chap2 solid state electronics
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Chapter 2
Solid-State Electronics
Microelectronic Circuit Design
Richard C. Jaeger
Travis N. Blalock
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Chapter Goals
Explore semiconductors and discover how engineers control
semiconductor properties to build electronic devices.
Characterize resistivity of insulators, semiconductors, and conductors.
Develop covalent bond and energy band models for semiconductors.
Understand bandgap 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.
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The Inventors of the Integrated Circuit
Jack KilbyAndy Grove, Robert Noyce, and
Gordon Moore with Intel 8080 layout.
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The Kilby Integrated Circuit
Semiconductor dieActive device
Electrical contacts
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Solid-State Electronic Materials
Electronic materials fall into three categories:
Insulators Resistivity > 105-cm
Semiconductors 10-3 < < 105 -cm
Conductors < 10-3-cm
Elemental semiconductors are formed from a single type ofatom, typically Silicon.
Compound semiconductors are formed from combinationsof column III and V elements or columns II and VI.
Germanium was used in many early devices. Silicon quickly replaced silicon due to its higher bandgap
energy, lower cost, and is easily oxidized to form silicondioxide insulating layers.
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Covalent Bond Model
Silicon diamondlattice unit cell. Corner of diamondlattice showing
four nearest
neighbor bonding.
View of crystallattice along a
crystallographic axis.
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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.
Increasing temperature adds energy to the
system and breaks bonds in the lattice,
generating electron-hole pairs.
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Intrinsic Carrier Concentration
The density of carriers in a semiconductor as a function of temperature
and material properties is:
EG = semiconductor bandgap energy in eV (electron volts)
k = Boltzmanns constant, 8.62 x 10-5 eV/K
T = absolute temperature, 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.
ni2 BT3 exp
EG
kT
cm
-6
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Intrinsic Carrier Concentration (cont.)
Electron density is n(electrons/cm3) and nifor intrinsic materialn = ni.
Intrinsic refers toproperties of purematerials.
ni 1010 cm-3 for Si
In
trinsiccarrierdensity(cm
-3)
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Electron and 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). Hole density is represented byp.
For intrinsic silicon, p = ni and n = ni.
The product of the electron and hole concentrations ispn = ni2.
The pn product above holds when a semiconductor is inthermal equilibrium (not with an external voltage or otherstimulation applied).
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Drift Current
Electrical resistivity and its reciprocal, conductivity, characterizecurrent flow in a material when an electric field is applied.
Charged particles move ordriftunder the influence of the appliedfield.
The resulting current is called drift current. 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 onthe context.
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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/Vs)
Hole mobility is less than electron since hole current is theresult of multiple covalent bond hops, while electrons can
move freely about the crystal.
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Velocity Saturation
At high fields, carriervelocity saturates andthis effect places upper
limits on the speed ofsolid-state devices.
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Example: Calculate the resistivity ofintrinsic 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
mobilities for intrinsic silicon were given following Eq. 2.4. Forintrinsic silicon, the electron and hole densities are both equal to ni.
Unknowns: Resistivityand classification.
Approach: Use Eqs. 2.7 and 2.8. [= q(n n +p p) (cm)-1]
Assumptions:Temperature is unspecified; assume room
temperature with ni = 1010/cm3.
Analysis:Next slide
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Example: Calculate the resistivity ofintrinsic silicon (cont.)
Analysis: Charge density of electrons is Qn = -qni and for holes is Qp =+qni. Substituting into Eq. 2.7:
= (1.60 x 10-10)[(1010)(1350) + (1010)(500)] (C)(cm-3)(cm2/Vs)
= 2.96 x 10-6(cm)-1 ---> = 1/= 3.38 x 105cm
From Table 2.1, intrinsic silicon is near the low end of the insulatorresistivity range
Check of Results: Resistivity has been found, and intrinsic silicon is apoor insulator.
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Semiconductor Doping
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.
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Donor Impurities in Silicon
A phosphorous (or other
column V element) atom
replaces a silicon atom in the
crystal lattice.
Since phosphorous has fiveouter shell electrons, there is
now an extra electron in the
structure.
Material is still charge neutral,
but very little energy is requiredto free the electron for
conduction since it is not
participating in a bond.
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Acceptor Impurities in Silicon
A boron (column III element)
atom can replace a silicon atom.
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.
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Acceptor Impurities in Silicon (cont.)
A Hole is propagating through the silicon.
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Doped Silicon Carrier Concentrations
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 = ni
2, even for doped
semiconductors in thermal equilibrium.
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n-type Material
Substituting p = ni2/n into q(ND + p - NA - n) = 0
yields n2 - (ND - NA)n - ni2 = 0.
Solving for n
For (ND - NA) >> 2ni, n (ND - NA) .
n (ND NA ) (ND NA )
2 4ni2
2and p
ni2
n
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p-type Material
Similar to the approach used with n-type material we find
the following equations:
We find the majority carrier concentration from charge
neutrality (Eq. 2.10) and find the minority carrier conc.
from the thermal equilibrium relationship (Eq. 2.2).
For (NA - ND) >> 2ni, p (NA - ND) .
p (NA ND ) (NA ND )2
4ni2
2and n ni
2
p
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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 n-type and p (NA - ND) for p-type material.
Typical doping ranges are 1014/cm3 to 1021/cm3.
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Mobility and Resistivity inDoped Semiconductors
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Diffusion Current
In practical semiconductors, it is quite useful to create
carrier concentration gradients by varying the doping
concentration and/or the doping 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.
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Diffusion Current (cont.)
Carriers move toward regions of
lower concentration, so diffusion
current densities are proportional
to the negative of the carrier
gradient.
Diffusion currents in the
presence of a concentration
gradient.
jpdiff (q)Dp
p
x
qDp
p
xA/cm2
jndiff
(q)Dn
p
x
qDnn
x A/cm2
Diffusion current density equations
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Diffusion Current (cont.)
Dp and Dn are the hole and electron diffusivitieswith units cm2/s. Diffusivity and mobility arerelated by Einsteinss relationship:
The thermal voltage, VT=kT/q, is approximately25 mV at room temperature. We will encounterVT throughout this book.
Dnn
kTq
Dpp
VT Thermal voltage
Dn nVT , Dp pVT
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Total Current in a Semiconductor
Total current is the sum of drift and diffusion current:
Rewriting using Einsteins relationship (Dp = nVT),
jnT qn nE qDn
n
x
jpT qppE qDp px
jnT
qn n E
VT
1
n
n
x
jpT qpp E VT
1
p
p
x
In the following chapters, we will
use these equations, combined with
Gauss law, (E)=Q, to calculate
currents in a variety of
semiconductor devices.
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Semiconductor Energy Band Model
Semiconductor energyband model. EC and EV
are energy levels at the
edge of the conduction
and valence bands.
Electron participating ina covalent bond is in a
lower energy state in the
valence band. This
diagram represents 0 K.
Thermal energy breakscovalent bonds and
moves the electrons up
into the conduction
band.
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Energy Band Model for a DopedSemiconductor
Semiconductor with donor or n-type
dopants. The donor atoms have extra
electrons with energy ED. Since ED is
close to EC, (about 0.045 eV forphosphorous), it is easy for electrons
in an n-type material to move up into
the conduction band.
Semiconductor with acceptor or p-
type 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.
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Energy Band Model forCompensated Semiconductor
A compensated semiconductor has
both n-type and p-type dopants. If ND
> NA, there are more ND donor levels.
The donor electrons fill the acceptorsites. The remaining ND-NA electrons
are available for promotion to the
conduction band.
The combination of the
covalent bond model andthe energy band models
are complementary and
help us visualize the hole
and electron conductionprocesses.
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Integrated Circuit Fabrication Overview
Top view of an integrated pn diode.
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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.
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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.
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End of Chapter 2