Transcript Conduction and Semiconductors

MSE-630 Week 3
Semiconductor Operation
IC Fabrication
Quantum Mechanics: Particle in a box
Junctions and
Semiconductors
Theories and practical devices
View of an Integrated Circuit
• Scanning electron micrographs of an IC:
Al
Si
(doped)
(d)
(d)
(a)
45 mm
0.5 mm
• A dot map showing location of Si (a semiconductor):
-- Si shows up as light regions.
(b)
• A dot map showing location of Al (a conductor):
-- Al shows up as light regions.
(c)
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Metallic and Semiconductor
Junctions
Each conductor has a unique quantity of energy that is required to
free an electron. This energy is called the work function energy,
qF. Values for qF for various metals are given in the table below:
In figure A, two dissimilar metals are not
in contact. When they come into
contact as shown in B, their respective
Fermi energies must equilibrate
throughout. To do this, electrons
transfer from B to the lower unfilled
levels of A until the level of the electron
“sea” in both metals is equal. This
causes A to become negatively
charged, and B to become positively
charged. The resulting potential is
called the contact potential (qVC)
The Contact Potential, qVC, is equal to the
difference in the respective work functions:
qVC = EF(B)-EF(A), or qVC=qF(A)-qF(B)
Although a potential exists, no work can be extracted, because
when we attach leads, (i.e., metal C) the sum of the work
functions is zero:
qFnet = q(FC-FA)+(FA-FB)+FB-FC)] = 0
If we join an “n” type
region, which has excess
negative charges, with a
“p” type region, i.e. a “p-n”
junction” a charged region
develops a the interface:
Electrons and holes recombine at
the interface, depleting the
available electrons in the n
material making it more positive,
and holes in the p material,
making it more negative. This
creates a built-in electric field that
discourages further transfer across
the interface.
Metallic and Semiconductor
Junctions
Each conductor has a unique quantity of energy that is required to
free an electron. This energy is called the work function energy,
qF. Values for qF for various metals are given in the table below:
In figure A, two dissimilar metals are not
in contact. When they come into
contact as shown in B, their respective
Fermi energies must equilibrate
throughout. To do this, electrons
transfer from B to the lower unfilled
levels of A until the level of the electron
“sea” in both metals is equal. This
causes A to become negatively
charged, and B to become positively
charged. The resulting potential is
called the contact potential (qVC)
The Contact Potential, qVC, is equal to the
difference in the respective work functions:
qVC = EF(B)-EF(A), or qVC=qF(A)-qF(B)
Although a potential exists, no work can be extracted, because
when we attach leads, (i.e., metal C) the sum of the work
functions is zero:
qFnet = q(FC-FA)+(FA-FB)+FB-FC)] = 0
Electron band diagrams are a way to visualize what happens at a p-n junction, using
the following rules:
1. The Fermi level must be at the same level on both sides of the junction when there
is no applied field
2. Far from the junctions, the materials inherent electrical structure exists
3. He bands are bent, or curved, where the built-in electric fields exist at the junction
4. A potential energy step, qVc, due to contact potential Vc, develops at the junction. It
is equal in magnitude to EF(n)-EF(p) or, equivalently qF(p)-qF(n)
5. Externally applied electric potentials displace the relative positions of EF and the
band edges by amounts over and above those produced by the above rules.
If we apply a “reverse bias”, as depicted in A above and in figure B
on the left, the barrier at the junction increases to q(Vo+V), thus
increasing the barrier to current flow. If we apply a forward bias, as
in B above and C, left, we annihilate EHPs and have a positive
current flow
If we join an “n” type
region, which has excess
negative charges, with a
“p” type region, i.e. a “p-n”
junction” a charged region
develops a the interface:
Electrons and holes recombine at
the interface, depleting the
available electrons in the n
material making it more positive,
and holes in the p material,
making it more negative. This
creates a built-in electric field that
discourages further transfer across
the interface.
p-n Rectifying Junction
• Allows flow of electrons in one direction only (e.g., useful
to convert alternating current to direct current).
• Processing: diffuse P into one side of a B-doped crystal.
+ p-type
+ +
+ +
-- No applied potential:
no net current flow.
-- Forward bias: carriers
flow through p-type and
n-type regions; holes and
electrons recombine at
p-n junction; current flows.
-- Reverse bias: carriers
flow away from p-n junction;
junction region depleted of
carriers; little current flow.
n-type
-
-
-
-
p-type
+
-
+ - n-type
+
++- - + -
+ p-type
+ +
+ +
n-type
-
-
-
-
+
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Properties of Rectifying Junction
Forward biasing causes current to flow; reverse
biasing causes it to stop flowing in a p-n junction.
This can be represented in the junction equation:
j = jR[exp (eV/kT)-1]
V is positive for forward biasing, and negative for
reverse biasing.
jR is the reverse biased current
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Tunnel Diodes
Tunnel diodes act as oscillators.
Current increases up to Vp,
decreases between Vp and Vc, then
increases beyond Vc
As shown at left, the Fermi level
exists in the conduction zone of the
n-type material and the valence
zone of the p-type material. When a
biasing voltage is applied, the
electrons jump, or “tunnel” across
the forbidden gap at the junction.
When Vp<V<Vc, the gap widens
and tunneling becomes small.
Then, when V>Vc, tunneling can
begin again.
Zener diodes
Zener diodes are used to
regulate voltages in circuits.
When the voltage becomes
sufficiently large (10-1000V,
depending on doping level), it
reaches a “limiting” or “break
down” voltage, and current is
shunted to ground.
Transistors: triodes, npn and pnp
junctions
Junction Transistor
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MOSFET Transistor
Integrated Circuit Device
• MOSFET (metal oxide semiconductor field effect transistor)
• Integrated circuits - state of the art ca. 50 nm line
width
– ~ 1,000,000,000 components on chip
– chips formed one layer at a time
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Current flow in a transistor vary with
emitter voltage, Ve:
I = Ioexp(Ve/B)
Where Io and B are constants
MOS-FET
Numerous transistors, resistors
and electronic elements can be
incorporated on a single wafer
of semiconductor material,
thus creating the integrated
circuit
Thermocouples and other thermoelectric devices
If opposite ends of a metal bar
are maintained at different
temperatures, electrons will flow
from the hot end to the cold end.
As electrons pile up at the cold
end, it creates a net
electromotive force, or Seebeck
voltage, opposing further
charge transfer.
Seebeck voltage varies
sensitively with temperature,
and are 1000-fold larger in
semiconductors than in metals.
Using semiconductors used to
measure changes in voltage are
called thermistors, and can very
accurately measure temperature
Other devices that measure
temperature or have
thermoelectric properties include
thermocouples, Peltier effect and
thermoelectric refrigerators.
When metals with different work
functions are joined, they generate a
voltage that varies with temperature.
Thermocouples accurately measure
temperature by measuring this
voltage difference.
When current flows through a junction,
heat may be generated or absorbed,
depending on current polarity. This
enables the design of electric
refrigerators
IC Processing
Semiconductors are built in
layers.
Each layer involves several
steps:
1. Placing a film of light
sensitive emulsion on the Si
substrate
2. Covering the areas to be
protected
3. Exposing to light
4. Removing exposed emulsion
5. Etching away exposed
substrate
6. Removing mask
7. Depositing dopants
8. Diffusing dopants into
substrate
Outline the steps needed to make a
NPN transistor
Initial Steps: Forming an active region
Photoresist
is chemically
removed in
acid, or
stripped in
an O2
plasma
Si3N4 is etched away using an F-plasma:
Si3dN4 + 12F → 3SiF4 + 2N2
Or removed in hot phosphoric acid
After stripping
photoresist,
field oxide is
grown. Field
oxide provides
insulation
between
adjacent
junctions
N and P wells are formed
Photoresist mask is applied, and active ions implanted by ion
bombardment. Typically, 150-200 keV accelerating energy
After implantation, ions
are diffused into
substrate to form wells
After well formation, additional N and P layers are formed in respective N and P
wells, then a layer of polysilicon is deposited. Polysilicon is electrically
conductive and used for gate voltage connections.
Insulating layers of SiO2 are grown around the gate, followed by N or P
bombardment for form the NMOS or PMOS source and drain regions.
After forming gate, source and drain
regions, Ti film is deposited by
sputtering to act as electrical
interconnect
Ti is reacted with N2 to form TiSi2 where it contacts silicon (black
regions) or TiN elsewhere. Then, it is coated with photoresist and
etched, followed by deposit of another insulating SiO2 layer.
Another coat of photoresist followed by
etching exposes gates for connections
A barrier region of TiN is applied, followed
by thin-film application of W, which
undergoes CMP to provide a flat surface
with exposed contacts
Finally, aluminum is sputtered on wafer,
masked and plasma etched. Additional
interconnect layers may be added the
same way.
Quantum Mechanics: Particle
in a box
Wave-Particle Duality
Photons
In trying to explain black body radiation and thermoelectric effect, Max Planck and Albert Einstein developed theories
that when put together led to the following principles.
1. Light is made up of particles called photons.
2. The energy of a photon is dependent only upon its frequency.
E = hn = hc/l
Where h is Planck’s constant (h = 6.626 x 10-34 J-s).
What this means is that if an object is giving off (or absorbing) light it is actually emitting (absorbing) photons. The
energy of each photon is dependent only upon its frequency (or wavelength or color).
In 1925, Louis DeBroglie hypothesized that if light, which everyone thought for so long was a wave, is a particle, then
perhaps particles like the electron, proton, and neutron might have wave-like behaviors.
In the same way that waves are described by their wavelength, particles can be described by their momentum, p
p = mv
where m is the mass of the particle and v is its velocity.
We can relate the velocity of a wave-particle with its wavelength by equating Planck’s relationship for the energy of a
photon with Einstein’s Law of Relativity:
E = hn = hc/l
E = mc2
If we equate these two equations we get a relationship between momentum (a particle property) and wavelength (a
wave property)
hc/l = mc2 = pc
p = h/l
Or by substituting mv for momentum we can wavelength of any object to its velocity and mass.
l= h/mv
Element spectral lines were empirically
described using the integer values of ‘n’
The only problem with
these models is that they
do not account for line
splitting
Bohr Model of the Atom
1. Electrons are in stable circular orbits
about the nucleus and do not decay
2. Electrons move to higher orbit by gaining
energy (absorbing a photon of energy
hn), or drop to a lower orbit, emitting a
photon
3. Electron angular momentum, pq is an
integer multiple of n, or pq = nh/2p
• What was correct about Bohr’s Model:
– Electrons reside in quantized energy levels.
– The Bohr model accurately and quantitatively
predicts the energy levels of one electron
atoms.
• What was incorrect about Bohr’s Model:
– Electrons don’t orbit the nucleus in well
defined circular orbits.
– Fails to accurately predict the energy levels in
multielectron atoms.
Heisenberg Uncertainty Principle
Uncertainty Principle → It is not possible to
precisely determine the momentum (hence the
energy) and the position of a particle
simultaneously. This is quantified in the
mathematical expression:
Dx Dp = h/4p
Dx m Dv = h/4p
where Dx represents the uncertainty in the position
of the particle and Dp represents the uncertainty
in the momentum of the particle (p = mv).
Results of Uncertainty Principle
We cannot say where a particle (electron) is,
only the probability of finding it at that
particular place
Quantum mechanics defines the functional
relationships we can use to solve for
properties such as position, momentum
and energy, using a wave function, y
The Schrödinger Equation, Wave Functions and
Hamiltonians
In one dimension, we can describe the energy of a particle
in terms of its wave function as:
p2
h d 2y ( x, t )
h dy ( x, t )
V = E 
 V ( x)y ( x, t ) = 
2
2
2m
4pi
dx
2pi
dt
Writing y(x,t) as two separate variables, y(x)f(t), we get
independent equations in terms of position and time:
d 2y 4pm
 2  2 E  V ( x) y ( x) = 0
dx
h
and
d 2f 4pi
 2 Ef (t ) = 0
2
dx
h
The Hydrogen Atom
We can solve the wave
function for the
Hydrogen atom by using
spherical coordinates
(r,q,f) and solving the
independent wave
equations using
separation of variables:
Y(r,q,f) = yrQqFf
This leads to three of the four
quantum numbers: n,l,m and
s