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7/31/2019 Lecture 3 Given [Compatibility Mode]
1/23
EL 511
VLSI Design
Instructor:
Mazad S. Zaveri
Faculty Block 4, Room 4206
ma : maza _zaver a c .ac. nhttp://intranet.daiict.ac.in/~mazad_zaveri/
EL 511 VLSI Design
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7/31/2019 Lecture 3 Given [Compatibility Mode]
2/23
We will have a Quiz-1 today. (10 minutes)
Homework-1 has been posted
Gate-length 45 nm 32 nm =
45*0.7 nm
22 nm =
45*0.7*0.7 nm
Year 2009 2011 2013
Generation x Next after x next after (next after x)
EL 511 VLSI Design
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7/31/2019 Lecture 3 Given [Compatibility Mode]
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-1. A software has 500 lines of code. Of
, ,
100 lines can run only sequentially.
a s e max mum spee -up max
How many processors are needed to- . max
2. What is the reason behind using high-k
ga e-ox e n newer genera on o n eprocessors? Briefly explain, atleast two
EL 511 VLSI Design
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reasons.
7/31/2019 Lecture 3 Given [Compatibility Mode]
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Conceptual Energy Band ModelElectron
Ec
Energy (E)
Ev
When silicon atoms come
New electron energy band modelis created
EL 511 VLSI Design
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of the band model
7/31/2019 Lecture 3 Given [Compatibility Mode]
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E = Conduction Band
Electron
Energy (E)
(starting) level Ev = Valence Band
Ec
Ev
Conduction Band
Band Gap
en ng eve
EG = Energy band gap
Valence Band
No Allowed states
EG = Ec Ev
E= Electron energy Unit is electron-volt (eV)
EL 511 VLSI Design
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Types of Carriers- Electron & HoleWhen no bonds in the (lattice) or bondingmodel are broken, there are no carriers
(In terms of energy band model) No carriers
are present Valence band is completely filled
When Si-Si bond breaks, the associated electron
with electrons; and Conduction band is devoid
of any electrons
s ree o wan er n e a ce, e re ease
electron is a carrier
(In terms of energy band model) Excitation of
carrier Electrons in conduction band are carriers
When Si-Si bond breaks, in addition to electron
release we have a missin bond void in the
lattice). Nearby electrons may jump to fill this
bond, creating a void in a new place. This void is
called Hole
EL 511 VLSI Design
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(In terms of energy band model) Flow of void in
the valence band, due to motion of electrons inthe valence band
7/31/2019 Lecture 3 Given [Compatibility Mode]
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Material Classification based on Band Gap
Insulator
Bad conductor large energy band gap (EG)
Semiconductor on uc s on y w en exc a on energy s prov e s G
between the EG of metal and insulator Metal Good conductor Very narrow EG
Electron-volt (eV) is an unit of
energy equal to 1.6 x 10-19joules
EL 511 VLSI Design
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electron = 1.6 x 10-19 coulomb
7/31/2019 Lecture 3 Given [Compatibility Mode]
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Carrier numbers in Intrinsic Semiconductor
Intrinsic semiconductor
Extremely pure semiconductor
Without any externally added impurity (dopants)
n= number of electrons/cm3
p= number of holes/cm
In intrinsic semiconductor, Underequilibrium conditions
Electron concentration = hole concentration
n= = n
For silicon (at room temp), ni = 1 x 1010 / cm3
Holes and electrons are created only in pairs in intrinsic
semiconductors
EL 511 VLSI Design
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7/31/2019 Lecture 3 Given [Compatibility Mode]
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Doping manipulation of carrier numbers
Doping Means the addition of controlled amounts of specific
Why? Purpose of increasing either the electron or the hole
concentration
How? Replace some Si atoms with some dopant atoms
Density of Si atoms in the Si crystal is 5 x 1022 / cm3
ope sem con uc or s ca e x r ns csemiconductor
To increase electron concentration
Use Donors (Column V elements in periodic table) P (Phosphorus), As (Arsenic), Sb (Antimony)
To increase hole concentration
EL 511 VLSI Design
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se ccep ors o umn e emen s n per o c a e B (Boron), Ga (Gallium), In (Indium)
7/31/2019 Lecture 3 Given [Compatibility Mode]
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Donor (n-type material) Column V elements
Have five valence electrons
,
Si atom with a donor atom Four out of five electrons of the donor
are use n orm ng our on s sotightly bound
Fifth electron is loosely bound to
Can be easily released at roomtemperature acts as a carrier
If released from the donor site leaves
P+
behind a +ve charged donor ion Donor ion cannot move around in the
crystal
EL 511 VLSI Design
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7/31/2019 Lecture 3 Given [Compatibility Mode]
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Acceptor (p-type material) Column III elements
Have 3 valence electrons
Inside a silicon crystal, we replace Sia om w an accep or a om Three electrons of the acceptor will form three
out of four bonds
Electron from other nearby Si-Si bond, will be
taken or accpeted and the incomplete bond
will be completed ,
will now have a missing bond, and will act as ahole
The acceptor atom, accepted an electron so will
Holes can be easily formed at room temperature acts as a carrier
Acceptor ion cannot move around in the crystal -
EL 511 VLSI Design
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-
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Donor and Acceptor
Visualization in terms of energy band model Donor
Weekly bound electrons are in a donor site
Need only about 0.05 to 0.1eV to excite and jump to conduction band
Donor
A new electronic level (EA )is introduced in the forbidden gap, above Ev Electrons from valence band will excite/jump to this new level, creating holes
Acce tor
EL 511 VLSI Design
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Fermi Function 1= erm unc on
Specifies, under equilibrium
( ) /1 F
E E kTe +
,
an available state at an EnergyE will be occupied by an
EF = Fermi Level or Fermi energy
k= Boltzmann constant
k= 8.617 x 10-5 eV/K
T= Temperature in Kelvin (K)
Indicates the relative
concentration of electrons in
EL 511 VLSI Design
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7/31/2019 Lecture 3 Given [Compatibility Mode]
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Semiconductor classification based on Fermi-level
Intrinsic Fermi level Lies in the middle of ener band a
Ei = (Ec + Ev )/2 and Ei = EF
N-type semiconductor F > i
P-type semiconductor E < E
EL 511 VLSI Design
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Carrier distributions
N-type
conduction band
( ) ( )c
g E f E
Intrinsic
Distribution of holes
(unfilled states) in valence
band
( ) 1 ( )vg E f E
P-type
EL 511 VLSI Design
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n= number of electrons/cm3
p= number of holes/cm3
In intrinsic semiconductor n= p= ni
Ei EF and np ni
Use these equations to find the electron and holeconcen ra ons
Valid only under equilibrium conditions of the semiconductor
( ) /F iE E kT
in n e= ( ) /i FE E kTip n e
=2
inp n=
EL 511 VLSI Design
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Intrinsic carrier concentration
As temperature increases, thenumber of intrinsic carriers increase
But for intrinsic carriers n= p= ni
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Charged entities in an extrinsic semiconductor
Electron (n) and +ve charged donor ions (ND)
Holes (p) and ve charged acceptor ions (NA)
For an extrinsic semiconductor Assuming both type of dopants (donor and acceptors)
Uniformly doped semiconductor
Assuming equilibrium conditions No electric fields (built-in or external)
This semiconductor is charge-neutral
0D A
p n N N+ + =
Only some dopant atoms are ionized
EL 511 VLSI Design
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D A Valid forT> room temp
When all dopant atoms are ionized
7/31/2019 Lecture 3 Given [Compatibility Mode]
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The eneral case
Assume both types of dopants in the semiconductor For simplicity, assume that all dopant atoms are
on ze room emp
1/ 22
2
1/ 2
2 2
D A D Ai
n n
= + +
2
2 2
i A D A Di
n N N N N p nn
= = + +
EL 511 VLSI Design
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Electron-Hole concentration from doping
concen ra ons
D A
D i
N N
N n
2
D
inpN
=
use
When
A DN N Ap Nuse
A iN n2
i
A
nn
N=
When
EL 511 VLSI Design
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Electron-Hole concentration from doping
concen ra onsuse
When n N N
The above condition can also occur with increasing temperature.
in the intrinsic carrier concentration. At sufficiently high temperatures niwill
eventually equal and then exceed net doping concentration
All semiconductors become intrinsic at sufficientl hi h tem eratures
1/ 2
useWheni A Dn N N
2
1/ 222
2 2D A D A
iN N N Nn n
n N N N N
= + +
EL 511 VLSI Design
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2 2i
p nn
= = + +
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Position of Fermi-level from do in concentration
useWhen DN =D A
N NF i
i
n
D iN n
Whenln Ai F
i
E E kTn
=
A D
A iN n
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Temperature dependence of carrier concentrations
Plot is for phosphorus ND = 1015/cm3
ambient temperature, causes
monotonic increase in the
intrinsic carrier concentration. At
sufficiently high temperatures ni
will eventually equal and thenexceed net doping concentration
All semiconductors become
intrinsic at sufficiently high
temperatures
-123C 0C27C
C = K - 273
EL 511 VLSI Design
23(= -273C)