Diffusion

1
Diffusion 1

• ECE/ChE 4752 Microelectronics Processing
  Laboratory

Gary S. May January 29, 2004
2
Outline

• Introduction
• Apparatus Chemistry
• Ficks Law
• Profiles
• 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
• Apparatus Chemistry
• Ficks Law
• Profiles
• Characterization

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Schematic
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Dopant Sources

• Inert carrier gas N2
• Dopant gases
• P-type diborane (B2H6)
• N-Type arsine (AsH3), phosphine (PH3)
• Other sources
• Solid BN, As2O3, P2O5
• Liquid BBr3, AsCl3, POCl3

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Solid Source
Example reaction 2As2O3 3Si ? 4As
3SiO2 (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
• gt surface concentration set by temperature of
  bubbler diffusion system
• Example 4BBr3 3O2 ? 2B2O3 6Br
• gt preliminary reaction forms B2O3, which is
  deposited on the surface forms a glassy layer

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Gas Source

• Examples
• a) B2H6 3O2 ? B2O3 3H2O (at 300 oC)
• b) i) 4POCl3 3O2 ? 2P2O5 6Cl2
• (oxygen is carrier gas that initiates
  preliminary reaction)
• ii) 2P2O5 5Si ? 4P 5SiO2

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Outline

• Introduction
• Apparatus Chemistry
• Ficks Law
• Profiles
• Characterization

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Diffusion Mechanisms

• Vacancy atoms jump from one lattice 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 (Ea 3 eV ? hard)

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Interstitial Diffusion

• Interstitial between lattice sites
• Ea 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
• Dopant atoms diffuse away from a
  high-concentration region toward a
  lower-concentration region.

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Conservation of Mass

• 1st 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.

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Temperature Effect

• Diffusivity varies with temperature
• D0 diffusion coefficient (in cm2/s)
  extrapolated to infinite temperature
• Ea activation energy in eV

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Outline

• Introduction
• Apparatus Chemistry
• Ficks Law
• Profiles
• Characterization

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Solving Ficks Law

• 2nd order differential equation
• Need one initial condition (in time)
• Need two boundary conditions (in space)

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Constant Surface Concentration

• Infinite source diffusion
• Initial condition C(x,0) 0
• Boundary conditions
• C(0, t) Cs
• C(8, t) 0
• Solution

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Key Parameters

• Complementary error function
• Cs surface concentration (solid solubility)

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Total Dopant

• Total dopant per unit area
• 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 1019 cm3
  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 1015 cm3.

SOLUTION The diffusion coefficient of boron at
1000 C is about 2 1014 cm2/s, so that the
diffusion length is
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Example (cont.)
When C 1015 cm3, xj is given by
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Constant Total Dopant

• Limited source diffusion
• Initial condition C(x,0) 0
• Boundary conditions
• C(8, t) 0
• Solution

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Example

• Arsenic was pre-deposited by arsine gas, and the
  resulting dopant per unit area was 1014 cm2. How
  long would it take to drive the arsenic in to xj
  1 µm? Assume a background doping of Csub 1015
  cm-3, and a drive-in temperature of 1200 C. For
  As, D0 24 cm2/s and Ea 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
• y t log t and y 10.09t 8350.
• Therefore, t 1190 seconds ( 20 minutes).

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Diffusion Profiles
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Pre-Deposition

• Pre-deposition infinite source
• xj junction depth (where C(x)Csub)

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Drive-In

• Drive-in limited source
• After subsequent heat cycles

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Multiple Heat Cycles

• where
  (for n heat cycles)

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Outline

• Introduction
• Apparatus Chemistry
• Ficks Law
• Profiles
• Characterization

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Junction Depth

• Can be delineated by cutting a groove and etching
  the surface with a solution (100 cm3 HF and a few
  drops of HNO3 for silicon) that stains the p-type
  region darker than the n-type region, as
  illustrated above.

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Junction Depth

• If R0 is the radius of the tool used to form the
  groove, then xj is given by
• In R0 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
• r (V/I)tF
• where t wafer thickness
• F correction factor (accounts for probe
  geometry)
• OR Rs (V/I)F
• where Rs sheet resistance (W/?)
• gt r Rst

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Resistivity

• where s conductivity (W-1-cm-1)
• r resistivity (W-cm)
• mn electron mobility (cm2/V-s)
• mp hole mobility (cm2/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 Rs (W/square)
• Rs is measured with the 4-point probe
• Count squares to get L/w
• Resistance in W Rs(L/w)

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Sheet Resistance (cont.)

• Relates xj, mobility (m), and impurity
  distribution C(x)
• For a given diffusion profile, the average
  resistivity ( Rsxj) is uniquely related to
  Cs and for an assumed diffusion profile.
• Irvin curves relating Cs and have been
  calculated for simple diffusion profiles.

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Irvin Curves