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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

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Outline Introduction Introduction Apparatus & Chemistry Apparatus & Chemistry Ficks Law Profiles Profiles Characterization 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. 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)

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Constant Surface Concentration Infinite source diffusion Initial condition: C(x,0) = 0 Boundary conditions: C(0, t) = C s C(, t) = 0 Solution:

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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

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Constant Total Dopant Limited source diffusion Initial condition: C(x,0) = 0 Boundary conditions: C(, t) = 0 Solution:

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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.

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Irvin Curves