diffusion [compatibility mode]
TRANSCRIPT
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VLSI Process Technology
Lecture:DIFFUSION
MSc Microelectronics, UKM
Prof. Dr. Burhanuddin Yeop Majlis
What is Diffusion?
• Thermally Driven Process – statistical net motion of regions of high
i l iconcentration to low concentration • Key Mechanism in Deposition Processes
– introducing impurities to silicon
• Used Extensively in IC and MEMS Fabrication – control electrical properties of silicon
Prof. Dr. Burhanuddin Yeop Majlis, UKM 2
p p• resistors, diodes, BJTs, MOSFETs, …
– control chemical/mechanical properties • p+ etch stop (greatly slows down KOH and EDP etch) • piezoresistors (change in stress = change in resistance)
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What is Solid-State Diffusion?
• A method of “deposition” by modifying the atomic composition of materials – controlled “contamination”
– high temperature process (700 - 1200ºC) – used extensively in commercial ICs and MEMS
• Typical Dopants (gives or takes an e-) – Donor Atoms (n-type)P, As, …
Prof. Dr. Burhanuddin Yeop Majlis, UKM 3
– Acceptor Atoms (p-type) B, Ga, Al – Unwanted Dopants Au, Fe, Cu, Ni, …
• can ruin solid-state electronic devices • fast diffusers (high diffusivity)
Si
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Vacancy
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Interstitial Diffusion
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Interstitial-Substitutional Diffusion
Si
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Si
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Interstitial-Substitutional Diffusion (Kick Out)
Si
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Si
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Si
Si
Si
Si
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Si
Si
Si
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Substitutional Diffusion
Si
Si Si
Si
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Si Si
Si
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Si
Si
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Flux (atoms/cm2·sec)
Fick’s 1st Law of Diffusion(Concentration Gradient Driven Flux)
NHI J⎟⎠⎞
⎜⎝⎛⋅−=
dxdNDJ
Flux (atoms/cm sec)– diffusivity D, flux J – negative slope cancels with minus
sign and yields a positive flux – dopant concentration N in atoms/cm3
NLO
0 x(surface)
J
Diffusion Coefficient (cm2/sec)
Prof. Dr. Burhanuddin Yeop Majlis, UKM 5
( )– strong function of temperature – Arrhenius relationship – Activation Energy (Ea) – Boltzmann’s constant (1.38×10-23 J/K)
⎟⎠⎞
⎜⎝⎛−
⋅= kTEa
eDD 0
Fick’s 2nd Law of Diffusion(Time Dependence of Concentration and Flux)
Start with Continuity Equation ⎟⎠⎞
⎜⎝⎛−=
dxdJ
dtdN
⎠⎝
Incoming Outgoing
J1
J2
0 x2
Accumulation
positive=dtdN
⎟⎠⎞
⎜⎝⎛⋅−=
dxdNDJ
Prof. Dr. Burhanuddin Yeop Majlis, UKM 6
Combining with Fick’s 1st law yields:
typically ignored -> 0Less true with As due to its
Concentration-dependent diffusivity
Finally: The diff eq. we will solve
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⎟⎟⎠
⎞⎜⎜⎝
⎛⋅= 2
2
dxNdD
dtdN
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅+⎥⎦
⎤⎢⎣⎡ ⋅=⎥
⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛⋅−⋅⎟
⎠⎞
⎜⎝⎛−= 2
2
dxNdD
dxdN
dxdD
dxdND
dxd
dtdN
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Diffusion Coefficients• When temp. increases impurities get more energy
and increase diffusion speed.• Diffusion coefficients, D, is used to represent rate
of diffusion of materials.• D depend on T,
– where D and k is constant T temperature in
D D EkTo
a= −exp( )
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– where Do and k is constant , T temperature in Kelvin and Ea activation energy of impurities.
ln ( ) lnDT
Ek
Dao= − +
1
Diffusion Coefficients• Plot ln D vs 1/T is a straight line with negative
gradient.gradient.– This shows that diffusion speed or D very
sensitive to temperature.– A few degree change in T enough to destroy
base transistor– Furnace tem. Must be controlled with ± 0.25 °C.
Prof. Dr. Burhanuddin Yeop Majlis, UKM 8
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⎟⎠⎞
⎜⎝⎛−
⋅= kTEa
eDD 0
Diffusion Coefficients
⎟⎠⎞
⎜⎝⎛−
⋅= kTEa
eDD 0
Diffusion Coefficients
⎟⎠⎞
⎜⎝⎛−
⋅= kTEa
eDD 0 eDD 0 eDD 0 eDD 0
Prof. Dr. Burhanuddin Yeop Majlis, UKM 9
Fast DiffusersTypically Undesirable
Slow Diffusers Fast DiffusersSlow Diffusers (useful)
⎟⎠⎞
⎜⎝⎛−
⋅= kTEa
eDD 0
Prof. Dr. Burhanuddin Yeop Majlis, UKM 10
Over 106 times faster!
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Solving the Diffusion Equations
• Boundary Conditions ⎟⎟⎠
⎞⎜⎜⎝
⎛⋅= 2
2
dxNdD
dtdN
– Constant Source or Supply of Dopants • infinite supply of dopants is provided at the surface to
insure that the concentration of dopants at the surfaceis held constant
• N(x=0,t) = No
• Typical situation with a solid source on the substrate – Constant Dose or Fixed Number of Dopants
Prof. Dr. Burhanuddin Yeop Majlis, UKM 11
– Constant Dose or Fixed Number of Dopants • fixed (finite) amount of dopants in the substrate at all times • Integral of N(x,t) = Q (dose) is constant • Typical situation after an implant or short and shallow
pre-diffusion
Solving Fick’s 2nd Law with the boundary condition: Constant Source:
Case #1: Constant SourceConcentration at Surface is Fixed
( ) 0,0 NtxN ==•Co sta t Sou ce- infinite supply of dopants is provided at the surface to insure that the concentration of dopants at the surface is held constant
yields:
( ) ⎟⎠
⎞⎜⎝
⎛⋅
⋅=tD
xNtxN2
erfc, 0
( ) 0,0 NtxN
Prof. Dr. Burhanuddin Yeop Majlis, UKM 12
erfc is the Complementary Error Function– comes from probability and statistics
– derived by integrating the normal probability function
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Case #1: Constant Source (continued)
Concentration at Surface is Fixed
Prof. Dr. Burhanuddin Yeop Majlis, UKM 13
• Plot on a semi-log graph • Longer time or higher diffusivity D
results in a deeper diffusion
Solid Solubility
• Solid solubility is a maximum concentration of dopant• Solid solubility is a maximum concentration of dopantcan diffuse into solid at certain temp..
• Solid solubility increase with temperature.• Solid solubility is the surface concentration of dopant
for constant source diffusion.
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Solid Solubility
M i t ti
Prof. Dr. Burhanuddin Yeop Majlis, UKM 15
• Maximum concentration without precipitation is the solid solubility – function of temperature – function of dopant
Type of Dopant and SourceDopant Solid solubility Source compound Formula ConditionType nantimony (Sb) 7x1019(1,250 °C) antimony trioxide Sb2O3 solidType nA i (A ) 1 8 1021 (1150°C) i t i id A O lidArsenic (As) 1.8x1021 (1150°C) arsenic trioxide As2O3 solid
arsine AsH3 gasType nPhosphorus (P) 4x1021 (1,150°C) pentoxide P2O5 solid
phosoxychloride POCl3 liquidphosphinen PH3 gassiliconpyrophosphade SiP2O7 solid
Prof. Dr. Burhanuddin Yeop Majlis, UKM 16
Type pboron (B) 5x1020 (1,250°C) boron tryoxida B2O3 solid
boron tribromide BBr3 liquiddiborane B2H6 gasboron trychloride BCl3 gasboron nitride BN solid
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Total Dose (Q)
Q1 Q2 Q3 Q1 < Q2 < Q3
atoms/cm2
Prof. Dr. Burhanuddin Yeop Majlis, UKM 17
• Total Dose is simply the integral of the distribution
( )∫∞ ⋅
⋅⋅=⋅=0
02,π
tDNdxtxNQ
Junction Depth (xj)
xj1 xj2 xj3
Prof. Dr. Burhanuddin Yeop Majlis, UKM 18
• Junction Depth is simply the intersection of the profile N(x,t) with the background concentration NB, thus where N(x,t) = NB
xj1 xj2 xj3
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Junction Depth (xj)
Prof. Dr. Burhanuddin Yeop Majlis, UKM 19
Case #2: Constant DoseTotal Number of Dopants is Fixed
Starting with a mathematical impulse function of dopants (nonphysical, but convenient mathematically):
•
N Total number of dopants is Q
Depth
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅= 2
2
dxNdD
dtdN
solving:
yields:
Prof. Dr. Burhanuddin Yeop Majlis, UKM 20
( )2
2,⎟⎠
⎞⎜⎝
⎛⋅
−
⋅⋅⋅
= tDx
etD
QtxNπ
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Case #2: Constant DoseTotal Number of Dopants is Fixed
• Surface concentration drops with time
• Depth of profile increases with time
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Diffusion of Buried Dopants
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• Half the dopants diffuse to the left, the other half diffuse to the right – so peak concentration is half
( ) ( )2
2buried 2
,,⎟⎠
⎞⎜⎝
⎛⋅
−
⋅⋅⋅
== tDx
etD
QtxNtxNπ
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2-D and 3-D DiffusionAn Isotropic Process
• Isotropic diffusion can diffuse under the diffusion mask just
Prof. Dr. Burhanuddin Yeop Majlis, UKM 23
under the diffusion mask just like an isotropic etch does under and etch mask
Sources of Dopants: Gas
Prof. Dr. Burhanuddin Yeop Majlis, UKM 24
• Gas Sources: HAZAROUDS!!! – B2H6 – Diborane – PH3 – Phosphine – AsH3 - Arsine
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Sources of Dopants: Solid
S i O Gl
Prof. Dr. Burhanuddin Yeop Majlis, UKM 25
• Spin-On Glasses – has a volatile solve just like PR
• Previously Deposited Films – deposit at low temp and drive in at high
temperatures (e.g., oxides, polysilicon)
Sheet Resistance⎟⎠⎞
⎜⎝⎛=⎟
⎠⎞
⎜⎝⎛⎟⎠⎞
⎜⎝⎛=
⋅=
WLR
WL
tALR s
ρρResistance:
I
• Resistance R [Ohm]
W
Lt
I
1 2 3 4 5
L/W = 5 (total # of squares)
I
Prof. Dr. Burhanuddin Yeop Majlis, UKM 26
• Resistance R [Ohm] • Resistivity ρ [Ohm-m] • Resistor Length L, Width W, Thickness t • Sheet Resistance Rs [Ohm/square]
– square is unit less (the aspect ratio of the resistor)
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Sheet Resistance
No
N(x))()()( xNxqx ⋅⋅= μσ
∫==
jxj
s
dxxx
R)(
1
σ
ρ
∫=
jxs
dxxNxqR
)()(
1
μ
xj
NB
• Conductivity σ [ohm-1-m-1] Charge on Electron q [coulombs]
∫ ⋅dxx0
)(σ ∫ ⋅⋅⋅ dxxNxq0
)()(μ
Prof. Dr. Burhanuddin Yeop Majlis, UKM 27
Resistivity ρ [Ohm-m] Free Carrier Mobility µ [cm2v-1s-1]
Sheet Resistance Measurement
ρ F ρ measured.
• 4-Point Probe:
:st >>:ts >>
IVs ⋅⋅⋅= πρ 2 I
Vt⋅
⋅=
)2ln(πρ
IV
tRs ⋅==
)2ln(πρ
Prof. Dr. Burhanuddin Yeop Majlis, UKM 28
– avoids contact resistance – pass current through one pair of
electrodes (contact R and film R) – sense induced voltage with an inner pair
of electrodes across only film R due to high impedance measurement
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Irvin’s Curves (N-Type)Relationship between: Rs, xj, and No
300 K300 K
Prof. Dr. Burhanuddin Yeop Majlis, UKM 29
300
Irvin’s Curves (P-Type)Relationship between: Rs, xj, and No
300 K300 K
Prof. Dr. Burhanuddin Yeop Majlis, UKM 30
300
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Bulk Resistivity
Prof. Dr. Burhanuddin Yeop Majlis, UKM 31
PROBLEM• Determine the concentration of diffused boron at 1 μm from the
surface. Diffusion was carried out at temperature of 1,100 °C for4 hours where the initial concentration, No equal to 4 × 1018 cm-2., o q
• Diffusion temperature 1,100 °C = 1,373 K
• From Fig 5.7, diffusion coefficient boron 4 × 10-13 cm2.s-1
73.0137310001000
==T
66010 4−x
Prof. Dr. Burhanuddin Yeop Majlis, UKM 32
• From erfc plot at Rajah 5.6, N/No = 0.45• Then N = 0.45 x 4 x 1018 = 1.8 x 1018 cm-2
66.06060410422 13
=××××
=−Dt
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P-Type Doping• Impurities
– Boron(B), gallium(Ga), aluminium(Al), and indium(In).
• boron normally used for p-type doping. • Ga has higher diffusion coefficient in oxide
– Oxide can not be used as an mask.
• In has acceptor level 0.16 eV, while boron only 0.01 eV, as a result not all acceptor level ionised at room temperature.
Prof. Dr. Burhanuddin Yeop Majlis, UKM 33
te pe atu e• Al not suitable because easily react with oxygen in
substrate.
Boron Source
• Boron deposited on Si substrate as boron trioxide (B2O3)– solid boron trioxide (B2O3) also called boron glass– In contact with Si surface, boron trioxide will formed a layer
with boron riched• B2O3 can be obtained by,
– Oxidation of diborane gas (B2H6),,• B2H6 + 3O2 B2O3 + 3H2O
– Or using boron nitride (BN) wafer, put together with Si waferin diffusion furnace
Prof. Dr. Burhanuddin Yeop Majlis, UKM 34
– B2O3 layer can also be formed using polymer material suchPBF coated on Si surface.
• Diborane gas is more popular because flow rate of as can becontrolled and the concentration of boron can be controlled.
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BN Wafer Polymer Materialwafer BN wafer silikon
PBF
Bot kuarza
wafer
PBF
B O B Oresapan
pembakaran
wafer wafer
2 3 2 3
wafer
penyalutan
Prof. Dr. Burhanuddin Yeop Majlis, UKM 35
N-Type Doping• Impurities Type n,
– phosphorous, antimony, and arsenic. • arsenic and antimony have low diffusion
coefficient– To impurities at initial stage of process because.
• Used to formed a burried layer in BJT and n well for CMOS.
arsenic has higher solid solubility can give high
Prof. Dr. Burhanuddin Yeop Majlis, UKM 36
– arsenic has higher solid solubility – can give high surface concentration.
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Source for arsenic and antimony
• Source for arsenic is arsine gas (AsH3) and antimony stibnine gas(SbH3).
• These gases react with oxygen to form an oxide,
2AsH3 + 3O2 →As2O3 + 3H2Oand
2SbH3 + 3O2 →Sb2O3 + 3H2O
Prof. Dr. Burhanuddin Yeop Majlis, UKM 37
3 2 2 3 2
• Both gases are flammable and highly toxic.•
Phosphorous Sources• Source for phosphorous oxide are,
– Phosphine gas (PH3), liquid phosphorous oxychloride (POCl3) and solid SiP Ooxychloride (POCl3), and solid SiP2O7
• Polymer materila used in spin coating techniques is OCD.
• Phosphine gas more porpular, but this as is higher toxic and easily explode.
• Phosphine(PH3) and phosphorous oxychloride(POCl3)react with oxygen form phosphorous oxide
Prof. Dr. Burhanuddin Yeop Majlis, UKM 38
(POCl3)react with oxygen form phosphorous oxide(P2O5),
2PH3 + 4O2 P2O5 + 3H2O2POCl3 + 3O2 P2O5 + 3Cl2
• phosphorous atoms from P2O5 diffuse into silicon.
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Diffusion system for liquid source
Prof. Dr. Burhanuddin Yeop Majlis, UKM 39
EVALUATION OF DIFFUSED LAYER
• There are four parameters,– surface concentration, No,
B k d t ti N– Background concentration, NB, – junction depth, Xj, and– Sheet resistance, Rs.
• Junction depth measurement• colour the n and p type region• There are two technique angle lapping and wafer
Prof. Dr. Burhanuddin Yeop Majlis, UKM 40
• There are two technique, angle lapping, and wafer grooving.
•
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Angle Lapping• Sample is stick on the block with sloping surface
Xj = d sin θ• Surface cutting at very small angle (0.5°) enable a
distance d at the junction can be measured under
np
d
x j
0
np
optical flat
Prof. Dr. Burhanuddin Yeop Majlis, UKM 41
distance, d, at the junction can be measured under microscope.
• The junction is coloured using stain material, a mixture of hydrofluoric acid and 0.5% nitric acid to darken the p-type material.
Wafer Grooving
• Using cylinder with radius R• Using cylinder with radius R to make groove on the wafer surface.
• The groove will cut and expose the junction.
• Stain material is used to differentiate p-type and n-type
22 aR −
Prof. Dr. Burhanuddin Yeop Majlis, UKM 42
type.
Xj
R
b
an
p
22 bR −
x y
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Wafer Grooving
In practice, it is easier to measure x
= − − −R bR
aR( ) ( )1 1
22
22
12
12
because a << R and b << R, then
⎥⎥⎦
⎤
⎢⎢⎣
⎡−−−= 2
1222122 )()( aRbRX j
p ,and y, where
x = a - b and y = a + b
xy = a2 - b2
X xyRj =
12
Prof. Dr. Burhanuddin Yeop Majlis, UKM 43
X R bR
aRj ≈ − − +( )1 2 1 2
22
22
=−1
2
2 2a bR
R2
Sheet Resistance• If the length of sample, l, width w and thickness, t, then, the
resistance between point A and B is,
l)( l)(w
• Where ρ(t) resistivity as a function of distant t inside the samplefrom surface.
• Ratio between resistivity to layer thickness is called sheetresistance, Rs,
wtltR )(ρ
=wl
tt)(ρ
=
tR )(ρ
l
tArus I
Prof. Dr. Burhanuddin Yeop Majlis, UKM 44
• When length, l, equal to width, w, thenR = Rs
tRs =
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Four Point Probes
••V
I I
s s s= 4 5324. /V
IΩ square
Prof. Dr. Burhanuddin Yeop Majlis, UKM 45
1 2 3 4t
I
Carier Type Determination• Hot probe will push carrier from the surface and leave only ion
charge, if the semiconductor is n-type then the region is consist of positive ion.
• As a result, the region under the hot probe become more positive compare to the other probe.
• If the semiconductor is p-type, the region is more negative compare with the other probe (cold).
• The deflection direction depends on whether the semiconductor is n or p-type.
+ - +-
Prof. Dr. Burhanuddin Yeop Majlis, UKM 46
coldhot
N-type wafer
Heatingcoil
coldhot
P-type wafer
Heating coil
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Surface Concentration• Surface concentration, No, can be determined by measuring the
sheet resistance and junction depth.• If we know N diffusion profile can be obtained using GaussIf we know No, diffusion profile can be obtained using Gauss
and erfc relationship.• For diffused layer with background concentration, NB, sheet
resistance is given by,
• A computer calculation had been done by Irvin. [Irvin.1962] to
[ ]R
q x N x N dxs
B
X j=
−∫1
0μ ( ) ( )
Prof. Dr. Burhanuddin Yeop Majlis, UKM 47
p y [ ]get No from the value of Rs and xj for various value of NB
• Irvin produced a plot for relationship of average conductivity andsurface concentration, No, for p-type and n-type materials forboth Gaussian and erfc distribution.
PROBLEM
• A phosphorous dopant is diffused on p-type subtrate with• A phosphorous dopant is diffused on p-type subtrate with doping concentration of 1016 cm3. From four point probe measurement Rs = 5 Ω, and from junction depth measurement, Xj = 0.8 μm. Determine the surface concentration No?
• From Irvin plot (refer Ghandi S.K. 1994) with NB = 1016 cm2,
js XR1
=σ
Prof. Dr. Burhanuddin Yeop Majlis, UKM 48
p ( ) B ,then, No = 9 x 1016 cm-3