Basic Physics of Semiconductors (1)

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Basic Physics of Semiconductors (1)
Section 2.1

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Eat your broccoli before having desert. Need to
know your device physics before getting started
with circuit design.
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Today
Next time
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Atom is the smallest particle of an element.
Nucleus consists of positively charged particles
called protons and uncharged particles called
neutrons. The negative charged particles are
called electrons.
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Electrons orbit the nucleus of an atom at certain
distance from the nucleus. Electrons near the
nucleus have less energy than those in more
distant orbits
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Valence Electrons

• Valence electrons electrons in the outermost
  shell.
• Electrons that are in orbits farther from the
  nucleus have higher energy and are less tightly
  bound to the atom than those close to the
  nucleus.
• Electrons with the highest energy exist in the
  outermost shell of an atom and are relatively
  loosely bound to the atom.

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Silicon Atom
Silicon is the most popular material in
microelectronics. It has four valence electrons.
(Nice tutorial on making silicon wafer,
http//www.youtube.com/watch?vaWVywhzuHnQ)
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Sharing of Electrons in Silicon
A silicon atom with its four valence electrons
shares an electron with each of its four
neighbors. This effectively creates eight shares
valence electrons for each atom and produces a
state of chemical stability. The sharing of
valence electrons produce the covalent bonds that
hold the atoms together each valence electron
is attracted equally by the two adjacent atoms
which share it.
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• As electrical engineers, we are primarily
  interested
• in how we can get the electrons to move. We need
• to introduce a couple of concepts
• Holes
• Free electrons
• Bandgap
• Electron density

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An electron leave behind a void because the bond
is now incomplete. A void is called a hole. A
hole can absorb an free electron if one becomes
available.
At T0K
Electrons gain thermal energy and break away from
the bonds. They begin to act as free charge
carriersfree electron.
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Movement of electrons and holes
One electron has traveled from right to left. One
hole has traveled from left to right.
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Bandgap Energy
QDoes any thermal energy create free electrons
(and holes) in silicon? A No. A minimum
energycalled the bandgap energy is required
to dislodge an electron from a covalent bond.
For silicon, the bandgap energy is 1.12 eV.
Note eV represents the energy necessary to
move one electron across A potential difference
of 1V. 1 eV 1.6 x 10-19 J Insulators display a
higher Eg . (e.g. 2.5 eV for diamond) Semiconduct
ors usually have a moderate Eg between 1 eV and
1.5 eV.
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Electron Density
Q How many free electrons are created at a given
temperature?
electron density
where k1.38 x 10-23 J/K is called the
Boltzmann constant. As expected, materials
having a larger bandgap (Eg)exhibit a smaller
ni . Also, as T pproaches zero, ni approaches
zero.
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Making sense of electron density
Determine the electron density in silicon at
T300K. Use the electron density formula with
Eg1.12 eV, ni _at_ 300 T is 1.08 x 1010
Electrons per cm3. Silicon has 5 x 1022 atoms
per cm3. What this means is that there is only
one electron for 5 x 1012 atoms at room
temperature.
How do we increase the electron density?
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Intrinsic Semiconductor
The pure silicon has few electrons in comparison
to the numbers of atoms. Therefore, it is
somewhat resistive. In an intrinsic
semiconductors, the electron density(n or ni) is
equal to the hole density (p). (each electron
is created by leaving behind a hole.) So npni2
holes
electron
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Can we use something other than silicon?
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Phosphorus has 5 valence electrons. The 5th
electron is unattached. This electron is free
to move and serves as a charge carrier.
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Doping
The controlled addition of an impurity such as
phosphorus to an intrinsic (pure) semiconductor
is called doping. And phosphorus itself is a
dopant. Providing many more free electrons
than in the intrinsic state, the doped silicon
crystal is now called extrinsic, more
specifically, an n-type semiconductor to
emphasize the abundance of free electrons.
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Hole density in an n-type semiconductor
Many of the new electrons donated by the dopant
recombine with the holes that were created in
the intrinsic material. As a consequence, in an
n-type semiconductor. The hole density will drop
below its intrinsic level.
npni2
In an n-type semiconductor, Electrons are the
majority carriers. Holes are the minority
carriers. If a voltage is applied across an
n-type materials, the current consisting
predominantly of electrons is produced!
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if we dope silicon with an atom that provides an
insufficient number of electrons, then we may
obtain many incomplete covalent bonds. A boron
has only 3 valence electrons and can form only 3
covalent bonds. Therefore, it contains a hole
and is ready to absorb a free electron.
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Summary
In n-type material,
In p-type material,
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Applications 1Hot-Point Probe Test
Hot probesoldering iron Cold probeprobe at room
temperature. The electrons around the hot probe
have higher thermal velocity, therefore on
average move toward the cold side at a higher
rate than the electrons on the cold side move to
the hot side. The imbalance causes the
electrons to accumulate on the cold side and
build up a negative voltage, which can be
detected by a voltmeter.
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Application 2 Thermoelectric Generator
Early satelite use decay of radioactive material
as the heat source. It is also possible to use
waste energy from automobile as the heat
source. The same concept is also used for energy
harvesting from a wrist watch. (22 uW of power)
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A material can conduct current in response to a
potential difference. The field accelerates the
charge carriers in the material, forcing some to
flow from one end to the other. Movement of
charge carriers due to an electric field is
called drift.
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Mobility
We expect the carrier velocity to be proportional
to the electric field strength (E).
Mobility 1350 cm2/(VS) for electrons
480 cm2/(VS) for holes.
since electrons move in a direction opposite to
the electric field, we must express the velocity
vector as
For electrons
For holes
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Example 2.5
A uniform piece of n-type of silicon that is 1
um long senses a voltage of 1 V. Determine the
velocity of the electrons.
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of charges passing x1 in 1 s
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Divide the current by Wh gives you the current
density
 
 
 
In the presence of both electrons and holes
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if the electric field approaches sufficiently
high levels, the velocity no longer follows the
electric field linearly. This is because the
carriers collide with the lattice so frequently
and the time between the collisions is so short
that they cannot accelerate much.
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Building a Resistor on Silicon
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Building a Resistor on Doped Silicon
Problem the mobility is a function of
temperature. So the resistance will change with
T.
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Diffusion
Suppose a drop of ink falls into a glass of
water. Introducing a high local concentration of
ink molecules, the drop begins to diffuse, that
is, the ink molecules tend to flow from a region
of high concentration to regions of low
concentration. This mechanism is called
diffusion.
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if charge carriers are dropped (injected) into
a semiconductor so as to create a nonuniform
density. Even in the absence of an electric
field, the carriers move toward regions of low
concentration, thereby carrying an electric
current so long as the nonuniformity is sustained.
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Diffusion current due to Holes
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Diffusion Current Due to Electron
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Divide by area to get current density
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Einstein Relation
µ and D are related via D/ µkT/q
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Overflow Material
http//www.youtube.com/watch?vRHAso1yM-D4