Basic Physics of Semiconductors (1)

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Basic Physics of Semiconductors (1)
Sonoma State University Engineering Science Jack
Ou
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Atom is the smallest particle of an element that
retains the characteristics of that 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 has four valence electrons.
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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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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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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?
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 one
electron for 5 x 1012 atoms at room
temperature.
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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
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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 consists
predominantly of electrons.
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if we can 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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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 -type of silicon that is 1 m
long senses a voltage of 1 V. Determine the
velocity of the electrons.
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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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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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Einstein Relation
µ and D are related via D/ µkT/q
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