Basic Physics of
Semiconductors (1)
Section 2.1
Tentative Schedule
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1
L
Date
1/14
1/14
Day
Tuesday
Tuesday
2
1/16
Thursday
3
L
1/21
1/21
Tuesday
Tuesday
4
5
1/23
1/28
Thursday
Tuesday
L
6
7
L
1/28
1/30
2/4
2/4
Tuesday
Thursday
Tuesday
Tuesday
Topic
Diagnostic Test
Lab protocol, cleaning procedure,
Linus/Cadence intro
Fundamental concepts from
Electric Circuits
Basic device physics
I-V characteristics of a diode
(Simulation)
Physics of PN junction diode
Application of diodes: diode
logic/Review
Diode logic circuit
Characteristics of BJT
Test #1
Physics of a BJT
Section
2.1
2.2-2.3
4.1-4.3
Physics Matters!
Eat your broccoli before having desert.
Need to know your device physics before getting started with circuit design.
Today
Next time
Review of High School
Chemistry
•
•
•
•
Terminology
Energy of an Electron
Valence Electron
Covalent Bond
Terminology
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.
Energy of an Electron
Less
Energy
More
Energy
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
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.
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?v=aWVywhzuHnQ)
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.
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
Generation of Free Electrons
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 T=0K
Electrons gain thermal
energy and break away
from the bonds. They
begin to act as “free
charge carriers”—free
electron.
Movement of electrons and holes
One electron has traveled from right to left.
One hole has traveled from left to right.
Bandgap Energy
Q:Does any thermal energy create free electrons (and holes) in silicon?
A: No. A minimum energy—called 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)
Semiconductors usually have a moderate Eg between 1 eV and 1.5 eV.
Electron Density
Q: How many free electrons are created at a given temperature?
ni  52 10 T
15
3 2
exp
 Eg
2kT
electronscm3
electron density
where k=1.38 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.
Making sense of electron
density
Determine the electron density in silicon at T=300K.
Use the electron density formula with Eg=1.12 eV, ni @ 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?
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.)
nn=ni2
So
np=ni2
electron
holes
Can we use something other than silicon?
Add Phosphorous to Silicon to Create an
silicon
Phosphorus has 5 valence electrons. The 5th electron is “unattached”.
This electron is free to move and serves as a charge carrier.
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.
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.
np=ni2
This equation is true whether
we are dealing with an intrinsic
or extrinsic semiconductor.
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!
Add Boron to Silicon to Create a p-type
Silicon
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.
Summary
In n-type material,
MajorityCarriers  n  N
2 D
MinorityCarriers  p 
In p-type material,
ni

ND
MajorityCarriers  p  N A
ni2
MinorityCarriers  n 

NA
a
Vab    Edx
b
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.”
Mobility
We expect the carrier velocity to be proportional to the electric
field strength (E).
v   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


  n E 
v
e

v
h
For electrons

 p E 
For holes
Mobility of Various Doped
Semiconductor
Devices of higher mobility can be used to make higher speed transistors!
Drift Current
Drift current is composed of the drift current due to holes and the
drift current due to electrons.
Concept of a Current Density
The current density is the charge per second crossing a unit area .
Velocity Saturation
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.
Microscopic View of Charge Movement
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.”
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.
Diffusion current due to Holes
Where does the – sign come from?
Diffusion Current Due to
Electron
Summary
μ and D are related via D/ μ=kT/q
This is known as Einstein’s relation
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