Transcript Lecture 1 - web page for staff

ENE 311
Lecture 1
Syllabus
• Instructor:
Apichai Bhatranand
• E-mail:
[email protected]
• Phone:
02-470-9063
• Office:
CB 40903
• Office Hours:
By appointment. Walk-in is
also welcomed.
Syllabus
• Textbook: “Semiconductor Devices Physics and
Technology”, S. M. Sze, Wiley.
• References:
− “Lectures on the Electrical Properties of
Materials”, L. Solymar and D. Walsh, Oxford.
− “Solid State Electronic Devices”, B. G.
Streetman, Prentice Hall.
− “Microelectronic Devices”, E. S. Yang, McGrawHill.
Syllabus
• Grading:
Mid Term Exam
35 %
Final
45 %
Homeworks
20 %
• Exams: No cheating, please. If do so, students
may be punished by the school rules without
any excuses.
Syllabus
• Homework: Will not be graded, but I encourage you
to work them out for your quizzes. Solutions will be
provided a few days after the quiz.
• Attendance: No class roll will be taken. In case of
class absence, you need to hand me a strong evidence
that you have an emergency or are under unusual
circumstances. No excuses will be accepted.
Lecture plan
Week
Subject
• 1
Introduction, Semiconductor materials
• 2, 3
Schrodinger equation, Effective mass,
Electrons and holes, Energy bands
• 4,5
Bonds, Carrier Concentration,
Crystallography
• 6
Carrier Transport Phenomena
------ midterm ------
Lecture plan
Week
Subject
• 7
Classification of semiconductors
• 8-10
Semiconductor devices
• 11
Dielectric materials, Refractive index
• 12
Photonic Devices
• 13
Basic Semiconductor Fabrication
Introduction
• Electronic industry has become the largest
industry in the world since 1998.
• Semiconductor devices are the foundation of
this kind of industry.
• In order to understand how electronic devices
including optoelectronic devices work, we
need to be familiar with material properties
and electron behavior in the material.
GWP
-The semiconductor industry trending to grow at
very high rate.
- S/C industry have a contribution of 25% of the
electronic industry in the early of 21st century.
Basic block of S/C devices
(a)
(b)
(c)
(d)
Metal-semiconductor interface;
p-n junction;
Heterojunction interface;
Metal-oxide-semiconductor structure.
Metal-semiconductor
−
A metal-semiconductor contact was the first semiconductor
device in 1874.
− This can be used as a rectifying contact* or as an ohmic contact*.
− We can use this contact in many devices such as MESFET(metalsemiconductor field-effect transistor) where rectifying contact
used as a gate and ohmic contacts as a source and a drain.
*rectifying contact allows current to flow easily only in one direction.
*ohmic contact passes current in either direction with a negligibly small
voltage drop.
p-n junction
• Formed by putting p-type semiconductor (positively
charged carriers) to n-type semiconductor (negatively
charged carriers).
• This is a key building block for most semiconductor
devices.
• By adding another p-type semiconductor, p-n-p
bipolar transistor can be formed, but if three p-n
junctions are used, this can form p-n-p-n device called
a thyristor.
Heterojunction interface
• The heterojunction interface is formed
between two different semiconductors. This
kind of junction is the key component for
high-speed and photonic devices.
Metal-Oxide-Semiconductor structure
• The metal-oxide semiconductor is famously called
MOS structure.
• This structure usually uses with two p-n junctions to
form a famous device called MOSFET (MOS fieldeffect transistor).
Major S/C devices
Semiconductor materials
• We may group solid-state materials by using electrical
conductivities σ into 3 classes: insulators,
semiconductors, and conductors.
- Insulators have very low conductivities (10-18 –
10-8 S/cm) such as quartz or glass.
- Conductors have high conductivities (104 – 106
S/cm) such as copper and silver.
- S/C have conductivities between those of
insulators and those of conductors.
Semiconductor materials
• The conductivity of a semiconductor is sensitive to
temperature, illumination, magnetic field, and amounts
of impurity atoms.
• This sensitivity makes semiconductor one of the most
important materials for electronic applications.
Semiconductor materials
Periodic Table
Semiconductor materials
• If we look at the periodic table, the element
semiconductors, such as silicon (Si) or
germanium (Ge), can be found in column IV
of the table.
• In the early 1950s, Ge was the most important
semiconductor material, but, since the early
1960s, Si has played a major role and virtually
displaced Ge as the main material for
semiconductor material
Semiconductor materials
• The reasons of that are:
− Better properties at room temperature
− High-quality silicon dioxide (SiO2) can be grown
thermally.
− Si is second only to oxygen in great quantity.
− Devices made from Si cost less than any other
semiconductor material
− Silicon technology is by far the most advanced
among all semiconductor technologies.
Electrons
• Electrons behave like a wave and a particle at
the same time. There is no theory or
experiment to explain this electron’s behavior.
• If we consider electron as a particle, we may
start from the study of response of electrons to
perturbation such as electric field, magnetic
field, or EM waves.
Resistivity and Mobility
l
A = cross
section area
V
A voltage V is applied across a conductor
of length “l” and cross section area “A”.
Resistivity and Mobility
From Ohm’s law:
V
I
R
l
1 l
R
 
A  A
where  = resistivity [Ω-m]
 = conductivity [S/m] = 1/
Resistivity and Mobility
I
 AV
l
I
V
 
A
l

 E

where V/l = E (electric field)
J = current density [A/m2]
J E
Resistivity and Mobility
Under influence of electric field, electron
experience a force
F  eE  ma
eE
a
m
where e = electron charge = 1.6 x 10-19 C
m = mass of electron
a = acceleration
Resistivity and Mobility
• Without any applied electric field, the random
motion of electron leads to zero net
displacement over a long period of time.
• The average distance between collisions is
called the mean free path.
• The average time between collisions is called
the mean free time, .
• With applied electric field, electron does not
have constant acceleration. It suffers collision
that leads it to move with an average velocity
called “drift velocity”.
Resistivity and Mobility
A drift velocity can be written as
vD  a
 e 
vD    E
m
vD  e E
where µe = mobility of electron [m2/V-s]
Resistivity and Mobility
Resistivity and Mobility
By moving electrons in conductor, this
leads to have a current proportional to number
of electrons crossing a unit area [m2] per unit
time.
J  Ne .e.vD
where Ne = number of free electrons per
unit volume
Resistivity and Mobility
As electric field E increases, vD also
increases, therefore, J also increases. This
makes the conductor behave like a perfect
source. However, the velocity vD saturates to
a maximum value limited by thermal
velocity. The mean thermal velocity (vthermal)
of electron can be found from
1 2
3
mvthermal  kT
2
2
Resistivity and Mobility
1 2
3
mvthermal  kT
2
2
where m = effective mass of electron
k = Boltzmann’s constant = 1.38 x 10-23 J/K
T = absolute temperature (K)
kT/2 = average thermal energy of electron in one-dimension
J  ( Neee ) E
  Neee  e ( Nee)
where Nee = charge density
Resistivity and Mobility
• The conductivity depends on the charge density
and mobility.
• Metals have high conductivity due to their high
density of electrons although their mobilities
(μm/t ~ 10 cm2/V-s)are very low compared to
those of semiconductors (μS/C ~ 103 cm2/V-s).
Resistivity and Mobility
• The mobility is linearly dependent to the mean
free time between collisions which is caused by
two major mechanisms: lattice scattering and
impurity scattering.
• Lattice scattering is caused by the thermal
vibrations of the lattice atoms at any temperature
above absolute zero. As the temperature gets
higher, the mobility will get lower. This shows
that the mobility will decrease in proportion to
T-3/2.
Resistivity and Mobility
• Impurity scattering is caused when a charge carrier
past an ionized dopant impurity.
• The carrier will be deflected due to the Coulomb force.
The probability of impurity scattering depends on the
total concentration of ionized impurities.
•
Unlike lattice scattering, for impurity scattering, the
mobility due to impurity scattering will increase as the
temperature gets higher.
• This mobility in this case is shown to vary as T3/2/NT,
where NT is the total impurity concentration.
Resistivity and Mobility
where µL = mobility due
to lattice scattering
µI = mobility due
to impurity scattering
1 1
1


 L I
Resistivity and Mobility
In semiconductors, both electrons and
holes contribute to current in the same
direction. Hole current and electron current are
not necessarily equal because they have
different effective masses.
J S / C   Neee  N heh  E
 S / C   N e e  N h  h  e
Ex. Calculate the mean free time of an electron and mean
free path having a mobility of 1000 cm2/V-s at 300 K.
Assume me = 0.26m0, where m0 = electron rest mass =
9.1 x 10-31 kg.
Ex. Calculate the mean free time of an electron and mean
free path having a mobility of 1000 cm2/V-s at 300 K.
Assume me = 0.26m0, where m0 = electron rest mass =
9.1 x 10-31 kg.
Soln
me e
e
(0.26  9.1 1031 kg)(1000  10 4 m 2 .V -1.s -1 )

1.6  1019 C
 0.148 ps
From (5),  
mv 2 3kT

2
2
3kT
vth 
105 m/s
m
l  vth  14.8 nm
s
v ;
t
Ex. In metals, μe = 5 x 10-3 m3/(V-s) and l = 1 cm, V = 10
volts is applied. Find the drift velocity vD and compare
to thermal velocity vth.
Ex. In metals, μe = 5 x 10-3 m2/(V-s) and l = 1 cm, V = 10
volts is applied. Find the drift velocity vD and compare
to thermal velocity vth.
Soln
V 
vD   e E   e  
l 
2

3 m   10 V 
  5  10
 2

V.s
10
cm




vD  5 m/s
3kT
3  1.38  1023 J/K  300K
vth 

m
9.1  1031 kg
vth  1.17  105 m/s
vD  vth
The Hall Effect
d
Assume a p-type
semiconductor sample,
with electric field applied
along x-direction and a
magnetic field applied
along z-axis, the Lorentz
force qv x B (= qvxBz) due
to the magnetic filed will
exert an average upward
force on the holes flowing
in the x-direction.
The Hall Effect
d
Therefore, drifting holes
experienced an upward
force which deflects holes
upward toward the top of
the sample and makes
them accumulate there.
This sets up an electric
filed EH in y-direction
called “Hall field”. This
establishment of the
electric field is known as
the Hall Effect.
The Hall Effect
This establishment of the electric field is known
as the Hall Effect. At the steady-state, the electric
field along the y-axis exactly balances the Lorentz
force (or it is called “an equilibrium”); that is
qEy  qvx Bz or Ey  vx Bz
The Hall Effect
N h qEH
B
 1 
EH  
 BJ
 Nhq 
 1 
where RH  
  Hall coefficient
 Nhq 
J  N h qv 
This Hall coefficient for n-type semiconductor is
similar to the p-type one except it has an
opposite sign as
1
1
RH  

qNe Ne e
The Hall Effect
This Hall effect is often used to distinguish
an n-type from a p-type sample and also used
to calculate the free charge density and the
carrier mobility if the conductivity is known.
For example, we know that the induced
voltage VH known as “Hall Voltage” between
the top and bottom is expressed by
VH  EH d
The Hall Effect
Using a voltmeter to measure VH then
VH
EH 
d
I
J
Wd
 1 
EH  
 B.J
 Nee 
VH  1 

 B.J
d  Nee 
BI
Ne 
VH eW
The Hall Effect
If the conductivity σ is known, mobility can be
found as
  ( Ne e) e 
e  RH e
e
RH
The Hall Effect
Ex. A sample of Si is doped with 1016 phosphorus
atoms/cm3. Find the Hall voltage in a sample with d =
500 μm, A = 2.5 x 10-3 cm2, I = 1 mA, and Bz = 1
Tesla.
Note: 1 Tesla = 1 Wb/m2 = 104 G.
The Hall Effect
Soln
1
1
3
RH  



625
cm
/C
19
16
-3
eN e
1.6  10 C  10 cm
VH  EH d
 R .I .B 
  RH .J .B  d   H
d
 A 
cm3
103 A
104 Wb
4
 625



500

10
cm
-3
2
2
C 2.5  10 cm
cm
VH  1.25 mV