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Atomic Orbitals. s -orbitals. p -orbitals. d -orbitals. H B. H A. H A - H B. = H 2. Chemical Bonding. Overlap of half-filled orbitals - bond formation. Formation of Molecular Hydrogen from Atoms. Overlap of filled orbitals - no bonding. Periodic Chart. Crystal Bonding. - PowerPoint PPT Presentation
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Microelectronic Device Fabrication I (Basic Chemistry and Physics of
Semiconductor Device Fabrication)
Physics 445/545
David R. Evans
Atomic Orbitals
s-orbitals p-orbitals
d-orbitals
BE
*
s,p,d,etc. s,p,d,etc.
BE
*
s,p,d,etc. s,p,d,etc.
Chemical Bonding
Overlap of half-filled orbitals - bond formation
Overlap of filled orbitals - no bonding
HAHB
HA - HB = H2
Formation of Molecular Hydrogen from Atoms
Periodic Chart
Conduction Band
Valence Band
Egs3
p3
sp3
Si(separated atoms)
EV
EC
Si(atoms interact to formtetrahedral bonding geometry) Si crystal
Crystal Bonding
sp3 bonding orbitals
sp3 antibonding orbitals
Silicon Crystal Bonding
Semiconductor Band Structures
Silicon
Germanium
Gallium Arsenide
Eg
NE
EN
VV
CC
EF
Conduction Band
Valence Band
Intrinsic Semiconductor
Aggregate Band Structure
Fermi-Dirac Distribution
n-type Semiconductor
Aggregate Band Structure
Fermi-Dirac Distribution
Eg
NE
EN
VV
CC
E i
EF
Conduction Band
Valence Band
Shallow Donor States
Donor Ionization
p-type Semiconductor
Aggregate Band Structure
Fermi-Dirac Distribution
Eg
NE
EN
VV
CC
Ei
EF
Conduction Band
Valence Band
Shallow Acceptor States
Acceptor Ionization
Temperature Dependence
Fermi level shift in extrinsic silicon
Mobile electron concentration (ND = 1.15(1016) cm3)
Carrier Mobility
Carrier drift velocity vs applied field in intrinsic silicon
No Field Field PresentPictorial representation of carrier trajectory
Effect of Dopant Impurities
Effect of total dopant concentration on carrier mobility
Resistivity of bulk silicon as a function of net dopant concentration
The Seven Crystal Systems
Bravais Lattices
Diamond Cubic Lattice
a = lattice parameter; length of cubic unit cell edgeSilicon atoms have tetrahedral coordination in a FCC (face centered cubic) Bravais lattice
Miller Indices
O
z
y
x
O
z
y
x
O
z
y
x
100
110
111
Diamond Cubic Model
100
110
111
Cleavage Planes
Crystals naturally have cleavage planes along which they are easily broken. These correspond to crystal planes of low bond density.
100 110 111
Bonds per unit cell 4 3 3
Plane area per cell a2 22a 232a
Bond Density 24
a 221.2
223
aa 22
8.332aa
In the diamond cubic structure, cleavage occurs along 110 planes.
[100] Orientation
[110] Orientation
[111] Orientation
[100] Cleavage
[111] Cleavage
Czochralski Process
Seed Rod (Single Crystal Si)
dia. = ~1 cm
Czochralski Process Equipment
Image courtesy Microchemicals
Czochralski Factory and Boules
CZ Growth under Rapid Stirring
x=0
dxCs
Cl
Distribution Coefficients
0.01
0.1
1
10
0 0.2 0.4 0.6 0.8 1
Length Fraction
Dop
ant
Con
cent
rati
on R
atio
0.5
0.9
0.3
0.2
0.10.05 0.01
CZ Dopant Profiles under Conditions of Rapid Stirring
Enrichment at the Melt Interface
Si Ingot
Heater
Zone Refining
Ingot slowly passes through the needle’s eye heater so that the molten zone is “swept” through the ingot from one end to the other
Single Pass FZ Process
x=0 dx
L
x
C s C o
0.01
0.1
1
0 2 4 6 8 10
Zone Lengths
Dop
ant
Con
cent
rati
on R
atio
0.5
0.9
0.30.2
0.1
0.03
0.01
Multiple Pass FZ Process
0.01
0.1
1
0 2 4 6 8 10 12 14 16 18 20
Zone Lengths
Dop
ant
Con
cent
rati
on R
atio
0.50.9 0.3 0.2
0.1
0.03
0.01
Almost arbitrarily pure silicon can be obtained by multiple pass zone refining.
Vacancy (Schottky Defect)
“Dangling Bonds”
Self-Interstital
Dislocations
Edge Dislocation
Screw Dislocation
Burgers Vector
Screw Dislocation
Edge Dislocation
Dislocations in Silicon
[100]
[111]
Stacking Faults
Intrinsic Stacking Fault
Extrinsic Stacking Fault
Vacancy-Interstitial Equilibrium
Formation of a Frenkel defect - vacancy-interstitial pair
IVL
“Chemical” Equilibrium
]][[ IVKeq
Thermodynamic Potentials
E = Internal EnergyH = Enthalpy (heat content)
A = Helmholtz Free EnergyG = Gibbs Free Energy
For condensed phases: E and H are equivalent = internal energy (total system energy) A and G are equivalent = free energy (energy available for work)
T = Absolute TemperatureS = Entropy (disorder)
A E TS
WlnkS
Boltzmann’s relation
Vacancy Formation
eV 3.2~ vE
A M E T SMv v Mv
MvMv kS Wln
WMv
N
N M M
!
( )! !
!)!(
!lnWln
MMN
NkkS MvMv
)ln()( MNkTMN
MMkTNNkTEMA vMv lnln
Additional Vacancy Formation
M
A E kT M kT N MMv v ln ln( )
kT
ENM vexp
Vacancy “concentration”
Equilibrium Constant
Interstitial “concentration”
NN8
5
kT
EN
kT
ENM ii exp
8
5exp
kT
EENK iv
eq exp8
5 2
Internal Gettering
OO
O
OO
O
OO
O
O
O
O
O2O2
O2
O2
O2denuded zone
Gettering removes harmful impurities from thefront side of the wafer rendering them electricallyinnocuous.
oxygen nuclei
oxide precipitates(with dislocations and stacking faults)
High temperature anneal - denuded zone formation
Low temperature anneal - nucleation
Intermediate temperature anneal - precipitate growth
Oxygen Solubility in Silicon
1.0E+17
1.0E+18
1.0E+19
900 1000 1100 1200 1300
Temperature, deg C
Inte
rsti
tial
Oxy
gen
Con
cent
rati
on,
per
cm3
Oxygen Outdiffusion
Precipitate Free Energy
a) - Free energy of formation of a spherical precipitate as a function of radiusb) - Saturated solid solution of B (e.g., interstitial oxygen) in A (e.g., silicon crystal)c) - Nucleus formation
Ar
n E nT S g r 4
34
32
2 2
SiO SiO
rgSnTEnrAr
8422 SiOSiO
2
Critical Radius
a) – If critical radius exists, then a larger precipitate grows largeb) – If critical radius exists, then a smaller percipitate redissolves
gSnTEnrcrit
22 SiOSiO
2
Substrate Characterization by XRD
Constructive Interference Destructive Interference
Bragg pattern - [hk0], [h0l], or [0kl]
Wafer Finishing
Schematic of chemical mechanical polishing
Spindle
Pad
Table
Wafer Insert
Carrier
Capture Ring
Ingot slicing into raw wafers
Vapor-Liquid-Solid (VLS) Growth
substrate substrate
SiH4 SiH4
H2 H2 H2 H2
substrate
catalyst
Si nanowires grown by VLS (at IBM)
Gold-Silicon Eutectic
A B
liquid
solid
A – eutectic melt mixed with solid gold
B – eutectic melt mixed with solid silicon
Silicon Dioxide Network
Silanol
Non-bridgingoxygen
SiO4 tetrahedron
Thermal Oxidation
Thermal SiO 2 Film
F1
Si Substrate Gas
F2
F3
C
x
CGCS
Co
Ci
One dimensional model of oxide growth
Deal-Grove growth kinetics
Steady-state Fluxes
)(1 SGG CChF Mass transport flux
)(2 io CC
x
DF
Diffusion flux
isCkF 3
Reaction “flux”
1) Diffusion flux is “in-diffusion”. Any products, e.g., H
2, must “out-diffuse”.
However, out-diffusion is fast and generally not limiting.2) Mass transport is generally never limiting.
S
o
C
CH
Henry's Law
Distribution equilibrium (Henry's Law)
Reaction = Mass Transport
H
CChCk o
GGis
H
C
h
CkC o
G
isG
Steady-state Concentrations
Reaction = Diffusion
)( iois CC
x
DCk
Gas phase concentration related to reaction concentration
i
so C
D
xkC
1
i
s
G
sG C
HD
xk
Hh
kC
1
Deal-Grove Model
Relationship between thickness and time:
Gs
G
Gs h
H
ktt
ND
HC
h
H
kDx
1)(
210
2
What if an oxide of thickenss, x0, is
already on the wafer?Must calculate equivalent growth time under desired conditions
1
3 1
D
xk
h
HkHCk
dt
dxNF s
G
sGs
02
00
12
2x
h
H
kDx
DHC
Nt
GsG
Deal-Grove Rate Constants
B/A => Linear Rate Constant
B => Parabolic Rate Constant
Gs h
H
kDA
12
N
DHCB G2
Gs
G
hHkN
C
A
B
11
Oxidation Kinetics
Reactant
Product
Transition
Ea
E
Energy‡
Process Coordinate
Process B/A for [100] B/A for [111] B
Dry Oxidation 1.03(103) kTe
00.2 1.73(103)
kTe00.2
0.214 kTe
23.1
Steam Oxidation 2.70(104) kTe
05.2 4.53(104)
kTe05.2
0.107 kTe
79.0
Note: Activation energies are in eV’s, B/A is in m/sec, B is in m2/sec
Rate constants for wet and dry oxidation on [100] and [111] surfaces
Linear Rate Constant
Orientation dependence for [100] and [111] surfaces affects only the “pre-exponential” factor and not the activation energy
Parabolic Rate Constant
No orientation dependence since the parabolic rate constant describes a diffusion limited process
Pressure Dependence
Oxidation rates scale linearly with oxidant pressure or partial pressure
Rapid Initial Oxidation in Pure O2
This data taken at 700C in dry oxygen to investigate initial rapid oxide growth
1
2
2 1
EF1
EF2
EF
Evac
=
Metal-Metal Contact
Metal 1 Metal 2
Metal-Silicon Contact
EFSi
M
EF
Evac
EFM
Ec
Ev
Si
MSi
Metal Silicon
Effect of a Metal Contact on Silicon
Ec
Ev
FEF
Ei
Ec
Ev
F
EF
Ei
Depletion (p-type) Inversion (p-type)
Ec
Ev
F
EF
Ei
Ec
Ev
FEF
Ei
Accumulation (n-type) Flat Band (n-type)
Ec
Ev
FEi
EF
Depletion (n-type)
Metal-Oxide-Silicon Capacitor
EV
EC
EFSi
M
EF
Evac
EFM
Si
MSi
SiO2
Metal SiliconSilicon Dioxide
MOS Capacitor on Doped Silicon
EV
EC
EFM
EiFEFSi
EV
EC
EFM
Ei
FEFSi
Depletion (p-type) Accumulation (n-type)
Vg
0 vSchematic of biased MOS capacitor
EV
EC
FEiEi
EFSi
EFM
EV
EC
EFM
FEi
EFSi
Accumulation (p-type) Inversion (n-type)
EV
EC
EFM
EiFEFSi
EV
ECEFM
FEi
EFSi
Depletion (p-type) Depletion (n-type)
EV
EC
EFM
EiFEFSi
EV
EC
EFM
F Ei
EFSi
Inversion (p-type) Accumulation (n-type)
Biased MOS Capacitors
CV Response
n-type substrate
p-type substrate
0
1
2
3
4
5
6
7
8
9
10
-100 -50 0 50 100
Bias Voltage
Ca
pa
cit
an
ce
quasistatic
high frequency
depletion approximation
0
1
2
3
4
5
6
7
8
9
10
-50 -40 -30 -20 -10 0 10 20 30 40 50
Bias Voltage
Ca
pa
cit
an
ce
quasistatic
high frequencydepletion
approximation
Surface Charge Density
1
10
100
1000
10000
100000
1000000
10000000
-30 -20 -10 0 10 20 30
Bias Voltage
Su
rfa
ce
Ch
arg
e D
en
sit
y
inversion
accumulation
depletion
1
10
100
1000
10000
100000
1000000
10000000
-30 -20 -10 0 10 20 30
Bias Voltage
Su
rfa
ce
Ch
arg
e D
en
sit
y
accumulation
depletion
inversion
n type substrate
p type substrate
blue: positive surface chargered: negative
surface charge
s
x
dx
d
)(2
2
Capacitance, Charge, and Potential
Poisson’s equation (1-D)
Charge density for a uniformly doped substrate
AD NNxnxpqx )()()(
i
si nq
kT22
Intrinsic Debye Length: a measure of how much an external electric field penetrates pure silicon
The Depletion Approximation
)()(
2
2
xNxNq
dx
dAD
s
Carrier concentrations are negligible in the depletion region
i
DA
DA
sd n
NN
NNq
kTx ln
42
max
Maximum depletion width
DA
sD NNq
kT
2
Extrinsic Debye Length: a measure of how much an external electric field penetrates doped silicon
CV vs Doping and Oxide Thickness
Substrate Doping
Oxide Thickness
p-type substrate0
1
2
3
4
5
6
7
8
9
10
-100 -50 0 50 100 150
Cap
acit
ance
(dim
ensi
onle
ss li
near
sca
le)
0.1
1
10
100
1000
-150 -100 -50 0 50 100
Cap
acit
ance
(dim
ensi
onle
ss lo
gari
thm
ic s
cale
)
Bias Voltage (dimensionless linear scale)
CV Measurements
V
C
Cmin
Cox
Quasi-static CV
V
C
Cmin
Cox
High Frequency CV
V
C
Cox
Cmin slow sweepfastvery fast
extremely fast
Deep Depletion Effect
V
C
Cmin
Cox
FBC
VFB
VFB
Ideal
Actual
Flat Band Shift
V
C
Cmin
Cox
FBC
VFB
Ideal
Actual
Fast Interface States
Interface States
EV
EC
FEF
Ei
Interface states – caused by broken symmetry at interface
Interface states – p-type depletion
Interface states – n-type depletion
EV
ECEFM
FEi
EFSi
+++++
EV
EC
EFM
EiFEFSi
Interface State Density
Interface state density is always higher on [111] than [100]
IV Response
log J
E10 MV/cm
T hick
T hin
Very T hin
Logarithm of current density (J) vs applied electric field (E)
Fowler-Nordheim tunneling
avalanche breakdown
Conduction Mechanisms
E
EEAJ o
FN exp2 Fowler-Nordheim tunneling
kTqE
qEAJox
BFP exp
Frenkel-Poole emission
kTqE
qTAJox
B 4exp* 2
Schottky emission
kTEqEAJ aee expOhmic (electronic) conduction
kTEqT
EAJ ai
i exp Ionic conduction
3
2
8
9
o
oxeox
x
VJ
Mobility limited breakdown
current
total charge, Qtime, t, or
100%
0%
FailedPer cent
good reliabilitypoor reliability
“ infant” mortality
Oxide Reliability
QBD - “charge to breakdown” - constant current stressTDBD - “time dependent breakdown” - constant voltage stress
Each point represents a failed MOS structure - stress is continued until all devices fail
Linear Transport Processes
Ohm’s Law of electrical conduction: j = E = E/
J = electric current density, j
(units: A/cm2)
X = electric field, E = V
(units: volt/cm)V = electrical potential
L = conductivity, = 1/
(units: mho/cm) = resistivity ( cm)
Fourier’s Law of heat transport: q = T
J = heat flux, q(units: W/cm2)
X = thermal force, T
(units: K/cm)T = temperature
L = thermal conductivity,
(units: W/K cm)
Fick’s Law of diffusion: F = DC
J = material flux, F(units: /sec cm2)
X = diffusion force, C
(units: /cm4)C = concentration
L = diffusivity, D(units: cm2/sec)
Newton’s Law of viscous fluid flow: Fu = u
J = velocity flux, Fu
(units: /sec2 cm)X = viscous force,
u(units: /sec)
u = fluid velocity
L = viscosity, (units: /sec cm)
J = LX
J = Flux, X = Force, L = Transport Coefficient
Diffusion
Diffusion in a rectangular bar of constant cross section
C
tD
C
x
2
2
Fick’s Second Law
Dtxx
eDt
NtxC 4
20
2,
Instantaneous Source - Gaussian profile
Constant Source - error function profile
Dt
xxNtxC
2erfc
2, 00
A
x
x
F(x) xF(x )+
Instantaneous Source Profile
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5
0.1
1.0
0 0.5 1 1.5 2
Linear scale
Log scale
Constant Source Profile
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5
0.1
1.0
0 0.5 1 1.5 2
Linear scale
Log scale
Surface Probing
I
r
Substrate
Single probe injecting current into a bulk substrate
s ss
1 2 3 4
I I
Substrate
Four point probe
I
r
Substrate
T hin Film
xf
Single probe injecting current into a conductive thin film
Ei
EFn
EFp
Evac
Ec
Ev
EF
pn Junction
n type Silicon p type Silicon
Junction Depth
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5
0.01
0.10
1.00
0 0.5 1 1.5 2
xJ
xJ
red: background doping
black: diffused doping
Unbiased pn Junctions
EF
E
V
Electric Field
Band Diagram
Charge Density
Potential
Biased pn Junctions
IV Characteristics
V
I
I0
V
2
1
C
Vpn
CV Characteristics
Photovoltaic Effect
V
I
ISC
VOC
Solar Cell
typical cross section
equivalent circuit
Solar Cell IV Curve
ISC
VOC
I
P
Vmax
Imax
Effect of Parasitics, Temperature, etc.
effect of RS effect of RSH
effect of I0 effect of n
effect of T
Solar Cell Technology
Commercial solar cell
LED IV Characteristics
LED Technology
RGB spectrum
Commercial LED’s
white spectrum
(with phosphor)
Diffusion Mechanisms
Vacancy Diffusion - Substitutional impurities, e.g., shallow level dopants (B, P, As, Sb, etc.), Diffusivity is relatively small for vacancy diffusion.
Interstitial Diffusion - Interstitial impurities,e.g., small atoms and metals (O, Fe, Cu, etc.), Diffusivity is much larger, hence interstitial diffusion is fast compared to vacancy diffusion.
Interstitialcy Mechanism - Enhances the diffusivity of substitutional impurities due to exchange with silicon self-interstitials. This leads to enhanced diffusion in the vicinity of the substrate surface during thermal oxidation (so-called “oxidation enhanced diffusion”).
Defect-Carrier Equilibria
Vacancies interact with mobile carriers and become charged. In this case, the concentrations are governed by classical mass action equilibria.
V V h KV
Vpx
V x
V V h KV
VpV
V V e KV
Vnx
V x
V V e KV
VnV
Arrhenius Constants for Dopant Atoms
Atomic Species
I
Diffusion Mechanism rV
roID
(cm2/sec)
rIQ
(eV)
Si xV V V V
0.015
16
10
1180
3.89
4.54
5.1
5.09
As xV V
0.066
12.0
3.44
4.05
B xV V
0.037
0.76
3.46
3.46
Ga xV V
0.374
28.5
3.39
3.92
P xV V V
3.85
4.44
44.2
3.66
4.00
4.37
Sb xV V
0.214
15.0
3.65
4.08
N xV 0.05 3.65
Arrhenius Constants for Other Species
Atomic Species Mechanism, Temperature, etc.
DoI (cm2/sec)
QI (eV)
Ge substitutional )10(25.6 5 5.28
Cu (300 -700C)
(800 -1100C) )10(7.4 3
0.04
0.43
1.0
Ag )10(2 3 1.6
Au substitutional
interstitial
(800 -1200C)
)10(8.2 3
)10(4.2 4
)10(1.1 3
2.04
0.39
1.12
Pt 150-170 2.22-2.15
Fe )10(2.6 3 0.87
Co )10(2.9 4 2.8
C 1.9 3.1
S 0.92 2.2
O2 0.19 2.54
H2 )10(4.9 3 0.48
He 0.11 1.26
Solid Solubilities
Ion Implantation
Dopant species are ionized and accelerated by a very high electric field. The ions then strike the substrate at energies from 10 to 500 keV and penetrate a short distance below the surface.
b
iv
|| v̂
v̂
iv
i
s
sv
k̂
tangent plane(edge on)
Elementary “hard sphere” collision
Co-linear or “Centered” Collision
iiv|| v̂
v̂
iv
ssv
k̂
tangent plane(edge on)b=0
==0
isi
isi
si
sii v
mm
mvv
mm
mmv
2
;
Clearly, if mi<ms, then iv is negative. This means that light implanted ions tend to be
scattered back toward the surface. Conversely, if mi>ms, then iv is positive and heavy
ions tend to be scattered forward into the bulk. Obviously, if mi equals ms, then 0|| v̂v i
vanishes. In any case, recoiling silicon atoms are scattered deeper into the substrate.
Stopping Mechanisms
Nuclear Stopping - Direct interaction between atomic nuclei; resembles an elementary two body collision and causes most implant damage.
Electronic Stopping - Interaction between atomic electron clouds; sort of a “viscous drag” as in a liquid medium. Causes little damage.
Implant Range
Range - Total distance traversed by an ion implanted into the substrate.
Projected Range - Average penetration depth of an implanted ion.
Implant Straggle
Projected Straggle - Variation in penetration depth. (Corresponds to standard deviation if the implanted profile is Gaussian.)
Channeling
Channeling is due to the crystal structure of the substrate.
Implantation Process
For a light dose, damage is isolated. As dose is increased, damage sites become more dense and eventually merge to form an amorphous layer. For high dose implants, the amorphous region can reach all the way to the substrate surface.
Point-Contact Transistor
Bipolar Junction Transistor
n
n p
C B E
Junction FET
n
n p
S D G
MOSFET
p
n n
S D G
enhancement mode
p
n n
S D G
depletion mode
7 V
6 V
5 V
4 V
Enhancement Mode FET
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