Transcript Lecture 4 - The University of Texas at Dallas

Matthiessen’s Rule
 = T + I
 = effective resistivity, T = resistivity due to scattering by thermal
vibrations only, I = resistivity due to scattering of electrons from
impurities only.
 = T +  R
 = overall resistivity, T = resistivity due to scattering from thermal
vibrations, R = residual resistivity
Residual resistivity shows very little temperature dependence, while T = AT.
Therefore, effective resistivity is given by:
 = AT + B
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Definition of Temperature Coefficient of Resistivity
The fractional change in the resistivity per unit temperature increase at the
reference temperature To
1   
o   
 o  T  T To
o = TCR (temperature coefficient of resistivity),  = change in the
resistivity ( =  - o), o = resistivity at reference temperature To , T
= small increase in temperature (T = T – To), To = reference temperature
Temperature Dependence of Resistivity
 [1 + o(TTo)]
 = resistivity, o = resistivity at reference temperature, 0 = TCR
(temperature coefficient of resistivity), T = new temperature, T0 =
reference temperature
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Temp. Dependence of Resistivity
• When the resistivity follows the linear behavior
previously mentioned:
 = AT + B
• Then, in
1   
o 
 o  T  T T
o
• The o is constant over a temperature range
To to T and leads to:
 [1 + o(TTo)]
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Actually dominated by the
residual resistivity; thus,
relatively insensitive to temp
Fig 2.7
Magnetic materials (e.g., iron and
nickel) do not follow the expected
dependence
-Besides lattice vibrations, these
materials are also affected by the
magnetic interactions between
ions in the lattice
Expected linear dependence
The resistivity of various metals as a function of temperature above 0 °C. Tin melts at
505 K whereas nickel and iron go through a magnetic to non-magnetic (Curie)
transformations at about 627 K and 1043 K respectively. The theoretical behavior
( ~ T) is shown for reference.
[Data selectively extracted from various sources including sections in Metals Handbook,
10th Edition, Volumes 2 and 3 (ASM, Metals Park, Ohio, 1991)]
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
• Resistivity v. temperature
behavior of pure metals can
be empirically represented as:
Fig 2.8
• Obviously, the overly simple
linear prediction does not
represent resistivity at low
temperatures
• Lattice vibrations reduce
rapidly as temp reduces;
therefore less scattering and
simple model no longer works
The resistivity of copper from lowest to highest temperatures (near melting temperature,
1358 K) on a log-log plot. Above about 100 K,   T, whereas at low temperatures,
 T 5 and at the lowest temperatures  approaches the residual resistivity R. The inset
shows the  vs. T behavior below 100 K on a linear plot (R is too small on this scale).
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Power law fit:
-Notice near unity for pure metals
-Closer to 2 for the magnetic
Fig 2.8
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Solid Solutions and Nordheim’s Rule
• Isomorphous alloy of two metal (a binary
alloy that forms a solid solution) is expected
to follow:
 = T + I
– Along with temp-independent I increasing with
the concentration of solute atoms
• This means that as the alloy concentration
increases, the resistivity increases and
becomes less temperature dependent as I
overwhelms T
• This can be an advantage of alloying metals
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
• This table shows how alloying metals can affect the
resistivity
• “Buried” in this table is that when you alloy 80% nickel with
20% chromium, the resistivity of nickel increases almost 16
times!!
• This alloy is known as Nichrome, and it is used as a heater
wire in household appliances and industrial furnaces
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
(a) Phase diagram of the Cu-Ni alloy system. Above
the liquidus line only the liquid phase exists. In the
L + S region, the liquid (L) and solid (S) phases
coexist whereas below the solidus line, only the
solid phase (a solid solution) exists.
(b) The resistivity of the Cu-Ni alloy as a Function
of Ni content (at.%) at room temperature
• Both metals are FCC with Cu being only
~3% larger, so the alloy will remain FCC
• When Ni is added to Cu, the I in the
Matthiessen expression will increase
• Obviously, as the alloy becomes more Nirich (i.e., becoming pure Ni), resistivity
reduces as it should for pure metals
Fig 2.11
The Cu-Ni alloy system. SOURCE: Data extracted from Metals Handbook, 10th ed., 2 and 3
Metals Park, Ohio: ASM, 1991, and M. Hansen and K. Anderko, Constitution of Binary
Alloys, New York: McGraw-Hill, 1958.
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Nordheim’s Rule for Solid Solutions
An important semi-empirical equation that can be used to
predict the resistivity of an alloy is Nordheim’s Rule:
I = CX(1 X)
I = “impurity” resistivity due to scattering of electrons from
impurities
C = Nordheim coefficient: represents the effectiveness of the solute
atom in increasing the resistivity; assumes a dilute alloy mixture
X = atomic fraction of solute atoms in a solid solution
The Nordheim Rule Eqn. relates impurity resistivity to the
atomic fraction X of the solute atoms in a solid solution
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
• C depends on the type of solute and the solvent
• A solute atom that is drastically different in size to solvent atom will produce a larger
I, and therefore, lead to a larger C
• An important assumption in Nordheim’s rule is that alloying does not significantly vary
the number of conduction electrons/atom in the alloy
• This is true for alloys with the same valency (i.e., same column on the Periodic Table)
• However, it is not true for alloys with different valencies
• To correct for this, C must change to provide an effective Nordheim coefficient Ceff
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Combined Matthiessen and Nordheim Rules
 = matrix + CX(1 X)
Nordheim “component”
 = resistivity of the alloy (solid solution)
matrix = resistivity of the matrix due to scattering from thermal
vibrations and other defects in the absence of alloying
C = Nordheim coefficient
X = atomic fraction of solute atoms in a solid solution
C assumes a dilute alloy mixture
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Fig 2.12
Electrical resistivity vs. composition at room
temperature in Cu-Au alloys. The quenched
sample (dashed curve) is obtained by
quenching the liquid, and the Cu and Au
atoms are randomly mixed. The resistivity
obeys the Nordheim rule. When the quenched
sample is annealed or the liquid is slowly
cooled (solid curve), certain compositions
(Cu3Au and CuAu) result in an ordered
crystalline structure in which the Cu and Au
atoms are positioned in an ordered fashion in
the crystal and the scattering effect is reduced.
• In solid solutions, at some concentrations of certain binary alloys, the
annealed solid has an orderly structure where the two elements are not
randomly mixed, but occupy regular, ordered sites
• These can actually be viewed as a pure compound – like Cu3Au and CuAu
• Their resistivities will be less than the same composition random alloy due
to being quenched from the melt
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Resistivity of Mixtures and Porous Materials
Consider a material with two distinct phases  and b, as described below:
The effective resistivity of a material with a layered structure.
(a) Along a direction perpendicular to the layers.
(b) Along a direction parallel to the plane of the layers.
(c) Materials with a dispersed phase in a continuous matrix.
Fig 2.13
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Effective Resistance of Mixtures
Example: Effective resistivity for current flow in the x direction
L  Lb b
Reff 

A
A
Reff = effective resistance
L = total length (thickness) of the -phase layers
 = resistivity of the -phase layers
A = cross-sectional area
Lb = total length (thickness) of the b-phase layers
b = resistivity of the b-phase layers
c = volume fractions of the phases
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Resistivity-Mixture Rule
eff = c cbb
eff = effective resistivity of mixture, c= volume fraction of the phase,  = resistivity of the -phase, cb = volume fraction of the bphase, b= resistivity of the b-phase
Conductivity-Mixture Rule
eff = c cbb
eff = effective conductivity of mixture, c= volume fraction of the
-phase,  = conductivity of the -phase, cb = volume fraction of
the b-phase, b= conductivity of the b-phase
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Non-ideal Case
• Those two rules pertain to two special
cases
• However, in general, a random mixture of
the two phases usually exists
• Therefore, we would not expect either
equation to apply rigorously
• If resistivity of one phase is very different
than the other, there are two semiempirical rules that are quite useful
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Mixture Rule (d > 10c )
eff
1
(1  cd )
2
 c
(1 c d )
Dispersed phase is
much more resistive
with respect to the
continuous phase
eff = effective resistivity, c = resistivity of continuous phase, cd =
volume fraction of dispersed phase, d = resistivity of dispersed phase
Mixture Rule (d < 0.1c )
eff
(1  c d )
 c
(1  2 c d )
Dispersed phase is
much less resistive
with respect to the
continuous phase
eff = effective resistivity, c = resistivity of the continuous phase, cd
= volume fraction of the dispersed phase, d = resistivity of the
dispersed phase
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Two-Phase Alloy Resistivity and Electrical Contacts
Eutectic-forming alloys, e.g., Cu-Ag.
(a) The phase diagram for a binary,
eutectic-forming alloy.
(b) The resistivity versus composition
for the binary alloy.
Fig 2.15
• For most compositions, alloys form a
two-phase heterogenous mixture of
phases  and b as shown in the figure
• Between 0 and X1,  increases with the
concentration by virtue of Nordheim’s
rule
• At X1, the solid solubility limit of one
metal into another is reached. Now,
two phases are present, so  is given
by the resistivity-mixture rule
• As with the 0 to X1 region, at the other
metal end, between X2 and 100%, the
resistivity becomes Nordheim’s rule
again because only one phase exists
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Hall Effect
Fig 2.16
• “Electron as a particle” allows to
us to readily explain the Hall effect
• Magnetic field is in a perpendicular
direction to the applied field that is
driving the current
• The result is a transverse field in
the sample that is perpendicular to
the direction of both the applied
field, Ex, and the magnetic field, Bz
• The Hall voltage can be obtained
• Applied electric field drives a
current Jx where the electrons
move in the –x direction with drift
velocity vdx.
Illustration of the Hall effect.
The z direction is out of the plane of the paper. The externally applied magnetic field is
along the z direction.
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Hall Effect (cont.)
• Due to the magnetic field, there is
a force, known as the Lorentz
force, acting on each electron
given by
• The direction of this Lorentz force
is in the –y direction and governed
by the vector product
Fig 2.16
• Since Lorentz force is in the –y
direction, electrons are forced
downward
• As a result, negative charge builds
up near the bottom and positive at
the top due to exposed metal ions
https://www.youtube.com/watch?v=Ip43wws6FEw
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
F = qv  B
F = force, q = charge, v = velocity of charged particle, B = magnetic
field
Fig 2.17
A moving charge experiences a Lorentz force in a magnetic field.
(a) A positive charge moving in the x direction experiences a force downwards.
(b) A negative charge moving in the -x direction also experiences a force downwards.
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Lorentz Force
• Accumulation of electrons near the bottom results in an internal electric field, EH, in
the –y direction. This is called the Hall field and give rise to the Hall voltage, VH
between the top and bottom of the sample
• Electron accumulation continues until the increase in EH is sufficient to stop further
accumulation
• When this happens, the magnetic force that pushes the electrons down just
balances the force eEH, that prevents further accumulation, so at steady state:
• However:
• Therefore, we can substitute for vdx to obtain:
Hall Coefficient
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Definition of Hall Coefficient
RH 
Ey
J x Bz
• Measures the resulting Hall field, along y, per unit
transverse applied current and magnetic field
• The larger the RH, the greater the field
• Therefore, RH is a gauge of the magnitude of the
Hall effect
RH = Hall coefficient, Ey = electric field in the y-direction, Jx = current
density in the x-direction, Bz = magnetic field in the z-direction
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Thermal Conduction
• Metals: Heat
transport/conduction
is accomplished by
the electron gas
• Nonmetals:
conduction is due to
lattice vibrations
Fig 2.19
Thermal conduction in a metal involves transferring energy
from the hot region to the cold region by conduction
electrons. More energetic electrons (shown with longer
velocity vectors) from the hotter regions arrive at cooler
regions and collide there with lattice vibrations and transfer
their energy. Lengths of arrowed lines on atoms represent the
magnitudes of atomic vibrations.
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Thermal Conductivity
Thermal Conductivity: measures the ease with which heat transports through a medium
Rate of heat flow:
Fig 2.20
Heat flow in a metal rod heated at one end.
Consider the rate of heat flow, dQ/dt, across a thin section δx of the rod. The
rate of heat flow is proportional to the temperature gradient δT/δx and the crosssectional area A.
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Fourier’s Law of Thermal Conduction
dQ
dT
Q¢ =
= - kA
dt
dx
, aka thermal conductivity, is material
dependent; negative sign denotes that
heat flow direction is that of decreasing T
Q = rate of heat flow, Q = heat, t = time,  = thermal conductivity, A
= area through which heat flows, dT/dx = temperature gradient
Ohm’s Law of Electrical Conduction
dV
I = - As
dx
Electric Field
I = electric current, A = cross-sectional area,  = electrical
conductivity, dV/dx = potential gradient (represents an electric field),
V = change in voltage across x, x = thickness of a thin layer at x
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
“Driving Forces”
dQ
dT
Q¢ =
= - kA
dt
dx
dV
I = - As
dx
• The driving force for heat flow is the
temperature gradient
• The driving force for electric current is the
potential gradient, i.e., electric field
• In metals, electrons engage in charge and
heat transport, which are described by 
and , respectively
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Wiedemann-Franz-Lorenz Law
Charge and heat transport described by  and , are related through this expression
k
-8
-2
= CWFL = 2.45´10 W W K
sT
 = thermal conductivity
 = electrical conductivity
T = temperature in Kelvins
CWFL = Lorenz number
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
• Experiments on a wide variety of
metals – includes pure metals and
alloys
• WFL Law is reasonable obeyed
from around room temp and above
Fig 2.21
Thermal conductivity  versus electrical
conductivity  for various metals (elements
and alloys) at 20 ˚C.
The solid line represents the WFL law with
CWFL ≈ 2.44  108 W  K-2.
• Since electrical conductivity of pure
metals is inversely proportional to
the temperature, we can
immediately conclude that thermal
conductivity must be relatively
temperature independent at room
temp and above
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Thermal Conductivity v. Temperature:
Fig 2.22
Thermal conductivity versus temperature for two pure metals
(Cu and Al) and two Alloys (brass and Al-14% Mg).
SOURCE: Data extracted form I.S. Touloukian, et al.,
Thermophysical Properties of Matter, vol. 1: “Thermal
Conductivity, Metallic Elements and Alloys, “ New York:
Plenum, 1970.
• Respective  for Cu and Al become
temperature independent above
~100 K
• Heat conduction depends
primarily on the rate at which the
electrons transfers energy from
one atomic vibration to another
as it collides with them
• The mean speed, u, of the
electron determines the rate o
energy transfer
• u increases only fractionally with
temperature in this range
• Moreover, this fractional
increase is easily enough to
carry the energy from one
collision to another, thereby
exciting more energetic lattice
vibrations in colder regions
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
More on Thermal Conductivity
The stronger the coupling, the greater will be the thermal conductivity
• Nonmetals do not have any free conduction electrons;
therefore, the energy transfer involves lattice vibrations
• Recall: the “ball and spring” model
• Kinetic molecular theory dictates that all atoms will be
vibrating and the average vibrational kinetic energy
would be proportional to the temp
• The springs couple the vibrations to neighboring atoms
thereby allowing large amplitude vibrations to
propagate as a vibrational wave to cooler regions of
the crystal
• The efficiency of heat transfer is not solely a function of
the efficiency of interatomic bonding (coupling between
atoms), but also on how the vibrational waves
propagate in the crystal which is determined by:
• Scattering by crystal imperfections, and
• Interactions with other vibrational waves
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Vibrational Wave
If left-end atom vibrates violently (due to heat), then vibrational
waves propogate down the ball-spring-ball chain
Fig 2.23
Conduction of heat in insulators involves the generation and propagation of atomic
Vibrations through the bonds that couple the atoms (an intuitive figure).
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
• Thermal conductivity, in
general, depends on
temperature
• Different types of
materials exhibit
different  values and
also different  versus
T behavior
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Thermal Resistance
T
T
T
Q  A
 A

x
L L / A
Conduction of heat through a component in (a) can be modeled as a thermal resistance
 shown in (b) where Q = T/ 
From Principles of Electronic Materials and Devices,
Fig 2.24
Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Fourier’s Law
DT
DT
Q¢ = A k
=
L
(L / kA)
Q = rate of heat flow or the heat current, A = cross-sectional area,  =
thermal conductivity (material-dependent constant), T = temperature
difference between ends of component, L = length of component
Ohm’s Law
V
V
I

R
( L / A)
I = electric current, V = voltage difference across the conductor, R =
resistance, L = length,  = conductivity, A = cross-sectional area
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Definition of Thermal Resistance
Q¢ =
DT
q
Q = rate of heat flow, T = temperature
difference,  = thermal resistance
Thermal Resistance
L
q=
Ak
DT
DT
Q¢ = A k
=
L
(L / kA)
 = thermal resistance, L = length, A = cross-sectional area,
 = thermal conductivity
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Electrical Conductivity in Nonmetals
• It is possible to empirically classify various
materials into conductors, semiconductors, and
insulators
• Obviously, nonmetals are not necessarily perfect
insulators with zero conductivity
• Also, there is no well-defined, sharp boundary
between insulators and semiconductors
• Typically, current conduction is due to drift of
mobile charge carriers through a solid by the
application of an electric field
• Each of the drifting species of charge carriers
contributes to the observed current
– Drifting species of charge carriers contribute to the
observed current
– Metals only have free electrons
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Range of conductivites exhibited by various materials
From Principles of Electronic Materials and Devices,
Fig 2.25
Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
(a) Thermal vibrations of the atoms rupture a bond and release a free electron into the
crystal. A hole is left in the broken bond which has an effective positive charge.
(b) An electron in a neighboring bond can jump and repair this bond and thereby create a
hole in its original site; the hole has been displaced.
(c) When a field is applied both holes and electrons contribute to electrical conduction.
From Principles of Electronic Materials and Devices,
Fig 2.26
Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Covalent Bonds in Silicon Crystal
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
41
Free Electrons in N-type Silicon
Si
Si
Si
Si
Si
Si
Si
Si
P
Si
Si
Si
P
Si
Si
Si
Si
Si
Si
Si
P
Si
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.
42
Holes in P-type Silicon
Si
Si
Si
Si
Si
Si
Si
B
Si
Si
Si
Si
B
Si
Si
Si
Si
Si
Si
Si
B
Si
Si
Si
Si
Si
Si
Si
Hole (+)
Boron atom serves as
P-type dopant
Acceptor atoms provide a deficiency of electrons to form
P-type silicon.
43
Flow of Electrons in Copper Wire
Positive
terminal from
voltage supply
Negative
terminal from
voltage supply
eeeeValence electron freed from copper atom
44
Flow of Free Electrons in N-type Silicon
Positive terminal
from voltage supply
Negative
terminal from
voltage supply
eeeeFree electrons flow toward positive
charge
45
Flow of +Holes in P-type Silicon
Positive terminal
from voltage supply
Negative
terminal from
voltage supply
eee+Holes flow toward
negative terminal
-Electrons are supplied by
the voltage source
46
Importance of Diffusion
• Introduce impurities
• Control majority carrier type
• Control resistivity of Si
Ion implantation
Si substrate
Diffusion to drive
impurity in to Si
IC Technology -Dr. W. Hu
Impurity Diffusion
• Diffusion Mechanisms
• Substitutional
• Interstitial
IC Technology -Dr. W. Hu
Substitutional Diffusion
•
Figure 3.6 The kick-out (left) and Frank–Turnbull mechanisms (right).
Fabrication Engineering at the
Micro and Nanoscale, 4/e
Stephen A. Campbell
Copyright © 2014 by Oxford University Press
Impurity Exchange
•
Figure 3.3 Diffusion of an impurity atom by direct exchange (A) and by vacancy
exchange (B). The latter is much more likely owing to the lower energy required.
Fabrication Engineering at the
Micro and Nanoscale, 4/e
Stephen A. Campbell
Copyright © 2014 by Oxford University Press
Interstitial Diffusion
•
Figure 3.5 In interstitialcy diffusion, an interstitial silicon atom displaces a
substitutional impurity, driving it to an interstitial site, here it diffuses some
distance before it returns to a substitutional site.
Fabrication Engineering at the
Micro and Nanoscale, 4/e
Stephen A. Campbell
Copyright © 2014 by Oxford University Press
Ion Implant Basic Concepts
Ion implantation is doping of a substrate by a flux of energetic ions. Ions
accelerated to high energy “slam” into substrate and embed dopants
Advantages
Disadvantages
Precise control of dose, depth,
profile and area uniformity
Excellent reproducibility
Wide choice of masks
Low temperature processs
Small lateral spread of dopants
Vacuum cleanliness
Expensive & complicated
equipment
Lack of junction passivation
Typical Ion-Implantation Parameters
•
•
•
•
•
•
•
Species: P, As, Sb, B, In, O
Dose: 1011 cm-2 - 1016 cm-2
Energy: 5 KeV - 400 KeV
Depth of Implant: 500 Å - 1 µm
Reproducibility & Uniformity: ±1%
Temperature: room temp
Flux: 1012 - 1014 ions cm-2 s-1
IC Technology -Dr. W. Hu
Ion Implantation Overview
• Wafer is Target in High Energy Accelerator
• Impurities “Shot” into Wafer
– Introduces ionized projectile atoms (or molecules) with enough
energy to penetrate beyond the surface regions
– Ions loose energy by scattering and ultimately come to rest
within the target substrate
• Expensive Systems
• Vacuum System
http://exploration.vanderbilt.edu/news/features/vo2shutter/news_shutter2.htm
Why Ion Implantation (II)?
• Precise dose control
– Ion implant  1%
– Other methods  5-10%
• Precise depth control by modulation of implant
energy
• Unique profile capability (e.g., peak is inside rather
than at the surface
• Low temperature – maximizes processing options
• High purity
• Can introduce dopant above the equilibrium solid
solubility
http://www.hzdr.de/db/Pic?pOid=28718
http://www.thin-film.de/en/technology/pbii-plasma-based-ion-implantation.html
Implant Damage
• Implant region becomes amorphous and
defective (i.e., crystallographic defects)
Conductivity of a Semiconductor
• n and p are concentrations of electrons and holes in a semiconductor crystal
• Electrons and holes have drift mobilities, so overall conductivity of the crystal can
be given by:
 = ene + eph
 = conductivity, e = electronic charge, n = electron concentration,
e = electron drift mobility, p = hole concentration, h = hole drift mobility
Drift Velocity and Net Force
ve =
me
e
Fnet
ve = drift velocity of the electrons, e = drift mobility of the electrons,
e = electronic charge, Fnet = net force
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Intrinsic Carrier Concentration
• Figure 3.4 Intrinsic carrier concentration of silicon, GaAs, and
GaN as a function of temperature
Fabrication Engineering at the
Micro and Nanoscale, 4/e
Stephen A. Campbell
Copyright © 2014 by Oxford University Press
Resistivity vs. Doping
    1  q nn   p p
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n  type :   q n ND  NA 
1


p  type :   q p NA  ND 
IC Technology -Dr. W. Hu
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