271
Electronic ECE Circuits I
Topic 2
Semiconductors Basics
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 1
Chapter Goals
Characterize resistivity of insulators, semiconductors, and conductors.
Develop covalent bond and energy band models for semiconductors.
Understand band gap energy and intrinsic carrier concentration.
Explore the behavior of electrons and holes in semiconductors.
Discuss acceptor and donor impurities in semiconductors.
Learn to control the electron and hole populations using impurity
doping.
Understand drift and diffusion currents in semiconductors.
Explore low-field mobility and velocity saturation.
Discuss the dependence of mobility on doping level.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 2
The Inventors of the Integrated Circuit
Jack Kilby
NJIT ECE-271 Dr. S. Levkov
Andy Grove, Robert Noyce, and
Gordon Moore with Intel 8080 layout.
Chap 2 - 3
Solid-State Electronic Materials
Electronic materials fall into three categories (WRT resistivity):
Insulators
> 105 -cm (diamond = 1016 )
Semiconductors 10-3 < < 105 -cm
Conductors
< 10-3 -cm (copper = 10-6 )
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 4
Solid-State Electronic Materials
Electronic materials fall into three categories (WRT resistivity):
Insulators
> 105 -cm (diamond = 1016 )
Semiconductors 10-3 < < 105 -cm
Conductors
< 10-3 -cm (copper = 10-6 )
Elemental semiconductors are formed from a single type of atom
of column IV, typically Silicon.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 5
Solid-State Electronic Materials
Electronic materials fall into three categories (WRT resistivity):
Insulators
> 105 -cm (diamond = 1016 )
Semiconductors 10-3 < < 105 -cm
Conductors
< 10-3 -cm (copper = 10-6 )
Elemental semiconductors are formed from a single type of atom
of column IV, typically Silicon.
Compound semiconductors are formed from combinations of
elements of column III and V or columns II and VI.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 6
Solid-State Electronic Materials
Electronic materials fall into three categories (WRT resistivity):
Insulators
> 105 -cm (diamond = 1016 )
Semiconductors 10-3 < < 105 -cm
Conductors
< 10-3 -cm (copper = 10-6 )
Elemental semiconductors are formed from a single type of atom
of column IV, typically Silicon.
Compound semiconductors are formed from combinations of
elements of column III and V or columns II and VI.
Germanium was used in many early devices.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 7
Solid-State Electronic Materials
Electronic materials fall into three categories (WRT resistivity):
Insulators
> 105 -cm (diamond = 1016 )
Semiconductors 10-3 < < 105 -cm
Conductors
< 10-3 -cm (copper = 10-6 )
Elemental semiconductors are formed from a single type of atom
of column IV, typically Silicon.
Compound semiconductors are formed from combinations of
elements of column III and V or columns II and VI.
Germanium was used in many early devices.
Silicon quickly replaced germanium due to its higher bandgap
energy, lower cost, and ability to be easily oxidized to form
silicon-dioxide insulating layers.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 8
Solid-State Electronic Materials (cont)
Bandgap is an energy range in a solid where no electron
states can exist, refers to the energy difference between the
top of the valence band and the bottom of the
conduction band in insulators and semiconductors
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 9
Semiconductor Materials (cont.)
Semiconductor
Bandgap
Energy EG (eV)
Carbon (diamond)
5.47
Silicon
1.12
Germanium
0.66
Tin
0.082
Gallium arsenide
1.42
Gallium nitride
3.49
Indium phosphide
1.35
Boron nitride
7.50
Silicon carbide
3.26
Cadmium selenide
1.70
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 10
Covalent Bond Model
Silicon has four electrons in the outer shell.
Single crystal material is formed by the covalent bonding of each
silicon atom with its four nearest neighbors.
Silicon diamond lattice unit
cell.
NJIT ECE-271 Dr. S. Levkov
Corner of diamond lattice
showing four nearest
neighbor bonding.
View of crystal
lattice along a crystallographic
axis.
Chap 2 - 11
Silicon Covalent Bond Model (cont.)
Silicon atom
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 12
Silicon Covalent Bond Model (cont.)
Silicon atom
NJIT ECE-271 Dr. S. Levkov
Silicon atom
Chap 2 - 13
Silicon Covalent Bond Model (cont.)
Silicon atom
NJIT ECE-271 Dr. S. Levkov
Covalent bonds in silicon
Chap 2 - 14
Silicon Covalent Bond Model (cont.)
What happens as the temperature increases?
Near absolute zero, all bonds are complete
Each Si atom contributes one electron to
each of the four bond pairs
The outer shell is full, no free electrons,
silicon crystal is an insulator
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 15
Silicon Covalent Bond Model (cont.)
Near absolute zero, all bonds are complete
Each Si atom contributes one electron to
each of the four bond pairs
The outer shell is full, no free electrons,
insulator
NJIT ECE-271 Dr. S. Levkov
Increasing temperature adds energy to the
system and breaks bonds in the lattice,
generating electron-hole pairs.
The pairs move within the matter forming
semiconductor
Some of the electrons can fall into the holes
recombination.
Chap 2 - 16
Intrinsic Carrier Concentration
The density of carriers in a semiconductor as a function of temperature
and material properties is:
E
2
3
n = T e p G
B x
i
k
T
6
cm
EG = semiconductor bandgap energy in eV (electron volts)
k = Boltzmanns constant, 8.62 x 10-5 eV/K
T = absolute termperature, K
B = material-dependent parameter, 1.08 x 1031 K-3 cm-6 for Si
Bandgap energy is the minimum energy needed to free an electron by
breaking a covalent bond in the semiconductor crystal.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 17
Intrinsic carrier density (cm-3)
Intrinsic Carrier Concentration (cont.)
NJIT ECE-271 Dr. S. Levkov
Electron density is n
(electrons/cm3) and for
intrinsic material n = ni.
Intrinsic refers to properties
of pure materials.
ni 1010 cm-3 for Si
The density of silicon atoms
is na 5x1022 cm-3
Thus at a room temperature
one bond per about 1013 is
broken
Chap 2 - 18
Electron-hole concentrations
A vacancy is left when a covalent bond is broken.
The vacancy is called a hole.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 19
Electron-hole concentrations
A vacancy is left when a covalent bond is broken.
The vacancy is called a hole.
A hole moves when the vacancy is filled by an electron from
a nearby broken bond (hole current).
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 20
Electron-hole concentrations
A vacancy is left when a covalent bond is broken.
The vacancy is called a hole.
A hole moves when the vacancy is filled by an electron from
a nearby broken bond (hole current).
The electron density is n (ni for intrinsic material)
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 21
Electron-hole concentrations
A vacancy is left when a covalent bond is broken.
The vacancy is called a hole.
A hole moves when the vacancy is filled by an electron from
a nearby broken bond (hole current).
The electron density is n (ni for intrinsic material)
Hole density is represented by p.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 22
Electron-hole concentrations
A vacancy is left when a covalent bond is broken.
The vacancy is called a hole.
A hole moves when the vacancy is filled by an electron from
a nearby broken bond (hole current).
The electron density is n (ni for intrinsic material)
Hole density is represented by p.
For intrinsic silicon, n = ni = p.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 23
Electron-hole concentrations
A vacancy is left when a covalent bond is broken.
The vacancy is called a hole.
A hole moves when the vacancy is filled by an electron from
a nearby broken bond (hole current).
The electron density is n (ni for intrinsic material)
Hole density is represented by p.
For intrinsic silicon, n = ni = p.
The product of electron and hole concentrations is pn = ni2.
The pn product above holds when a semiconductor is in
thermal equilibrium (not with an external voltage applied).
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 24
Drift Current
Charged particles move or drift under the influence of the applied field.
The resulting current is called drift current.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 25
Drift Current
Charged particles move or drift under the influence of the applied field.
The resulting current is called drift current.
Electrical resistivity and its reciprocal, conductivity , characterize current
flow in a material when an electric field is applied.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 26
Drift Current
Charged particles move or drift under the influence of the applied field.
The resulting current is called drift current.
Electrical resistivity and its reciprocal, conductivity , characterize current
flow in a material when an electric field is applied.
Drift current density is
j = Qv [(C/cm3)(cm/s) = A/cm2]
j = current density, (Coulomb charge moving through a unit area)
Q = charge density, (Charge in a unit volume)
v = velocity of charge in an electric field.
Note that density may mean area or volumetric density, depending on the context.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 27
Mobility
At low fields, carrier drift velocity v (cm/s) is proportional
to electric field E (V/cm). The constant of proportionality
is the mobility, :
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 28
Mobility
At low fields, carrier drift velocity v (cm/s) is proportional
to electric field E (V/cm). The constant of proportionality
is the mobility, :
vn = - nE and vp = - pE , where
vn and vp - electron and hole velocity (cm/s),
n and p - electron and hole mobility (cm2/V s)
n 1350 s), (cm2/V p 500 (cm2/V s),
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 29
Mobility
At low fields, carrier drift velocity v (cm/s) is proportional
to electric field E (V/cm). The constant of proportionality
is the mobility, :
vn = - nE and vp = - pE , where
vn and vp - electron and hole velocity (cm/s),
n and p - electron and hole mobility (cm2/V s)
n 1350 (cm2/V s), p 500 (cm2/V s),
Hole mobility is less than electron since hole current is the
result of multiple covalent bond disruptions, while
electrons can move freely about the crystal.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 30
Velocity Saturation
At high fields, carrier
velocity saturates and
places upper limits on
the speed of solid-state
devices.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 31
Intrinsic Silicon Resistivity
Given drift current and mobility, we can calculate
resistivity (Q is the charge density) :
jndrift = Qnvn = (-qn)(- nE) = qn nE A/cm2
jpdrift = Qpvp = (+qp)(+ pE) = qp pE A/cm2
jTdrift = jn + jp = q(n n + p p)E = E
This defines electrical conductivity:
= q(n n + p p) ( cm)-1
E
m
Resistivity is the reciprocal of conductivity: =V/c = c
m
=
j
Ac
/m
= 1/ ( cm)
di t
rf
T
NJIT ECE-271 Dr. S. Levkov
2
Chap 2 - 32
Example: Calculate the resistivity of
intrinsic silicon
Problem: Find the resistivity of intrinsic silicon at room temperature and
classify it as an insulator, semiconductor, or conductor.
Solution:
Known Information and Given Data: The room temperature motilities. For intrinsic
silicon, the electron and hole densities are both equal to ni.
Unknowns: Resistivity and classification.
Assumptions: assume room temperature with ni = 1010/cm3.
Analysis: Charge density of electrons is Qn = -qni and for holes is Qp = +qni. Thus:
= (1.60 x 10-10)[(1010)(1350) + (1010)(500)] (C)(cm-3)(cm2/V s)
= 2.96 x 10-6 ( cm)-1 ---> = 1/ = 3.38 x 105 cm
Recalling the classification in the beginning, intrinsic silicon is near the low end of the
insulator resistivity range
Conclusions: Resistivity has been found, and intrinsic silicon is a poor insulator.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 33
Semiconductor Doping
The interesting properties of semiconductors
emerges when impurities are introduced.
Doping is the process of adding very small well
controlled amounts of impurities into a
semiconductor.
Doping enables the control of the resistivity and
other properties over a wide range of values.
For silicon, impurities are from columns III and V
of the periodic table.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 34
Donor Impurities in Silicon
Phosphorous (or other column V
element) atom replaces silicon
atom in crystal lattice.
Since phosphorous has five outer
shell electrons, there is now an
extra electron in the structure.
Material is still charge neutral, but
very little energy is required to
free the electron for conduction
since it is not participating in a
bond.
NJIT ECE-271 Dr. S. Levkov
A silicon crystal doped by a pentavalent element (f. i.
phosphorus). Each dopant atom donates a free electron and is
thus called a donor. The doped semiconductor becomes n type.
Chap 2 - 35
Acceptor Impurities in Silicon
Boron (column III element) has
been added to silicon.
There is now an incomplete bond
pair, creating a vacancy for an
electron.
Little energy is required to move
a nearby electron into the
vacancy.
As the hole propagates, charge
is moved across the silicon.
NJIT ECE-271 Dr. S. Levkov
A silicon crystal doped with a trivalent impurity (f.i.
boron). Each dopant atom gives rise to a hole, and the
semiconductor becomes p type.
Chap 2 - 36
Acceptor Impurities in Silicon (cont.)
Hole is propagating through the silicon.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 37
Doped Silicon Carrier Concentrations
(how to calculate)
In doped material, the electron and hole concentrations are
no longer equal.
If n > p, the material is n-type.
If p > n, the material is p-type.
The carrier with the largest concentration is the majority
carrier, the smaller is the minority carrier.
ND = donor impurity concentration atoms/cm3
NA = acceptor impurity concentration atoms/cm3
Charge neutrality requires q(ND + p - NA - n) = 0
It can also be shown that pn = ni2, even for doped
semiconductors in thermal equilibrium.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 38
n-type Material
Substituting p = ni2/n into q(ND + p - NA - n) = 0
yields n2 - (ND - NA)n - ni2 = 0.
Solving for n
2
2
( D A ( D A 2+ n
N N)
N N) 4 i
n
n
=
a dp i
n=
2
n
For (ND - NA) >> 2ni, n (ND - NA) .
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 39
p-type Material
Similar to the approach used with n-type material we find
the following equations:
2
2
( A D ( A D 2+ n
N N)
N N) 4 i
n
p
=
a dn i
n=
2
p
We find the majority carrier concentration from charge
neutrality and find the minority carrier conc. from the
thermal equilibrium relationship.
For (NA - ND) >> 2ni, p (NA - ND) .
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 40
Practical Doping Levels
Majority carrier concentrations are established at
manufacturing time and are independent of
temperature (over practical temp. ranges).
However, minority carrier concentrations are
proportional to ni2, a highly temperature dependent
term.
For practical doping levels, n (ND - NA) for ntype and p (NA - ND) for p-type material.
Typical doping ranges are 1014/cm3 to 1021/cm3.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 41
Mobility and Resistivity in
Doped Semiconductors
Impurities degrade mobility
(different size disrupt the lattice,
atoms ionized electrons
scatter ) see on the left.
However, doping vastly
increases the density of majority
carriers dramatically
decreases resistivity despite the
lower mobility.
= qn (ND NA) for n-type
= qp (NA ND) for p-type
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 42
Diffusion Current
In practical semiconductors, it is quite useful to create
carrier concentration gradients by varying the dopant
concentration and/or the dopant type across a region of
semiconductor.
This gives rise to a diffusion current resulting from the
natural tendency of carriers to move from high
concentration regions to low concentration regions.
Diffusion current is analogous to a gas moving across a
room to evenly distribute itself across the volume.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 43
Diffusion Current (cont.)
A bar of silicon (a) into which holes are injected, thus creating
the hole concentration profile along the x axis, shown in (b).
The holes diffuse in the positive direction of x and give rise to a
hole-diffusion current in the same direction. Note that we are
not showing the circuit to which the silicon bar is connected.
NJIT ECE-271 Dr. S. Levkov
If the electron-concentration profile shown is
established in a bar of silicon, electrons diffuse in
the x direction, giving rise to an electron-diffusion
current in the negative -x direction.
Diffusion current density equations
Chap 2 - 44
Diffusion Current (cont.)
Carriers move toward regions of
lower concentration, so diffusion
current densities are proportional
to the negative of the carrier
gradient.
j
diff
p
diff
jn
p
p
= (+ q ) D p = qD p
A/cm 2
x
x
n
n
= (q ) Dn = + qDn
A/cm 2
Diffusion currents in the
x
x
presence of a concentration
Diffusion current density equations
NJIT ECE-271 Dr. S. Levkov
gradient.
Chap 2 - 45
Diffusion Current (cont.)
Dp and Dn are the hole and electron diffusivities
with units cm2/s. Diffusivity and mobility are
related by Einsteinss relationship:
D
n
n
=
k
TD
p
=
=V =T e a v lta e
h rm l o g
T
q p
D = V , D =pV
n
nT
p
T
The thermal voltage, VT = kT/q, is approximately
25 mV at room temperature. We will encounter
VT throughout this book.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 46
Total Current in a Semiconductor
Total current is the sum of drift and diffusion current:
n
T
jn = qnnE+ qDn
x
p
jT = qp pE qDp
p
x
Rewriting using Einsteins relationship (D p = nVT),
1 n
= qnnE +VT
n x
1 p
T
j p = qp pE +VT
p x
T
jn
NJIT ECE-271 Dr. S. Levkov
In the following chapters, we will
use these equations, combined with
Gauss law, (E)=Q, to
calculate currents in a variety of
semiconductor devices.
Chap 2 - 47
Semiconductor Energy Band Model
Semiconductor energy
band model. EC and EV
are energy levels at the
edge of the conduction
and valence bands.
NJIT ECE-271 Dr. S. Levkov
Electron participating in
a covalent bond is in a
lower energy state in the
valence band. This
diagram represents 0 K.
Thermal energy breaks
covalent bonds and
moves the electrons up
into the conduction
band.
Chap 2 - 48
Energy Band Model for a Doped
Semiconductor
Semiconductor with donor or n-type
dopants. The donor atoms have free
electrons with energy ED. Since ED is
close to EC, (about 0.045 eV for
phosphorous), it is easy for electrons
in an n-type material to move up into
the conduction band.
NJIT ECE-271 Dr. S. Levkov
Semiconductor with acceptor or ptype dopants. The donor atoms have
unfilled covalent bonds with energy
state EA. Since EA is close to EV,
(about 0.044 eV for boron), it is easy
for electrons in the valence band to
move up into the acceptor sites and
complete covalent bond pairs.
Chap 2 - 49
Integrated Circuit Fabrication Overview
Top view of an integrated pn diode.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 50
Integrated Circuit Fabrication (cont.)
(a) First mask exposure, (b) post-exposure and development of photoresist, (c) after
SiO2 etch, and (d) after implantation/diffusion of acceptor dopant.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 51
Integrated Circuit Fabrication (cont.)
(e) Exposure of contact opening mask, (f) after resist development and etching of contact
openings, (g) exposure of metal mask, and (h) After etching of aluminum and resist removal.
NJIT ECE-271 Dr. S. Levkov
Chap 2 - 52