ECE 6466 “IC Engineering”
Dr. Wanda Wosik
Chapter 1
Review of Devices; cnt’d
:
Silicon VLSI Technology
Fundamentals, Practice and Modeling
by J. D. Plummer, M. D. Deal,
and P. B. Griffin
UH; F2014
Review: materials and devices
(after Streetman & Kano)
Semiconductors: Si, Ge, and Compound (III-V, II-VI)
Four valence
electrons
Covalent bonding:
no free electrons at
0K
N-type dopants
P-type dopants
Dopants have
• to be compatible with processing (ex. slow
diffusion through oxide)
• to have high solubility in Si
Intrinsic Semiconductor
Electron and hole generation occur at
elevated temperature (above 0K).
n=p
Energy Band Gap determines the intrinsic carrier
concentration. ni EgGe< EgSi< EgGaAs
For devices we need concentrations: n and p>>ni
N- and p-type semiconductor
n≈ND
p≈NA
Ingot crystal
Possible dopant deactivation
& defect formation
Resistivity as a Function of Dopant Concentration
r=1/(qµnn+qµpp)
µ carrier mobility
depends on scattering
i.e. dopants, lattice
imperfections (defects)
and vibration
(temperature)
µn>µp
Electrical Properties of Semicondutors
Explained by a Band Model and Bond Model
Intrinsic (Undoped) Silicon
Energy Gap
n=p
T>0K
n=p=ni
Electrical Properties of Semicondutors Explained by a Band Model and Bond Model
n-type Silicon doped with As
n=NAs
Very small
ionization
energies ED and
EA
moves
Dopant Ionization
n-type semiconductor
nn>>pn
ni≈pi
intrinsic
semiconductor
ni=1.45x1010cm-3 at RT (300K)
Distribution of Free Carries (electrons and holes) Obeys Pauli Exclusion Principle
Fermi Dirac probability function:
1
F(E) =
E - EF
1+ exp(
)
kT
Intrinsic Semiconductor
Fermi level is the energy at which the
probability of finding an electron F(E) is 0.5
n-type Semiconductor
n=Nd
p=type Semiconductor
Conduction Band
Majority
carriers
EF ≈Eg/2
below Ei
above Ei
Majority
carriers
Valence Band
p=Na
Carriers’ Statistics
¥
1
n = ò F(E)N(E)dE @NC
E - EF
EC
1+ exp(
)
kT
Effective density of states NC and NV
2pm*e 3 / 2
NC = 2( 2 )
h
EV
p = ò [1- F(E)]N(E)dE @NV exp(-¥
E F - EV
)
kT
F-D statistics becomes Boltzmann if E-EF>>kT (low doped)
Pauli exclusion principle important here
Energy
n=niexp(EF-Ei/kT)
Parabolic
density of
states
np=ni2
2pm*h 3 / 2
NV = 2( 2 )
h
p=niexp(Ei-EF/kT)
Density of states
Probability function
Density of electrons
and holes
Carrier Concentrations
n= Ncexp[-(EC-EF)/kT]=niexp(EF-Ei/kT)
EC
EF
p= Ncexp[-(EF-EV)/kT]= niexp(Ei-EF/kT)
Heavy doping moves EF to EC
EG= EC-EV Band gap
EV
np=ni2 =NCNVexp(-EG/kT)=KT3exp(- EG/kT)
For small dopant concentrations or close to the intrinsic conditions (ex. at processing
temperatures) charge neutrality should be used:
ND++p=NA-+n then
n=1/2[N+D- N-A)+√(N+D - N-A)2+4ni2]
p=1/2[N-A -N+D)+√(N-A - N+D)2+4ni2]
EG shrinks with T
Energy Band Dependence on Temperature
Larger temperature weakens the
bonding between atoms causing
the band gap energy EG (energy
needed to free e-h pairs) to
decrease
EG(eV)=1.17-4 -4. 73x10-4T2/(T+636)
≈1.16 - (3x10-4)T
EF
Example: doping by As and B results in p-type
Si at RT
Energy levels for shallow
dopants are close to the
majority carrier bands
RT
1000°C
and in intrinsic Si at 1000°C
n≈p≈ni at 1000°C
p>>n
Recombination of Carriers
Si is an indirect semiconductor so indirect recombination (Shockley-Read-Hall) occurs
through traps located in the mid-gap
intrinsic Si
n-type Si; a trap (below EF) is always filled
with electron=majority carrier and waits
for a minority hole.
tR=1/svthNt
lifetime
capture cross section
thermal velocity, and traps
Carier Recombination and Generation
Traps (defects,metal impurities) present in silicon act either to annihilate carriers (recombination)
or produce (generation) them.
SRH recombination/generation rate
2
i
U=
np - n
ET - E i
t ( p + n + 2ni cosh(
))
kT
np>ni2 U>0 recombination
np<ni2 U<0 generation
lifetime tr≠tg
Umax for ET=Ei
Surface of Si with traps lead to the surface recombination velocity, which affects carrier lifetime
s=svthNit
s(np - n )
U=
ET - E i
p + n + 2n i cosh(
)
kT
2
i
Semiconductor Devices
p-n Diodes
n+ for low resistance
Reverse biased diode
Forward biased diode
after Kano, Sem. Dev.
p-n Diodes at Thermal Equilibrium
Dopants’ positions
are fixed
Majority
holes
Minority
holes
Minority
electrons
Majority
electrons
Carriers move and create
depletion layers
after Kano, Sem. Dev.
p-n Diodes at Thermal Equilibrium
At thermal equilibrium charge neutrality
qN+dxn=qN-Axp leads to asymmetrical depletion layers
Electric field
only in the
depletion layer
Uncompensated acceptors and
donors
p-n Diodes at Thermal Equilibrium
Build-in voltage determined by doping on
both sides of the p-n junction
n0n≈ND
p0n≈ni2/ND
No current flows at thermal equilibrium
after Kano, Sem. Dev.
p-n Diodes Under Bias
Reverse biased diode
I
(- +)
V
Minority electrons and holes drift
(small current)
Majority electrons (and holes) diffuse,
become minority carriers and produce large current
Forward biased diode
(+ -)
I
I~exp(qV/kT)
holes
V
after Kano, Sem. Dev.
p-n Diodes Under Forward Bias
Depletion layer shrinks
Electric field decreases
Junction potential decreases by Va
J
Energy barrier decreases by qVa
J~exp(qVa/kT)
after Kano, Sem. Dev.
p-n Diodes Under Reverse Bias
Depletion layer spreads mainly to the low doped side
Electric field increases
Junction potential increases by Va
Energy barrier increases by qVa
J 0A
after Kano, Sem. Dev.
Junction at Thermal Equilibrium
Minority and majority carriers
Boltzman
approximation
Built-in voltage
E=
1 dE i
q dx
E =-
E-field is where Ei=f(x)
df
E
;f = - i
dx
q
potential
Fermi potentials Electrostatic
in
n and p-regions
Poisson’s
r
e 0e Si
divE =
equation:
E peak
2Vb
=
xd
p-n Diodes Under Bias
Carrier
Injection and Extraction
No recombination
assumed in the
SCR
Current distribution in a p-n diode
For the forward biasing condition
after Neudeck
Breakdown of a p-n Diode
Zener effect
Avalanche effect
after Kano and Streetman
Breakdown Voltage of a p-n Diode
Eg 
5-7V
• Ebr field increases with ND but not very much
• Wdepl~1/√ND
Vbr=Ebr•Wdepl so Vbr decreases with ND
after Kano and Streetman
Transistors for Digital and Analog Applications
MOSFET and Bipolar Junction Transistors
Bipolar Transistors
E-B junction is forward biased=injects minority carriers to the base
Base (electrically neutral) is responsible for electron transport via diffusion (or drift also if the build in
electric field exists) to collector
C-B diode is reverse biased and collects transported carries
VBE>0
VBC<0
IE
IC
IB
IE=IEn+IEp
IC=aIE
IB=IEp+Irec
a<1
Bipolar Junction Transistors
p-n-p
Individual device
n-p-n
Integrated circuit BJT
Bipolar Junction Transistors
Forwards bias
Reverse bias
minority carriers
Injected
electrons
holes
Extracted
electrons
Bipolar Junction Transistors
Currents’ Components
small
Bipolar Junction Transistors
Early Effect
Forward Operation Mode
Early Voltage
Bipolar Junction Transistors
Breakdown Voltages
Common Emitter
Common Base
Collector-Base junction
Bipolar Junction Transistors
Current Gain b =a/1-a
b=IC/IB
Kirk Effect
Recombination in the E-B Space Charge Region
Gummel Plot
Bipolar Junction Transistors and a Switch
Schottky
Diode used in
n-p-n BJTs for
faster speed
MOS Field Effect Transistors (MOSFET)
NMOS and PMOS (used in CMOS circuits)
VG>VT to creates
strong inversion
Oxide
depletion
Operation of NMOS-FET
Linear Region, Low VD
Saturation Region, Channel Starts to Pinch-Off
Saturation Region,
channel shortens beyond pinch-off, L’<L
Operation of MOS-FET
ID(VD)
Channel-Length-Modulation
(Shorten by Depletion Layer)
ID=kp[(VG-VT)VD-VD2/2
Device transconductance kp=µnCoxW/L is larger for NMOS than PMOS
In CMOS for compensation of the mobility differences use Wp>Wn
Scaled Down NMOS
Drain Induced Barrier Lowering (DIBL)
Proximity of the drain
depletion layer
charge
sharing
DIBL
Modern MOS Transistors
Gate
Source
LDD used to reduce the electric field
in the drain depletion region and
hot carrier effects
Self aligned contacts decrease the resistance
LDD
isolation
Drain
Semiconductor Technology Families
First circuits were based on BJT as a switch because MOS circuits limitations
related to large oxide charges
isolation
BL
n-p-n
NMOS and CMOS Technologies
Enhancement NMOS
NMOS
Depletion NMOS
PMOS
1970s
1980s and beyond
Smaller power
consumption
Challenges For The Future
• Having a “roadmap” suggests that the future is well defined and there are
few challenges to making it happen.
• The truth is that there are enormous technical hurdles to actually achieving
the forecasts of the roadmap. Scaling is no longer enough.
• 3 stages for future development:
“Technology Performance Boosters”
Invention
Gate
Source
Drain
• Spin-based devices
• Molecular devices
• Rapid single flux quantum
• Quantum cellular automata
• Resonant tunneling devices
• Single electron devices
???
Materials/process innovations
NOW
Beyond Si CMOS
IN 15 YEARS??
Device innovations
IN 5-15 YEARS
Plummer et al.
The traditional finFET (upper left), a trigate on SOI (upper right), trigate on bulk silicon
(lower left) and a pseudo-trigate on SOI (lower right). (Source: Texas Instruments)
itrs
Broader Impact of Silicon Technology
Tip on Stage
Part of 12 x 12 array
Individual Actuator
Cornell University
0.0
-0.5
Drain
Source
-0.5V
-0.75V
-1V
1.25
V
-1.5V
SiO2
Gate
Id s (A)
-1.0
-1.5
-1.75V
-2.0
-2.5
-3.0x10
-2V
-2.25V
-6
-1.4
-1.2
-1.0
-0.8
-0.6
-2.5V V (V)
D
-0.4
-0.2
0.0
Stanford, Cornell
• Many other applications e.g. MEMs and many new device structures e.g. carbon
nanotube devices, all use basic silicon technology for fabrication.
46 et al.
Plummer
Summary of Key Ideas
• ICs are widely regarded as one of the key components of the information age.
• Basic inventions between 1945 and 1970 laid the foundation for today's
silicon industry.
• For more than 40 years, "Moore's Law" (a doubling of chip complexity every
2-3 years) has held true.
• CMOS has become the dominant circuit technology because of its low DC
power consumption, high performance and flexible design options. Future
projections suggest these trends will continue at least 15 more years.
• Silicon technology has become a basic “toolset” for many areas of science and
engineering.
• Computer simulation tools have been widely used for device, circuit and system
design for many years. CAD tools are now being used for technology design.
• Chapter 1 also contains some review information on semiconductor materials
semiconductor devices. These topics will be useful in later chapters of the text.
Plummer et al.