
• Insulators
• Semiconductors
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Energy Bandgaps
Electron Energy
Electron Energy
Electron Energy
Conduction
Band
Valence Band
Overlapping bands
- little energy is
needed for
conduction
Energy Gap
Energy Gap
Conduction
Band
Conduction
Band
Valence Band
Valence Band
Insulator
Conductor
Semiconductor
Figure 2.4 Quirk & Serda
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Energy Band Diagram for III-V
Semiconductor
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Covalent Bonding in Pure Silicon
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Silicon atoms share valence electrons
to form insulator-like bonds.
Figure 2.19 Quirk & Serda
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Doping of Silicon
Deposition Step
Drive-in & Diffusion Step
dopant dispenser
wafer substrate
Activation
Step
dopant layer
diffusion of dopant
atoms through silicon
wafer
Si
Si
PP
PP
Si
Si
Si
Si
P
Figure 2.21 Quirk & Serda
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Silicon Dopants
Acceptor Impurities
Semiconductor
Donor Impurities
Group III (p-type)
Group IV
Group V (n-type)
Boron
5
Carbon
6
Nitrogen
7
Aluminum
13
Silicon
14
Phosphorus
15
Gallium
31
Germanium
32
Arsenic
33
Indium
49
Tin
50
Antimony
51
* Items underlined are the most commonly used in silicon-based IC manufacturing.
Figure 2.22 Quirk & Serda
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Electrons in n-type Silicon with
Phosphorus Dopants
Si
Si
Si
Si
Si
Si
Si
Si
P
Si
Si
P
Si
Si
Si
Si
Si
Si
P
Si
Si
Si
Si
Si
Si
Excess electron (-)
Phosphorus atom
serves as n-type
dopant
Donor atoms provide excess electrons
to form n-type silicon.
Figure 2.23 Quirk & Serda
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Conduction in n-type Silicon
Positive terminal from
power supply
Negative terminal
from power supply
Free electrons flow toward
positive terminal.
Figure 2.24 Quirk & Serda
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Holes in p-type Silicon with Boron
Dopant
Si
Si
Si
Si
Si
Si
Si
Si
B
Si
+ Hole
Si
B
Si
Si
Si
Boron atom serves
as p-type dopant
Si
Si
Si
B
Si
Si
Si
Si
Si
Si
Acceptor atoms provide a deficiency
of electrons to form p-type silicon.
Figure 2.25 Quirk & Serda
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Conduction in p-type Silicon
Positive terminal
from voltage supply
Negative terminal
from voltage supply
-Electrons flow toward
positive terminal
+Holes flow toward
negative terminal
Figure 2.26 Quirk & Serda
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Impurity States
n-type
p-type
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Density of Impurity States
(for amorphous semiconductor)
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Density of Electrons and Hole in a
Semiconductor
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How Size affects Resistance
Low Resistance
R=
High Resistance
L
A
Figure 2.12 Quirk & Serda
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Electrical Conductivity and
Mobility
•
•
The simplest picture of electrical conductivity and mobility can be understood by
considering the electrons in a semiconductor as a classical gas in the body of the
material.
Then using the Maxwell-Boltzmann distribution function we can get the relation,
•
At a temperature of 300 K and using free electron mass for ‘m’, we have
•
•
The random nature of electron velocities means that the time average current that flows
is zero.
On application of an electric field to the semiconductor, the electrons will drift in the
opposite direction of the field, so that there is now a net flow of charge and hence a flow
of current. Therefore the equation of motion using drift velocity vd can be written as:
τ
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Electrical Conductivity and
Mobility(continued)
•
•
τ
The second term in the equation is introduced to prevent ever increasing electron
velocity with the electric field on. Therefore electrons are accelerated until a time τ and
then suffer scattering within the system and their velocity randomized.
In the absence of Electric field the equation becomes:
τ
•
The solution can be written as:
τ
•
•
The relaxation time represents the tendency of scattering in the semiconductor to return
the electron distribution to thermal equilibrium.
Therefore in the steady state the ‘d/dt’ term will not be there.
τ
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Electrical Conductivity and
Mobility(continued)
•
The current density ‘J’ is therefore given as:
τ
•
Where ‘n’ is the number of electrons per unit volume of the semiconductor. This is
Ohm’s Law
τ
σ
Or
•
τ
σ
Electrical Conductivity
The mobility is expressed as :
μ
| |
| |
τ
Mobility
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1021
Dopant Concentration (atoms/cm3)
Silicon
Resistivity vs.
Dopant
Concentration
1020
1019
1018
1017
n-type
1016
p-type
1015
1014
1013
10-3
10-2
10-1
100
101
102
103
Electrical Resistivity (ohm-cm)
Redrawn from VLSI Fabrication Principles, Silicon and Gallium Arsenide, John Wiley & Sons, Inc.
Figure 2.27 Quirk & Serda
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Cross-section of planar pn-junction
p-type Si
n-type Si
Figure 2.28 Quirk & Serda
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Flow of Free Electrons in Copper
One electron in
the valence ring
Copper atom
-
-
- -
-
-
- -
-
Cu 29
- -
-
- -
-
-
K
-
L
- M -
-
-
Figure 2.11 Quirk & Serda
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Maximum # Actual #
Shell # e- per shell e- per shell
2
2
K
8
8
L
18
18
M
32
1
N
60
29
Total #
-
N
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Alternative Semiconductor
Materials
Comparison of Some Physical Properties for Semiconductor Materials
Property
Si
Ge
GaAs
SiO2
Melting point
1700
1412
937
1238
(C)
(approx.)
Atomic Weight
28.09
72.60
144.63
60.08
Atomic Density
4.99 x1022
4.42x1022
2.21x1022
2.3x1022
3
(atoms/cm )
Energy Band
8
1.11
0.67
1.40
Gap (eV)
(approx.)
Table 2.3 Quirk & Serda
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Resistivity vs. Impurity
Concentration for Si and GaAs
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Electronic Properties of some
Semiconductors
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Physical Constants
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TFE4180 Semiconductor Manufacturing Technology, Characteristics of Semiconductor Materials