ECE/ChE 4752: Microelectronics Processing Laboratory Diffusion #1 ECE/ChE 4752: Microelectronics Processing Laboratory Gary S. May January 29, 2004

Outline Introduction Apparatus & Chemistry Fick’s Law Profiles Characterization

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

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

Outline Introduction Apparatus & Chemistry Fick’s Law Profiles Characterization

Schematic

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

Solid Source Example reaction: 2As2O3 + 3Si → 4As + 3SiO2 (forms an oxide layer on the surface)

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: 4BBr3 + 3O2 → 2B2O3 + 6Br => preliminary reaction forms B2O3, which is deposited on the surface; forms a glassy layer

(oxygen is carrier gas that initiates preliminary reaction) 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

Outline Introduction Apparatus & Chemistry Fick’s Law Profiles Characterization

Diffusion Mechanisms Vacancy: atoms jump from one lattice site to the next. Interstitial: atoms jump from one interstitial site to the next.

Vacancy Diffusion Also called “substitutional” diffusion Must have vacancies available High activation energy (Ea ~ 3 eV  hard)

Interstitial Diffusion “Interstitial” = between lattice sites Ea = 0.5 - 1.5 eV  easier

First Law of Diffusion C = dopant concentration/unit volume 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.

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

Fick’s Law When the concentration of dopant atoms is low, diffusion coefficient can be considered to be independent of doping concentration.

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

Outline Introduction Apparatus & Chemistry Fick’s Law Profiles Characterization

Solving Fick’s Law 2nd order differential equation Need one initial condition (in time) Need two boundary conditions (in space)

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

Key Parameters Complementary error function: Cs = surface concentration (solid solubility)

Total Dopant Total dopant per unit area: Represents area under diffusion profile

Example For a boron diffusion in silicon at 1000 °C, the surface concentration is maintained at 1019 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 1015 cm–3. SOLUTION: The diffusion coefficient of boron at 1000 °C is about 2 × 1014 cm2/s, so that the diffusion length is

Example (cont.) When C = 1015 cm–3, xj is given by

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

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:

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).

Diffusion Profiles

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

Drive-In Drive-in = limited source After subsequent heat cycles:

Multiple Heat Cycles where: (for n heat cycles)

Outline Introduction Apparatus & Chemistry Fick’s Law Profiles Characterization

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.

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:

4-Point Probe Used to determine resistivity

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/) => r = Rst

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)

Resistance

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)

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.

Irvin Curves