Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Foundation Course for IC Design MSc Program
(1nd term, 2003/2004 Academic Year)
• Lecturer: Prof. Jianbin XU
Rm. 428/222
Tel. 2609-8297
e-mail: jbxu@ee.cuhk.edu.hk
1
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Textbook and Reference Book
1. 半 导 体 器 件 - 物 理 与 工 艺, （美）施 敏 著, 科 学 出 版 社,
1992; Semiconductor Devices – Physics and Technology, S. M. Sze, 2nd
Ed., John Wiley & Sons, 2002
2. 半导体物理学, 刘恩科 朱秉升 罗晋生 等, 西 安 交 通 大 学 出 版
社, 1998
3. Understanding Semiconductor Devices, S. Dimitrijev, Oxford
University Press, 2000
4. S. O. Kaspa, Principle of Electronic Materials and Devices, McGraw
Hill, 2nd Ed., 2002
5. R. F. Pierret, Semiconductor Device Fundamentals, Addison Wesley,
1996
6. E. S. Yang, Microelectronic Devices, McGraw-Hill, 1988
7. B. G. Streetman, Solid State Electronic Devices, 5th Ed., Prentice- Hall,
2000
8. P. Bhattacharya, Semiconductor Optoelectronic Devices, 2nd, PrenticeHall, 1997
9. M. Shur, Physics of Semiconductor Devices, Prentice-Hall, 1990
2
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
‰ Websites and Ftp files
• Course web page: http://www.ee.cuhk.edu.hk/~jbxu/teaching.htm
• Course news group: cuhk.ee.xxxx
• Supplementary materials of the textbook
http://www.gu.edu.au/school/mee/PPages/Sima/
• A local version of a useful website of Semiconductor Applets Service
with animation http://jas2.eng.buffalo.edu/applets/index.html Please
see the course website.
• Webbook: http://ece-www.colorado.edu/~bart/book/
• Web of IBM: http://www.chips.ibm.com/gallery
• Hong Kong Science & Technology Parks: http://www.ee.cuhk.edu.hk/
hkstp/tech_conf/presentations.html
™ VCD show - Silicon Run
3
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
‰ Interactive MATLAB Animations
• The software is available via the CD-ROM attached to the
textbook. It is designed for a quicker and deeper introduction
and understanding of the underlying theoretical concepts. A
software is relevant to it.
‰ Factory Tour
• A factory tour may be arranged. The visit site is located in Tai
Pu Hong Kong Science Parks.
‰ Acknowledgement
The lecture notes are in part adopted from ELEC321 registered
at the Hong Kong University of Science and Technology. The
generous support by Prof. M. S. Chan is sincerely
acknowledged and greatly appreciated.
4
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Chapter 1 Review of Semiconductors
• 1.0 Systems of Units
• SI units: meter (m), kilogram (kg), second (s or sec), ampere (A), kelvin
(K), candela (cd).
• Frequently used SI prefixes:
Multiplier
Prefix
Symbol
tera
T
1012
109
giga
G
106
mega
M
103
kilo
k
10-3
milli
m
micro
µ
10-6
nano
n
10-9
10-12
pico
p
femto
f
10-15
5
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Early History of Electronics
In 1874, Ferdinand Braun, a German
scientist, discovered that crystals could
conduct current in one direction under
certain conditions. This phenomenon is
called rectification.
In 1895, the Italian Gugielmo Marconi first
showed a new technology invented by Nikola
Tesla through radio signals. This was the
beginning of wireless communications. Crystal
detectors were used in radio receivers. It is able to
separate the carrier wave from the part of the
signal carrying the information.
Source: http://www.lucent.com/minds/transistor/
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The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Fleming Valve: A rectifying vacuum tube
In 1904, John Ambrose Fleming, an English physicist,
devised the first practical electron tube known as the "Fleming
Valve”.
In the early 1910s, he ameliorated the reception of these signals
by building up his research on the "Edison Effect" (dark
particles smudge the inside of glass light bulbs as current
flows through one direction), Fleming attached a light
bulb outfitted with two electrodes to a receiving system.
In it, electrons flew from the negatively charged cathode
to the positively charged anode. As the current within the
tube was moving from negative to positive, the weak
incoming signal were rectified into detectable direct
current.
Source: http://www.lucent.com/minds/transistor/
7
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Audion: An Amplifying Vacuum Tube
In 1906, Lee de Forest, an American scientist, added a
third electrode (called a grid) to the electron tube, which
is now called a triode. This is a network of small wires
around the vacuum tube cathode . Thus, the amplifying
vacuum tube, the most recent ancestor of the transistor,
was born.
Although solid-state technology overwhelmingly dominates
today's world of electronics, vacuum tubes are holding out in
two small but vibrant areas. They do so for entirely different
reasons. Microwave technology relies on tubes for their powerhandling capability at high frequencies ["Tubes: still vital after
all these years," Robert S. Symons, IEEE Spectrum, April,
1998]. The other area--the creation and reproduction of music-is a more complicated and controversial story.
Sources: http://www.lucent.com/minds/transistor/
http://www.svetlana.com/docs/tubeworks.html
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The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
ENIAC: The First Electronic Computer
The University of Pennsylvania's ENIAC computer,
due to its incorporation of thousands of vacuum tubes
(18,000 vacuum tubes), filled several large rooms and
consumed enough power to light ten homes. The
vacuum tube's cathode required a good amount of heat
in order to boil out electrons and often burned out.
Also, the actual glass tube was fragile and bulky.
9
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
The First Transistor in 1947
1947
1st transistor
AT&T Bell Lab
1st commercially available transistor
Raytheon CK703, 1948
3 inventors of transistor,
John Bardeen (left), Walter
Brattain (right), and
William Shockley (middle)
at the Bell Labs shared the
Nobel Prize in Physics in
1956.
Source: http://www.lucent.com/minds/transistor/
1st commercially successful transistor
Raytheon CK722, 1953
Ge-based pnp low power transistor
Source: http://roiconnect.com/transistor.htm
10
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Senior Staff of Shockley Semiconductor Laboratory toast their boss at
a luncheon the day after the annoucement of his Nobel Prize in 1956.
They are the earlier explorers in the Silicon Valley. G. Moore is sitting
at the far left.
11
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
2000 Nobel Prize goes to semiconductor pioneers
2000 year's Nobel Prize in Physics has been awarded for the invention of
semiconductor lasers, integrated circuits and other high-speed electronic devices.
Zhores Alferov of the A F Ioffe Institute in St Petersburg, Russia, and Herbert
Kroemer of the University of California at Santa Barbara receive half the prize "for
developing semiconductor heterostructures used in high-speed- and optoelectronics." The other half goes to Jack Kilby of Texas Instruments "for his part in
the invention of the integrated circuits." The prize is worth 9 million Swedish
kroner (about £660 000). The Nobel foundation credits this year's prize-winners
with laying the foundations for modern information technology and
communications systems.
12
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
The First Integrated Circuit
Integrated Circuit (IC):
1958, Jack Kilby, Texas
Instrument
a large number of individual components
(transistors, resistors, capacitors, etc.) fabricated
side by side on a common substrate and wired
together to perform a particular circuit function. It
is widely recognized that IC was invented
separately by R. Noyse and
J. Kilby in the late of 1950s.
A part of news release: October 19, 1961
The aeronautical Systems Division, U.S. Air Force, and Texas Instruments Incorporated, Dallas, Texas, today demonstrated
in operation a microminiature digital computer utilizing semiconductor networks. The advanced experimental equipment has
a total volume of only 6.3 cubic inches and weighs only 10 ounces. It provides the identical electrical functions of a
computer using conventional components which is 150 times its size and 48 times its weight and which also was
demonstrated for purposes of comparison. It uses 587 digital circuits (Solid Circuit(tm) semiconductor networks) each
formed within a minute bar of silicon material. The larger computer uses 8500 conventional components and has a volume of
1000 cubic inches and weight of 480 ounces. Application of semiconductor networks will give equipments higher reliability
than can be achieved presently from conventional components. The improvement will be realized because the integrated
structure of the networks minimizes connections and eliminates the individual packaging required for conventional
components. In addition, the network is formed by relatively few process steps, allowing a high degree of control, and uses
only very high purity material for its fabrication.
http://www.ti.com/corp/docs/kilbyctr/jackbuilt.shtml
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The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Prof. Herbert Kroemer graduated from
Göttingen University, Germany. He was
with RCA, Varian, Fairchild, University of
Colorado at Boulder. He has been with
University of California at Santa Barbara
since 1976. In 1957, he published two
papers on how to use heterostructures to
increase transistor speed and make a laser.
Prof. Herbert Kroemer‘s favorite saying, “if in discussing a
semiconductor problem, you cannot draw an energy band diagram,
then you don’t know what you are talking point.”
“Certainly, when I thought of the heterostructure laser, I did not
intend to invent compact disc players….. The person who comes up
with applications thinks differently than the scientist who lays the
foundation.”
14
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Altair 8800 Computer
15
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Digital Equipment Corp. (DEC) introduced the PDP-8, the first commercially
successful minicomputer in 1966 (left). The PDP-8 sold for $18,000, one-fifth
the price of a small IBM 360 mainframe (right). The speed, small size, and
reasonable cost enabled the PDP-8 to go into thousands of manufacturing
plants, small businesses, and scientific laboratories.
16
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Fig. 1.00 Electric circuit of radio receiver
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The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Figure (a) A schematic diagram of the first nonvolatile semiconductor
memory (NVSM) with a floating gate. (b) A limiting case of the
floating-gate NVSM—the single-electron memory cell. (S. M. Sze)
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The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Exponential increase of
dynamic random access
memory density versus
year based on the
Semiconductor Industry
Association (SIA)
roadmap. (S. M. Sze)
19
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Moore’s Law
100000000
10000000
Alpha 21264: 15 million
Pentium Pro: 5.5 million
PowerPC 620: 6.9 million
Alpha 21164: 9.3 million
SPARC Ultra: 5.2 million
Pentium
i80486
Transistors
1000000
i80386
i80286
100000
i8086
10000
i8080
i4004
1000
1970
1975
1980
1985
1990
1995
2000
Year
20
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
Andrew Grove
IC Design MSc
Program
Gordon Moore
Robert Noyce
Three founders of Intel Corp that was found in 1968 by the three men
in Santa Clara, the Silicon Valley, California, USA. Now Intel Corp is
the largest semiconductor manufacturer in the world. Grove is
currently president of Intel Corp. Gordon is the biggest shareholder.
21
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Moore’s Law in IC Manufacturing
‰ Gordon Moore: a co-founder of Intel
“transistor number per chip
doubles every eighteen months.”
‰ Feature size reduction enables
the increase of complexity.
Acronym
Number
of devices
SSI (Small Scale IC)
1 ~ 100
MSI (Medium Scale
IC)
102 ~ 103
LSI (Large Scale IC)
103 ~ 105
VLSI (Very Large
Scale IC)
105 ~ 106
ULSI (Ultra Large
Scale IC)
106 ~ 109
GSI (Giga Scale
Integration)
109 ~
CSLC(Colossal Scale
Large Scale IC) ?
22
Next to GSI
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Exponential increase of microprocessor computational power versus
year. (S. M. Sze)
23
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Pentium Die View
Pentium -200MHz
Pentium II -450MHz
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The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Zoom in Intel Chip?
Time Magazine, July 1998
25
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Integrated Circuits
Die
Pentium 4 Processor
Wafer
26
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
The state-of-the-art CMOS technology developed by Intel will be
put into mass production soon.
27
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Figure 1.1. Gross world product (GWP) and sales volumes of the
electronics, automobile, semiconductor, and steel industries from
1980 to 2000 and projected to 2010.(Simon M. Sze)
28
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
1.1 Ohm’s Law
• Charge is an electrical property of the atomic particles of which matter
consists, measured in coulombs (C).
• 1 C = 6.24 ×1018 electrons, single electron has - 1.6 ×10-19 C (negative).
The laboratory values range from nC to µC. The mass of a free electron
is 9.11 ×10-31 kg, its radius is less than 10-22 m.
• Conservation of charges: charges can neither be created or destroyed,
only transferred. The algebraic sum of the electric charges in a closed
system does not change with time.
• Electric current is the time rate of change of charge, measured in
amperes (A). It has a specific direction. Reference direction.
dq
I=
dt
t
q = ∫ I dt
t0
• dc - direct current is a current that remains constant with time.
• ac - alternating current is a current that varies sinusoidally with time.
29
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Fig. 1.01 Conventional current flow
-
-
+
+
The direction of current flow is conventionally taken as the
direction of positive charge movement.
30
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
1.1 Ohm’s Law, cont’d
• Voltage (or potential difference) is the energy required to move a unit
charge through an element, measured in volts (V).
• Fig. 1.6 shows the voltage difference across an element connected to
points a and b. The plus (+) and minus (-) signs are used to define
reference direction or voltage polarity.
• The V can be interpreted in two ways:
(1) point a is at a potential of V volts higher than point b, or
(2) the potential at point a with respect to point b is V volts.
• It follows logically that in general
V = ϕ a − ϕb
31
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Fig. 1.02 Polarity of voltage V.
V=ϕa - ϕ b
32
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Fig. 1.03 Two equivalent representations of the same voltage V:
(a) point a is +9 V above point b, (b) point b is -9 V above point
a.
+9 V
-9 V
In Fig. 1.7 (a) there is a voltage drop from a to b, whereas equivalently there
is a voltage rise from b to a. In other words, a voltage drop from a to b is
equivalent to a voltage rise from b to a.
33
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
1.1 Ohm’s Law, cont’d
• The dependence of the current cross a resistor on the applied voltage is
expressed by Ohm’s law.
V
I=
R
(1.1)
• In integrated circuits, a resistor is constructed as shown in Fig. 1.2.
• Its resistance can be expressed by
L
R=ρ
xj W
(1.2)
where ρ is the resistivity. Its unit is Ω⋅cm.
• The conductivity is defined by
σ =1 ρ
(1.3)
• The unit of σ is (Ω⋅cm)-1or S⋅cm-1.
34
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Lecture 1: Introduction
Dept. of Electronic Engineering
Solid State
Materials
IC Design MSc
Program
we couldn't live without their
electronic properties…
35
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Aërodynamic
(gas)lubrication
36
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Table 1. 0 Typical range of conductivities for insulators,
semiconductors, and conductors. (from S. M. Sze)
37
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Fig. 1.2 Integrated-circuit resistor: (a) top view (b) cross
section
W
(a)
L
conductive stripe
y
resi st i ve body
xj
insulating medium
substrate (an IC chip)
38
insulator
x
(b)
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
1.1 Ohm’s Law, cont’d
• In IC design, it is more convenient to use the term of sheet resistance.
• The sheet resistance of the resistor is defined by
Rs =
ρ
(1.4)
xj
• Alternatively, the resistance of the resistor can be expressed by
L
R = Rs
W
(1.5)
• In IC fabrication, ρ or σ may depend on the location. This is illustrated
in Fig. 1.3. In this case, we introduce the average conductivity σ
∞
1
σ ≈ ∫ σ ( x)dx
xj 0
39
(1.7)
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Conductivity, σ ( Ω cm)
-1
12
10
σ (x) = σ (0) e
8
2
-(x/x0 )
6
_
σ (x) = σ
4
xj
2
0
0
1
2
Depth, x (µ m)
3
4
Fig. 1.3 A typical variation of conductivity from the top surface to
the bulk (bottom).
40
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
1.1 Ohm’s Law, cont’d
• Note that the unit of Rs is Ω/ .
• Ohm’s law can be rewritten as
j =σ E
(1.10)
where j is the current density (A/cm2).
• Or more restrictly
t
j = σ ⋅E
(1.11' )
t
• In most cases, we can simplify Eq. (1.11’) using σ (scalar) to replace σ .
j=σE
(1.11)
• Eq. (1.11) can be expressed in terms of electrical potential ϕ
j = −σ ∇ϕ
(1.14)
41
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
1.1 Ohm’s Law, cont’d
• Eq. (1.14) means that the electric current is induced by an electric
potential difference, or equivalently an electric field. This current is
called drift current.
• Currents can also be generated by carrier concentration difference or
temperature difference.
• Examples 1.3 and 1.4
42
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
1.2 Conductivity Ingredients
• Typical range of silicon (Si) conductivity is from 5 ×10-2 (Ω⋅cm)-1 to 5
×105 (Ω⋅cm)-1. This is a very vast range.
• Table 1.1 exhibits semiconductor related elements in the periodic table.
• Among them, silicon is the most frequently used semiconductor
material in microelectronics.
• Atomic structure of silicon atom is shown in the view diagram by M. S.
Chan.
• There are 4 electrons in the outer shell having 8 electron places.
• Silicon atoms are prone to either give away the 4 electrons or accept an
additional 4 electrons. These 4 electrons are called valance electrons.
• When silicon atoms pile up to form a silicon crystal, the electrons pair
up and form covalent bonds.
• As shown in Fig. 1.4, the bonds may be broken if T > 0. Once a bond is
broken, it creates a free electron and a hole (positively charged).
43
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Group IV elements…..
your should be familiar !
www.webelements.com
44
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Table 1.1 Semiconductor related elements
5
III
IV
V
+3
+4
+5
C
Carbon
12.01
14
Si
Silicon
28.09
32
Ge
Germanium
72.60
50
Sn
Tin
118.7
7
N
Nitrogen
14.008
15
P
Phosphorus
31.02
33
As
Arsenic
74.91
51
Sb
Antimony
121.8
B
Boron
10.82
13
Al
Aluminum
26.97
31
Ga
Gallium
69.72
49
In
Indium
114.8
6
45
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
Schematic representation of an isolated silicon atom.
46
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
47
IC Design MSc
Program
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
(a) A tetrahedron bond. (b) Schematic two-dimensional representation
of a tetrahedron bond.
48
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
(a)
IC Design MSc
Program
(b)
covalent
bonds
valence
electrons
+4
+4
+4
+4
+4
+4
+4
+4
+4
+4
+4
+4
hole
free
electron
+4
+4
+4
+4
+4
+4
T>0K
T=0K
Fig. 1.4 Two dimensional representation of silicon crystal
49
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
1.2 Conductivity Ingredients, cont’d
• Two types of current carriers in semiconductors: 1. electrons, 2. holes.
• The movement of holes looks very like the movement of bubbles in
water.
• Since both holes and electrons contribute to the total current in
semiconductors, the conductivity should include the both parts:
σ = qnµ n + q pµ p
(1.15)
where n and p are concentrations of the free electrons and holes,
respectively. µn and µp are the free-electron and hole mobilities,
respectively.
• An intrinsic semiconductor has only its own native atoms, without any
impurities.
• Obviously the concentration of holes is the same as that of free
electrons in an intrinsic semiconductor, as implied in Fig. 1.5.
50
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Prof. J. B. XU 許建斌
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IC Design MSc
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Electric Field
+4
+4
+4
+4
+4
+4
+4
+4
+4
+4
+4
+4
+4
+4
+4
hole
hole
hole
+4
free
+4
+4
electron
electron
Fig. 1.5 Model of holes as mobile carrier of positive charge.
Note that the movement direction of the hole is the same as
that of the electron.
51
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1.2 Conductivity Ingredients, cont’d
• This requires
n = p = ni
(1.16)
• For an intrinsic semiconductor, at a given temperature, ni, µn, and µp
are constant. However, they are temperature dependent.
• Table 1.2 Intrinsic properties of Si and GaAs at 300 K
ni [cm-3]
µn [cm2/(Vs)]
µp [cm2/(Vs)]
Si
GaAs
1.02 × 1010
1450
500
2.1 × 106
8500
400
• To fabricate useful devices, the conductivity must be varied by
technological means, mostly through introducing impurity atoms. This
is called doping.
52
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Intrinsic carrier densities in
Si and GaAs as a function of
the reciprocal of
temperature. 5-7 (from S. M.
Sze)
53
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Electron density as a
function of temperature for
a Si sample with a donor
concentration of 1015 cm-3.
At low temperature, partial
ionization of the impurities
occurs, n = ND+>> ni. At
intermediate temperature,
complete ionization of the
impurities appears, n = ND
>> ni. At high temperature,
carrier concentration is
dominated by the intrinsic
electron and hole
concentration, n = ni >> ND.
54
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1.2 Conductivity Ingredients, cont’d
• Semiconductors with technologically modified concentrations of free
electrons and/or holes are called doped semiconductors.
• Atoms used to replace parent atoms (e.g. Si) are called doping atoms or
impurity atoms.
• Doping atoms used to produce more electrons are called donors. Their
concentration is denoted by ND. And the doping is called N-type doing.
• Conversely, doping atoms used to generate more holes are called
acceptors. Their concentration is denoted by NA. And the doping is
called P-type doing.
• To preserve the electrical neutrality, an N-type doing semiconductor
will not only generate more electrons, but also more positive ions
which are mainly immobile or fixed.
• Similarly, a P-type doing semiconductor will not only generate more
holes, but also more negative ions which are mainly immobile or fixed.
55
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(a)
IC Design MSc
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(b)
+4
+4
+4
+4
+4
+4
+4
+5
+4
+4
+3
+4
+4
+4
positive
ion
+4
negative
ion
free
electron
+4
+4
+4
hole
P-type doping
N-type doping
Fig. 1.6 Effects of doping.
56
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Schematic bond pictures for (a) n-type Si with donor (arsenic) and
(b) p-type Si with acceptor (boron).
57
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1.2 Conductivity Ingredients, cont’d
• Table 1.3 Charges in N-type semiconductors
Mobile Charges
1. Thermally generated holes (minority carriers)
2. Thermally generated electrons (negligible)
3. Doping-induced electrons (≅ ND)
Fixed Charges
4. Doping-induced positive ions (≅ ND)
concentration of electrons >> concentration of holes
net charge = p - n + ND = 0 ⇒ n ≅ ND
• Due to the huge difference in charge concentrations, Eq. (1.15) can be
simplified as
σ ≈ qN D µ n
58
(1.18)
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1.2 Conductivity Ingredients, cont’d
• Table 1.4 Charges in P-type semiconductors
Mobile Charges
1. Thermally generated electrons (minority carriers)
2. Thermally generated holes (negligible)
3. Doping-induced holes (≅ NA)
Fixed Charges
4. Doping-induced negative ions (≅ NA)
concentration of holes >> concentration of electrons
net charge = p - n - NA = 0 ⇒ p ≅ NA
• Due to the huge difference in charge concentrations, Eq. (1.15) can be
simplified as
σ ≈ qN A µ p
59
(1.18' )
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Resistivity versus impurity concentration for Si and GaAs. (S. M. Sze)
60
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1.2 Conductivity Ingredients, cont’d
• Generation of free electrons and holes is a process that may include
1. liberation of bound electrons from parent atoms → electron-hole
pairs
2. liberation of bound electrons from donor-type atoms → electrons and
fixed positive charges
3. liberation of bound electrons from parent atoms to supply acceptortype atoms → mobile holes and fixed negative charges
• Recombination of a free electron and a hole is a process that the free
electron releases its energy and bond itself again when it finds a parent
atom with a hole in its bond structure.
• In thermal equilibrium, the generation rate is always equal to the
recombination rate. Both depend on temperature and doping
concentration.
• For a doped semiconductor, the carrier concentrations of electrons and
61
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Program
1.2 Conductivity Ingredients, cont’d
holes follow
n p = n i2
(1.21)
where p and n are the total concentrations of holes and electrons,
respectively. This means p or n includes the thermally generated carriers
and doping induced carriers.
• The detailed expression of ni can be found in the next slide.
• Examples: 1.5, 1.6, 1.7, 1.8
62
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The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
1.3 Fabrication of a Resistor and Diffusion
• Making a micropattern: lithography
• This process is illustrated in Fig. 1.9.
• It includes (a) growth of SiO2 layer, (b) photoresist deposition, (c) light
exposure, (d) photoresist developing, (e) etching of the underlying layer,
(f) photoresist stripping
• Contact lithography and projection lithography.
• Making an IC resistor
• Combing the lithography and the diffusion, an IC resistor can be
fabricated as shown in Fig. 1.10.
• Ohmic contacts. It is well known that metals create good ohmic contacts
with P-type silicon. However, good contacts to N-type silicon can be
achieved only with a highly doped N-type region (labeled as N+).
64
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SiO2
IC Design MSc
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photo-
{resist
N-type Si
(a)
- starting material
(b)
- photoresist deposition
- soft baking
UV light
{ glass
mask
(d)
- photoresist developing
- hard baking
(c)
- exposure
SiO2
N-type Si
(e)
- etching of the underlying layer
(f)
- photoresist stripping
65
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boron atoms
P type
(a)
- Boron diffusion
N type
phosphorus atoms
N+
P type
N type
A
B
V+
N+
P type
N type
(b)
- oxide removal
- oxide deposition
- photolithography
(N+-diff. windows)
- phosph. diffusion
(c)
- photolithography
(contact windows)
- metal deposition
- photolithography
(metal patterning)
Fig. 1.10 Process steps used in fabrication of an IC resistor.
66
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Doping Concentration, cm
-3
1019
NA(x)=NA(0) e-(x/x0 )
2
1018
1017
P type
ND
1016
1014
N type
xj
1015
0
1
2
3
4
Depth, x (µm)
Fig. 1.11 Diffusion of acceptors into an N-type substrate
creates a P-N junction: P-type semiconductor between the
surface and xj, and an N-type from xj into the bulk of the
substrate.
67
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1.3 Fabrication of a Resistor and Diffusion, cont’d
• In general, diffusion of particles creates an effective particle current
toward the points of lower particle concentration. An example is
depicted in Fig. 1.7
• The current of particles (charged or uncharged) produced by a
difference (or gradient) in the particle concentration is called diffusion
current.
• Diffusion occurs in gases, liquids, solids.
• Doping of a semiconductor by diffusion is schematically illustrated in
Fig. 1.8. Note that a high temperature is required in order to release a
sufficient number of semiconductor atoms from their thermal
equilibrium (or crystal-lattice) positions. The empty positions are called
vacancies.
• The diffusion current density can be expressed by Jdiff, its unit being s-1
m-2.
68
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I
Fig. 1.7 Smoke diffusion from the outside of the room into the
inside via a window.
69
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doping atoms
semiconductor crystal at high temperature (1000oC)
Fig. 1.8 Doping of a semiconductor by diffusion via a window.
70
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Program
1.3 Fabrication of a Resistor and Diffusion, cont’d
• As illustrated in Fig. 1.12, the net diffusion current is given by
J diff = J diff → − J diff ←
∝ N O − N I = − ∆N
(1.23)
where N is the particle concentration. Note the minus sign which
indicates that the concentration is decreasing along the x-axis.
• More generally, the net diffusion current is proportional to ∆N across
∆x, that is,
J diff
∆N
∝ −
∆x
(1.24)
J diff
∂N
= −D
∂x
(1.25)
• More precisely,
71
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∆x
O
I
NUMO
NUM I
∆A
(window
cross-section)
x
Fig. 1.12 Diffusion current from the left to the right.
72
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1.3 Fabrication of a Resistor and Diffusion, cont’d
• For three dimensions, Eq. (1.25) is modified by
J diff = − D∇N
(1.26)
where D is the diffusion coefficient, and ∇ represents the partial
derivatives in x, y, and z.
• The continuity equation can be derived according to the schematic
diagram illustrated in Fig. 1.13.
J diff
∂N
= −
∂x
∂t
∂N
∇ ⋅ J diff = −
∂t
73
(1.33)
(1.33' )
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I
i(x+∆x)
i(x)
∆x
∆A
x
Fig. 1.13 Diffusion current from the left to the right is proportional
to the concentration variation inside the box.
74
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1.3 Fabrication of a Resistor and Diffusion, cont’d
• Fick’s diffusion equation states that
∂N
∂ 2 N ( x, t )
=D
∂t
∂x 2
∂N
= D∇ 2 N ( x, y, z , t )
∂t
(1.34)
(1.34' )
• For diffusion of doping atoms, the diffusion coefficient exponentially
depends on the temperature:
D = D0 e
−
EA
kT
(1.35)
where T is the absolute temperature (in K), k is the Boltzmann constant,
the parameters, EA and D0 are the activation energy (in eV) and
frequency factor, respectively.
75
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1.3 Fabrication of a Resistor and Diffusion, cont’d
• Two different types of diffusions for IC fabrication
1. Constant-source diffusion (or predeposition)
2. Drive-in diffusion
• Usually the solid-solubility of doping atoms limit the maximum doping
concentration in semiconductors.
• In silicon, it is roughly 4 × 1020 cm-3 for B, 8 × 1020 cm-3 for P, 1.5 ×
1021 cm-3 for As, and 4 × 1019 cm-3 for Sb.
• For the constant-source diffusion, there are the initial and boundary
conditions,
N ( x,0) = 0, N (0, t ) = N 0 , N (∞,0) = 0
• This gives
 x 
N ( x, t ) = N 0 erfc

 2 Dt 
76
(1.36)
(1.37)
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100
10-1
erfc(z)
10-2
10-3
10-4
10-5
0
1
2
3
z=x/2(D t)1/2
77
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1.3 Fabrication of a Resistor and Diffusion, cont’d
• The drive-in diffusion requires the conditions
∫
∞
0
N ( x, t ) dx = Φ, N (∞, t ) = 0
(1.39)
where Φ is the dose of doping atoms that is incorporated into the
semiconductor during the predeposition.
• This gives
 x2 
Φ

exp −
N ( x, t ) =
π Dt
 4 Dt 
(1.40)
• Example 1.9
78
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(a)
100
(b)
N0=const
Φ =const
105
10-1
N/Φ (1/cm)
104
Dt =
0.25µm2
N/N0
10-2
10-3
103
Dt =
0.25µm2
102
0.05µm2
0.05µm2
101
10-4
0.0025µm2
10-5
IC Design MSc
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0.0025µm2
100
0
1
2
3
x (µm)
0
1
2
3
x (µm)
Fig. 1.15 Doping profiles: (a) predeposition, (b) drive-in
79
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1.4 Carrier Mobility
• Two types of carriers in semiconductors: electrons and holes.
• Free electrons and holes can be described by the electron/hole gas
model.
• This simplified model can be used for describing electrons and holes in
semiconductor crystals by introducing the effective mass - m*.
• Usually, m* is smaller than m0 - the free electron mass.
• The origin of the effective mass is due to the interaction between the
electron and the crystal lattice (a set of periodic atoms).
• The kinetic energy of a single carrier is given by
Ekin =
p
2
2m
(1.44)
*
where p = m*v is the carrier momentum.
• In one dimensional case, we have
80
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1.4 Carrier Mobility, cont’d
Ekin
p x2
=
2m*
(1.44' )
• For free carriers, the kinetic energy at temperature T is given by
Ekin
m * vth2
=
2


=


3
kT
2
(1.45)
1
kT
2
where k is the Boltzmann constant, vth is the thermal velocity. For T =
300 K, kT ≈ 0.026 eV, and vth ≈ 1.2 × 107 cm/sec.
This kind of motion is called thermal motion, mainly resulting from
collisions of carriers with defects in semiconductors. This scenario is
illustrated in Fig. 1.17 column (a).
81
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Ekin
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p x2
=
2m*
•-
h
px = m * vx =
kx
2π
Fig. 1.16 E-k dependence of a free electron
82
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1.4 Carrier Mobility, cont’d
• If an electric field is applied to the electron gas, the electric-field force
will affect the motion, which is schematically shown in Fig. 1.17.
• The current I is found to have a relationship with the applied field E,
I = −qnvd A
(1.46)
• Note that the velocity vd is the drift velocity under the field.
• More generally, the current density j (A/cm2) is used, that is,

j=

− qnvd
electrons
(1.47)
+ qnvd
holes
• The drift velocity vd versus E is depicted in Fig. 1.18. A saturation
appears after E is larger than 3 V/µm.
83
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E
Prof. J. B. XU 許建斌
(b)
(c)
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vt
h
Dept. of Electronic Engineering
(a) E=0
E Course of
Foundation
vd
vd=0
II
IIII
vvvd d
d
=0
vdvv=0
d=0
d
III
vd=0
vd
vd
vvvdd
d
Fig. 1.17 Drift velocity under E
I
vd
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Drift Velocity (µm/ps)
Dept. of Electronic Engineering
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T =300K
0.08
0.06
0.04
electrons
holes
0.02
0.00
0
1
2
3
4
5
Lateral Electric Field (V/µm)
Fig. 1.18 Drift velocity versus E in silicon
85
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1.4 Carrier Mobility, cont’d
• Ohm’s law in semiconductors can be rewritten by

j=

qµ n nE electrons
(1.48)
qµ p pE holes
• The drift velocity vd has a relationship with the mobility:
vd

=

− µ n E electrons
(1.49)
+ µ p E holes
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1.4 Carrier Mobility, cont’d
• Due to the nonlinear nature of vd at high fields (see Fig. 1.18), Eq.
(1.49) is only valid under small electric fields.
• Two factors may affect the mobility:
1. the effective mass of the carriers
2. the scattering probability between the carriers and atoms/defects
• The second point implies a smaller mobility for a higher doping level.
This is clearly seen in Fig. 1.19.
• The diffusion current can be described by
jdiff


=


∂n
qDn
∂x
electrons
(1.50)
∂p
− qD p
∂x
holes
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15
-3
104
ND=10 cm
103
10
17
102
10
19
2
Electron Mobility (cm /Vs)
Dept. of Electronic Engineering
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101
0
100
200
300
400
500
Temperature (K)
Fig. 1.19 Temperature dependence of mobility for three different
doping levels in silicon
88
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Si electrons
77 K
27 oC
o
75 C
125 oC
o
175 C
1500
2
Mobility (cm /Vs)
2000
1000
500
0
1015
(a)
1016
1017
1018
1019
1020
Fig. 1.20 Dependence of
mobility on doping level at
different temperature in
silicon
Doping Concentration (cm-3 )
1000
Si holes
77 K
o
27 C
75 oC
o
125 C
175 oC
2
Mobility (cm /Vs)
IC Design MSc
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500
(b)
0
1015
1016
1017
1018
1019
1020
Doping Concentration (cm-3 )
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1.4 Carrier Mobility, cont’d
• The drift and diffusion are two independent current mechanisms in
semiconductors.
• This is nicely demonstrated by the Haynes-Shockley experiment shown
in Fig. 1.22.
• The mobility of holes is given by
vd
L2
µp = =
E t maxV
(1.52)
• The diffusion process gives the widening time of the package ∆t:
4 D p (t max + ∆t )
∆x
∆t =
=
vd
vd
90
(1.53)
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(a) t = 0
flash
of
light
i
N-type Si
A
3
4
x (mm)
-3
14
14
-3
p (x10 cm )
L
2
0.15
0.20
∆t
1
0.10
/vd
0
pmax
tmax=
∆ x= 4Dpt
pmax /e
1.5
imax
-3
0.05
i (nA)
0.5 1.0
imax /e
14
0.0
0.00
(m s)
p (x10 cm )
V
T I M E
8
6
4
2
0
8
6
4
2
0
8
6
4
2
0
(b)
(b)
(c)
V=3 V
L=5 mm
2
A=0.5x2 mm
p (x10 cm )
L
5
0.25
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1.4 Carrier Mobility, cont’d
• Finally, Dp can be determined by setting vd = L / tmax, where tmax and ∆t
can be measured experimentally.
∆t 2 (L / t max )
Dp =
4(t max + ∆t )
2
(1.54)
• The Einstein relation bridges the drift process and diffusion process and
states that
Dn , p
kT
=
µ n, p
q
(1.55)
• This useful relation is valid for low carrier concentration.
92
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1.5 Energy-Band Model
• There are two models to describe semiconductors.
1. Chemical-bond model
2. Energy-band model
• The latter is much more important and should be reviewed thoroughly,
because it is very powerful and frequently used to explain
semiconductor devices.
• Brief review of quantum mechanism:
1. Wave-particle duality
λ = h mv0
(1.56)
2. Energy quantization
r = nh 2πmv
(1.58)
3. Quantum numbers → n, l, ml, ms.
4. Pauli exclusion principle
5. Electron configuration and valance electrons
6. Potential well and energy level
7. Formation of energy band
93
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The basic bond representation of intrinsic silicon. (a) A broken
bond at Position A, resulting in a conduction electron and a hole.
(b) A broken bond at position B.
94
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Dept. of Electronic Engineering
IC Design MSc
Program
The splitting of a degenerate state into a band of allowed energies.
95
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IC Design MSc
Program
Formation of energy bands as a diamond lattice crystal is
formed by bringing isolated silicon atoms together.
96
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Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
(a)
filled electron state
empty electron state
+4
n=3
(c) Si crystal
(b) Si atom
conduction band
0
2
Energy (eV)
3s
potential energy
6
total energy
3p
IC Design MSc
Program
EC
EV
energy gap
-5
valence band
-10
-15
-20
+4
+4
-0.20 -0.10 0.00 0.10
Distance (nm)
broken
covalent
bond
0.20
+4
+4
-0.30 -0.20 -0.10 0.00 0.10
Distance (nm)
97
0.20
0.30
The Chinese University of Hong Kong, 2003
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IC Design MSc
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1.5 Energy-Band Model, cont’d
• A typical situation with the semiconductor materials is that the valenceelectron levels of individual atoms produce two energy bands, so-called
valence and conduction bands.
• The electrons forming the covalent bonds are energetically located in
the valence band. But they are placed in the conduction band when the
bonds are broken.
• The electrons in the conduction band are mobile because there are
many free states in the band.
• Similarly, the holes in the valence band are mobile, whereas the
electrons there are immobile as they form the covalent bonds.
• There is no available energy level between the conduction band bottom
and the valence band top. This energy difference is called the energy
gap, Eg.
• The energy gap depends slightly on the temperature.
98
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1.5 Energy-Band Model, cont’d
• Table 1.5 Energy Gap Values for Different Materials at 300 K
Eg [eV]
λ = hc/Eg= 1.24 / Eg (eV) [µm]
Si
1.12
1.10
Ge
0.66
1.87
GaAs
1.42
0.87
GaN
3.5
0.35
SiO2
9
0.14
Si3N4
5
0.25
5.47
0.23
Carbon
• N-type doping, energy levels of donors
• P-type doping, energy levels of acceptors
99
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Dept. of Electronic Engineering
(a) metal
(b) semiconductor
small
energy gap 1~4 eV
IC Design MSc
Program
(c) insulator
large
energy gap
~9 eV
Fig. 1.24 Energy diagram for a metal (a), a semiconductor (b), and an
insulator (c).
100
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Foundation Course of
Prof. J. B. XU 許建斌
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Schematic energy band representations of (a) a conductor with two
possibilities (either the partially filled conduction band shown at the
upper portion or the overlapping bands shown at the lower portion),
(b) a semiconductor, and (c) an insulator.
101
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1.5 Energy-Band Model, cont’d
• In metals and semiconductors, the probability of an electron to occupy
an energy level E may not be 1.
• This probability is determined by the Fermi-Dirac distribution function.
• If the probability f is known, and there are Nc states per unit volume in
the conduction band, then the concentration of free elections can simply
be calculated by
n = Nc f
(1.59)
where f is given by
1
f =
 E − EF 
1 + exp

 kT 
(1.61)
and EF is a reference energy and called Fermi level or Fermi energy.
102
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Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
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Program
Fermi distribution function F(E) versus (E – EF) for various temperatures.
103
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Foundation Course of
Prof. J. B. XU 許建斌
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IC Design MSc
Program
Intrinsic semiconductor. (a) Schematic band diagram. (b) Density of
states. (c) Fermi distribution function. (d) Carrier concentration.
104
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Dept. of Electronic Engineering
(a)
(b)
1
1.0
10-4
10-6
hole
s
Probability
0.5
300K
10-2
EF
s
electrons
0K
300K
1200K
holes
300K
tron
elec
Probability
IC Design MSc
Program
10-8
10-10
0.0
Energy (0.1eV/div)
Energy (0.1eV/div)
EF
Fig. 1.26 Fermi-Dirac function for electrons (solid lines), and holes
(blue dashed lines, 1-f). (a) for linear scale, (b) for logarithmic scale.
105
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Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
1.5 Energy-Band Model, cont’d
• Fig. 1.26 shows the linear plot (a) and logarithmic plot (b) of f and 1-f.
• Note that the function of 1-f represents the probability for an hole to
occupy the energy level E.
• For an intrinsic semiconductor, it is anticipated that EF is located in the
middle of the energy gap Eg.
• For the intrinsic silicon, the conduction band bottom is about 0.56 eV
above the Fermi level, and the valence band top is about 0.56 eV below
the Fermi level. From Fig. 1.26, this means at these energies that the
probability to find an electron or hole is less than 10-9. In other words,
less than one state in every one billion is occupied by an electron in the
conduction band and by a hole in the valence band.
• If EC-EF>>kT, then the probability to find an electron at the energy EC is

 E − EF
f ( EC ) = 1 + exp C
 kT

−1

 EC − E F 
≅
exp

−

kT 


106
(1.62)
The Chinese University of Hong Kong, 2003
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Prof. J. B. XU 許建斌
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(a) N-type doping
IC Design MSc
Program
(b) P-type doping
C.B.
Eg
Eg
V.B.
+4
+5
+4
+4
+3
+4
Fig. 1.25 Effects of N-type (a) and P-type (b) doping in energydiagram model presentation. C. B. stands for conduction band; V.B.
for valance band.
107
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Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
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Program
Schematic energy band representation of extrinsic semiconductors
with (a) donor ions and (b) acceptor ions.
108
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Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
n-Type semiconductor. (a) Schematic band diagram.
(b) Density of states. (c) Fermi distribution function (d) Carrier
concentration. Note that np = ni2.
109
The Chinese University of Hong Kong, 2003
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Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
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Band diagram showing Fermi level EF and intrinsic Fermi level Ei.
110
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Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
1.5 Energy-Band Model, cont’d
• If EF-EV>>kT, then the probability to find an hole at the energy EV is

 E F − EV
f h ( EV ) = 1 − f ( EV ) = 1 + exp
 kT

−1

 E F − EV 
 ≅ exp −

kT 


(1.63)
• Eq. (1.62) and Eq. (1.63) are not valid for heavily doped
semiconductors.
• Finally, the concentration of electrons is described by
 2π m kT 
 EC − E F 

= 2
n = N c exp −

kT 

 h

*
n
2
3/ 2
 EC − E F 
exp −

kT


(1.64)
• Similarly, the concentration of holes is given by
 E F − EV
p = NV exp −
kT

 2π m kT 



 = 2 h




*
p
2
111
3/ 2
 E F − EV 
exp −
kT 

(1.65)
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
IC Design MSc
Program
1.5 Energy-Band Model, cont’d
• Table 1.6 Effective Density of States for Different Materials at 300 K
Effective Density of States at 300 K (cm-3)
Conduction Band
NC = ACT 3/2
Valence Band
NV = AVT 3/2
Si
2.86 × 1019
1.04 × 1019
Ge
1.0 × 1019
6.0 × 1018
GaAs
4.7 × 1017
7.0 × 1018
• Setting n ≈ ND for N-type doping, and p ≈ NA for P-type doping, the
Fermi energy level is obtained by
EF = EC − kT ln( N C N D )
EF = EV + kT ln( NV N A )
112
N − type (1.66)
P − type (1.67)
The Chinese University of Hong Kong, 2003
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Dept. of Electronic Engineering
IC Design MSc
Program
Energy (0.1eV/div)
(0.1eV/div)
Energy
(b) intrinsic
N-typeSi
SiSi
(a)
(c)
P-type
ECC
EF
EF
EF
E
EVV
ele
ele ctron
ctr
s
o
ele ns
ctr
EF ons
EF
EF
s
e
l
hosles
leo
h
o
h
-15 10-10
-10 10-5
-5
10
-15
10
10
10
Probability
Probability
11
Fig. 1.27 Position of EF for (a) intrinsic semiconductor, (b) N-type
semiconductor, and (c) P-type semiconductor.
113
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1.5 Energy-Band Model, cont’d
EC + EV kT  N C  kT  n 
 +
−
ln
ln 
EF =
2
2  NV  2  p 
(1.66' )
kT  n 
ln 
EF = Ei +
2  p
(1.67' )
EC + EV kT  N C  EC + EV
 ≈
−
ln
(1.68' )
Ei =
2
2  NV 
2
where Ei is the Fermi level of the intrinsic semiconductor and is
approximately located in the middle of the bandgap.
• Using Eqs. (1.64) and (1.65), we find that the product of electron and
hole concentration obeys the Law of Mass Action
 E − EV
np = N c NV exp − C
kT

114

2
=
n
i (T )


(1.68)
The Chinese University of Hong Kong, 2003
Foundation Course of
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IC Design MSc
Program
1.5 Energy-Band Model, cont’d
• Moreover, the the intrinsic carrier concentration ni is described by
 Eg 
ni = N c NV exp −

2
kT


(1.69)
where EC-EV = Eg.
• Using Eqs. (1.64), (1.65), (1.68), we find that the electron and hole
concentrations obey
 EF − Ei 
n = ni exp 

 kT 
 Ei − EF 
p = ni exp 

 kT 
115
(1.69' )
(1.69' ' )
The Chinese University of Hong Kong, 2003
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Prof. J. B. XU 許建斌
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IC Design MSc
Program
1.5 Energy-Band Model, cont’d
• If both donor concentration ND and acceptor concentration NA are not
negligible and very high, the charge neutrality and Eq. (1.68) are
preserved:
n+ N A = p + N D
• we find that
np = ni2

N A − N D  N A − E D 
2
+ 
p=
 + ni 
2
2



2

N D − N A  N D − E A 
2
+ 
n=
 + ni 
2
2



2
116
1/ 2
1/ 2
The Chinese University of Hong Kong, 2003
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IC Design MSc
Program
1.5 Energy-Band Model, cont’d
I. ND-NA >> ni (i.e., N-type)
n= N D − N A
p = ni2 / n
If ND >> NA, n = ND and p = ni2/ND.
II. NA-ND >> ni (i.e., P-type)
p= N A − N D
n = ni2 / p
If NA >> ND, p = NA and n = ni2/NA.
117
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Measured ionization energies (in eV) for various impurities in Si and GaAs. The
levels below the gap center are measured from the top of the valence band and are
acceptor levels unless indicated by D for donor level. The levels above the gap
center are measured from the bottom of the conduction band and are donor levels
unless indicated by A for acceptor level.8
118
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Fermi level for Si and GaAs as
a function of temperature and
impurity concentration. The
dependence of the bandgap on
temperature is shown.9
119
The Chinese University of Hong Kong, 2003
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1.5 Energy-Band Model, cont’d
• The electric potential energy Epot and the electric potential ϕ are linked
by
E pot = − qϕ
(1.70)
where q = +1.6 × 10-19 C.
• The electrical potential energy is a scalar and should have a reference.
Usually, EF or Ei is used for reference.
• If the potential energy is expressed in electron volts, the electric
potential and the potential energy have the same numerical values with a
different sign.
• When a bias voltage is applied to a semiconductor, the electric potential
changes linearly inside the semiconductor. Consequently, the potential
energies of electrons and holes linearly varies inside the semiconductor,
as illustrated in Fig. 1.28. Note that the electric potential energy in the
energy-band model is referenced for electron, not for hole.
120
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R
ϕ0
Fig. 1.28 Three presentations
of a biased resistor, different
in terms of complexity and
depth of insight: (a) resistor
symbol, (b) chemical-bond
model, (c) energy-band model.
Note that the electric potential
energy in the energy-band
model is referenced to
electron, not hole.
ϕ1
I
(a)
V
I
(b)
V
Ekin
IC Design MSc
Program
{
qV
I
(c)
V
121
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Prof. J. B. XU 許建斌
-
Energy
Dept. of Electronic Engineering
-
-
EC
EV
+
px = 2hπ kx
+
+
x
px = 2hπ kx
122
IC Design MSc
Program
Fig. 1.29 The relationship
between E-k and E-x
diagrams. Note that the
electron moves from a
higher energy level to a
lower level. Meanwhile,
its kinetic energy
increases. For the hole, the
scenario is the same.
Please keep in mind that
the diagram is referenced
to the electron, NOT to the
hole.
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
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The parabolic energy (E) vs. momentum (p) curve for a free electron.
123
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A schematic energymomentum diagram
for a special
semiconductor with
mn = 0.25 m0 and
mp = m0 .
124
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1.5 Energy-Band Model, cont’d
• Note that the E-k relationship in Fig. 1.70 also implies the direct
bandgap structure.
• Direct bandgap means for an electron the direct transition from Ec to Ev
is possible without involving the crystal momentum hk/2π of the
electron. The energy involved in such a transition is balanced by the
emission or absorption of a photon, that is, hv = Eg.
• Indirect bandgap means the direction transition from Ec to Ev is highly
impossible. The electron k value (or momentum) is varied during the
transition. The energy involved in such a transition is balanced either by
heat (typically lattice vibration) or a combination of heat and photon
emission. In this case, the probability of photon emission is extremely
low.
• GaAs, InP, GaN, AlGaAs are direct bandgap semiconductors. They are
of technological importance for light emitting devices or photonic
devices.
125
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Energy band structures of Si and GaAs. Circles (º) indicate holes in the
valence bands and dots (•) indicate electrons in the conduction bands.
126
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1.5 Energy-Band Model, cont’d
• In thermal equilibrium the relationship pn = ni2 is valid. If excess
carriers are introduced to a semiconductor so that pn = ni2, we have a
non-equilibrium scenario.
• Generation When a bond is broken, an electron-hole is generated. In
terms of the band diagram, the thermal energy enables a valance
electron to make an upward transition to the conduction band leaving a
hole in the valence band. This is called carrier generation.
• Recombination When an electron makes a transition downward from
the conduction band to the valence band, an electron-hole pair is
annihilated. The reverse process is called recombination.
• Generally, recombination phenomena can be classified as direct and
indirect processes. Direction recombination usually dominates in direct
bandgap semiconductors, while indirect recombination via bandgap
recombination centers dominates in indirect bandgap semiconductors,
such as silicon.
127
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1.6 Heterostructures and Junctions
• Homogeneous semiconductors are not very useful.
• Mostly used semiconductors are junctions composed of
either the same material with different doping concentrations
(homostructure), or the dissimilar materials with desired
doping concentrations (heterostructure).
• Basic junctions: PN junction, metal-semiconductor junction
• They form almost all of solid-state electronic and photonic
devices.
• Other useful structures: metal-insulator-metal (MIM)
structure, metal-insulator-semiconductor (MIS) structure
128
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129
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The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
p
IC Design MSc
Program
n
As+
(a)
e
Bh+
M
Metallurgical Junction
Neutral p-region Eo
Neutral n-region
(b)
M
log(n), log(p)
Wp
Wn
Space charge region
ppo
nno
(c)
ni
pno
npo
x
x=0
ρ net
M
eNd
-Wp
Wn
x (d)
-eNa
Fig. 6.1: Properties of the pn junction.
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca
130
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M
E (x)
-Wp
0
Wn
x
(e)
Eo
V(x)
Vo
(f)
x
PE(x)
eVo
Hole PE(x)
x
(g)
Electron PE(x)
-eVo
Fig. 6.1: Properties of the pn junction. (E0 is the electric field.)
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca
131
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Log(Concentration)
Neutral p-region
Eo - E
Neutral n-region
Minute increase
ppo
nno
(a)
npo
IC Design MSc
Program
pn(0)
Excess electrons
np(0)
Electron
diffusion
Excess holes
Hole
diffusion
pno
SCL
x
x'
(b)
Hole PE (x)
V
M
eVo
e(Vo-V)
W
Wo
x
Fig.6.2: Forward biased pn junction and the injection of minority
carriers. (a) Carrier concentration profiles across the device under
forward bias. (b) The hole potential energy with and without an
applied bias. W is the width of the SCL with forward bias
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca
132
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J
p-region
SCL
n-region
J = Jelec + Jh
Total current
Majority carrier
diffusion and drift
current
Jhole
Jelec
Minority carrier diffusion
current
x
–Wp
Wn
Fig. 6.3: The total current anywhere in the device is
constant. Just outside the depletion region it is due to the
diffusion of minority carriers.
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca
133
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Current
Ge
IC Design MSc
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Si GaAs
~0.1 mA
0 0.2 0.4 0.6 0.8 1.0
Voltage
Fig.6.4: Schematic sketch of the I-V characteristics of Ge, Si
and GaAs pn Junctions
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca
134
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p
IC Design MSc
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n
As+
(a)
e-
Bh+
M
Metallurgical Junction
Neutral p-region Eo
Neutral n-region
(b)
M
log(n), log(p)
Wp
Wn
Space charge region
ppo
nno
(c)
ni
pno
npo
x
x=0
ρ net
M
eNd
-Wp
Wn
x (d)
-eNa
Fig. 6.1: Properties of the pn junction.
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca
135
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Minority Carrier
Concentration
Eo-E
pn(0)
Excess
electrons
Electrons
IC Design MSc
Program
Excess
holes
Holes
np(0)
pno
n po
lp
x'
ln
W
x
V
Fig.6.5: Minority carrier injection and diffusion in a short diode.
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Dept. of Electronic Engineering
Log (carrier concentration)
p-side
n-side
SCL
ppo
Electrons
nM
nno
C
pM
Holes
np(0)
npo
p n(0)
B
A
IC Design MSc
Program
D
Wn
Wp
M
pno
x
V
Fig. 6.6: Forward biased pn junction and the injection of carriers
and their recombination in the SCL.
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Dept. of Electronic Engineering
138
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The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
139
IC Design MSc
Program
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
140
IC Design MSc
Program
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
141
IC Design MSc
Program
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
142
IC Design MSc
Program
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
143
IC Design MSc
Program
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
144
IC Design MSc
Program
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
145
IC Design MSc
Program
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
146
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Program
The Chinese University of Hong Kong, 2003
Foundation Course of
Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
Vo
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Eo
Vacuum
level
Metal
Φm
n-Type Semiconductor
Φn
EFm
Neutral
Metal
Depletion region semiconductor
χ CB
Ec
EFn
region
W
Φm- Φn
Ev
Φm- Φn=eV0
VB
EFm
ΦB
CB
Ec
EFn
Ev
Before Contact
VB
After Contact
Fig. 5.39: Formation of a Schottky junction between a metal and an
n-type semiconductor when Φ m > Φ n.
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Dept. of Electronic Engineering
V
Metal
Vr
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n-Type Semiconductor
e(V0-V)
CB
Ec
ΦB
Ev
e ( V 0 + V)
CB
Ec
Ev
VB
VB
(a) Forward biased Schottky
junction. Electrons in the CB of the
semiconductor can eadily overcome
the small PE barrier to enter the
metal.
I
(b) Reverse biased Schottky junction.
Electrons in the metal can not easily
overcome the PE barrier ΦB to enter the
semiconductor.
1 mA
1 µA
10 µA
0.2 V
V
(c) I-V Characteristics of a Schottky junction exhibits rectifying properties
(negative current axis is in microamps)
Fig. 5.40: The Schottky junction.
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Prof. J. B. XU 許建斌
Dept. of Electronic Engineering
hυ >Eg
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Program
Neutral n-type
Depletion semiconductor
Metal region
region
W
CB
Ec
EFm
Ev
VB
Vo
Eo
W
External Load
Fig. 5.41: The principle of the Schottky junction solar cell.
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Dept. of Electronic Engineering
hυ >Eg
IC Design MSc
Program
Vo+Vr
E >> Eo
iphoto
Metal
W
n-Si
Sampling
Resistor, R
Vr
Fig. 5.42: Reverse biased Schottky photodiodes are frequently
used as fast photodetectors.
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Φm
CB
Φn
EFm
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Ec
EFn
Ev
VB
n-type Semiconductor
Metal
Before Contact
Accumulation Region Bulk Semiconductor
Ohmic Contact
CB
Ec
EFn
EFm
Ev
VB
Metal
n-type Semiconductor
After Contact
Fig. 5.43: When a metal with a smaller workfunction than an n-type
semiconductor are put into contact, the resulting junction is an ohmic
contact in the sense that it does not limit the current flow.
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