Diffusion #1 ECE/ChE 4752: Microelectronics Processing
Laboratory Gary S. May January 29, 2004
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Outline Introduction Apparatus & Chemistry Apparatus &
Chemistry Ficks Law Ficks Law Profiles Profiles Characterization
Characterization
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Definition Random walk of an ensemble of particles from regions
of high concentration to regions of lower concentration In general,
used to introduce dopants in controlled amounts into semiconductors
Typical applications: Form diffused resistors Form sources/drains
in MOS devices Form bases/emitters in bipolar transistors
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Basic Process Source material transported to surface by inert
carrier Decomposes and reacts with the surface Dopant atoms
deposited, dissolve in Si, begin to diffuse
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Outline Introduction Introduction Apparatus & Chemistry
Ficks Law Ficks Law Profiles Profiles Characterization
Characterization
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Schematic
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Dopant Sources Inert carrier gas = N 2 Dopant gases: P-type =
diborane (B 2 H 6 ) N-Type = arsine (AsH 3 ), phosphine (PH 3 )
Other sources: Solid = BN, As 2 O 3, P 2 O 5 Liquid = BBr 3, AsCl
3, POCl 3
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Solid Source Example reaction: 2As 2 O 3 + 3Si 4As + 3SiO 2
(forms an oxide layer on the surface)
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Liquid Source Carrier bubbled through liquid; transported as
vapor to surface Common practice: saturate carrier with vapor so
concentration is independent of gas flow => surface
concentration set by temperature of bubbler & diffusion system
Example: 4BBr 3 + 3O 2 2B 2 O 3 + 6Br => preliminary reaction
forms B 2 O 3, which is deposited on the surface; forms a glassy
layer
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Gas Source Examples: a) B 2 H 6 + 3O 2 B 2 O 3 + 3H 2 O (at 300
o C) b) i) 4POCl 3 + 3O 2 2P 2 O 5 + 6Cl 2 (oxygen is carrier gas
that initiates preliminary reaction) ii) 2P 2 O 5 + 5Si 4P + 5SiO
2
Diffusion Mechanisms Vacancy: atoms jump from one lattice site
to the next. Interstitial: atoms jump from one interstitial site to
the next. Interstitial: atoms jump from one interstitial site to
the next.
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Vacancy Diffusion Also called substitutional diffusion Must
have vacancies available High activation energy (E a ~ 3 eV
hard)
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Interstitial Diffusion Interstitial = between lattice sites E a
= 0.5 - 1.5 eV easier
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First Law of Diffusion ) F = flux (#of dopant atoms passing
through a unit area/unit time) C = dopant concentration/unit volume
D = diffusion coefficient or diffusivity D = diffusion coefficient
or diffusivity Dopant atoms diffuse away from a high- concentration
region toward a lower- concentration region. Dopant atoms diffuse
away from a high- concentration region toward a lower-
concentration region.
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Conservation of Mass 1 st Law substituted into the 1-D
continuity equation under the condition that no materials are
formed or consumed in the host semiconductor 1 st Law substituted
into the 1-D continuity equation under the condition that no
materials are formed or consumed in the host semiconductor
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Ficks Law When the concentration of dopant atoms is low,
diffusion coefficient can be considered to be independent of doping
concentration When the concentration of dopant atoms is low,
diffusion coefficient can be considered to be independent of doping
concentration.
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Temperature Effect Diffusivity varies with temperature
Diffusivity varies with temperature D 0 = diffusion coefficient (in
cm 2 /s) extrapolated to infinite temperature D 0 = diffusion
coefficient (in cm 2 /s) extrapolated to infinite temperature E a =
activation energy in eV E a = activation energy in eV
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Outline Introduction Introduction Apparatus & Chemistry
Apparatus & Chemistry Ficks Law Ficks Law Profiles
Characterization Characterization
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Solving Ficks Law 2 nd order differential equation Need one
initial condition (in time) Need two boundary conditions (in
space)
Key Parameters Complementary error function: C s = surface
concentration (solid solubility)
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Total Dopant Total dopant per unit area: Total dopant per unit
area: Represents area under diffusion profile Represents area under
diffusion profile
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Example For a boron diffusion in silicon at 1000 C, the surface
concentration is maintained at 10 19 cm 3 and the diffusion time is
1 hour. Find Q(t) and the gradient at x = 0 and at a location where
the dopant concentration reaches 10 15 cm 3. SOLUTION: The
diffusion coefficient of boron at 1000 C is about 2 10 14 cm 2 /s,
so that the diffusion length is
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Example (cont.) When C = 10 15 cm 3, x j is given by
Example Arsenic was pre-deposited by arsine gas, and the
resulting dopant per unit area was 10 14 cm 2. How long would it
take to drive the arsenic in to x j = 1 m? Assume a background
doping of C sub = 10 15 cm -3, and a drive-in temperature of 1200
C. For As, D 0 = 24 cm 2 /s and E a = 4.08 eV. SOLUTION:
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Example (cont.) t log t 10.09t + 8350 = 0 The solution to this
equation can be determined by the cross point of equation: The
solution to this equation can be determined by the cross point of
equation: y = t log t and y = 10.09t 8350. Therefore, t = 1190
seconds (~ 20 minutes). Therefore, t = 1190 seconds (~ 20
minutes).
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Diffusion Profiles
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Pre-Deposition Pre-deposition = infinite source Pre-deposition
= infinite source x j = junction depth (where C(x)=C sub )
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Drive-In Drive-in = limited source Drive-in = limited source
After subsequent heat cycles: After subsequent heat cycles:
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Multiple Heat Cycles where: (for n heat cycles)
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Outline Introduction Introduction Apparatus & Chemistry
Apparatus & Chemistry Ficks Law Ficks Law Profiles Profiles
Characterization
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Junction Depth Can be delineated by cutting a groove and
etching the surface with a solution (100 cm 3 HF and a few drops of
HNO 3 for silicon) that stains the p-type region darker than the
n-type region, as illustrated above.
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Junction Depth If R 0 is the radius of the tool used to form
the groove, then x j is given by: In R 0 is much larger than a and
b, then:
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4-Point Probe Used to determine resistivity
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4-Point Probe 1) Known current (I) passed through outer probes
2) Potential (V) developed across inner probes = (V/I)tF where: t =
wafer thickness F = correction factor (accounts for probe geometry)
OR: R s = (V/I)F where: Rs = sheet resistance (W/) => = R s
t
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Resistivity where: = conductivity ( -1 -cm -1 ) = resistivity (
-cm) n = electron mobility (cm 2 /V-s) p = hole mobility (cm 2
/V-s) q = electron charge (coul) n = electron concentration (cm -3
) p = hole concentration (cm -3 )
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Resistance
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Sheet Resistance 1 square above has resistance R s ( /square) R
s is measured with the 4-point probe Count squares to get L/w
Resistance in = R s (L/w)
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Sheet Resistance (cont.) Relates x j, mobility ( ), and
impurity distribution C(x) Relates x j, mobility ( ), and impurity
distribution C(x) For a given diffusion profile, the average
resistivity ( = R s x j ) is uniquely related to C s and for an
assumed diffusion profile. For a given diffusion profile, the
average resistivity ( = R s x j ) is uniquely related to C s and
for an assumed diffusion profile. Irvin curves relating C s and
have been calculated for simple diffusion profiles. Irvin curves
relating C s and have been calculated for simple diffusion
profiles.