diffusion 1 l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Diffusion #1 PowerPoint Presentation
Download Presentation
Diffusion #1

Loading in 2 Seconds...

play fullscreen
1 / 42

Diffusion #1 - PowerPoint PPT Presentation


  • 396 Views
  • Uploaded on

Diffusion #1. ECE/ChE 4752: Microelectronics Processing Laboratory. Gary S. May January 29, 2004. Outline. Introduction Apparatus & Chemistry Fick’s Law Profiles Characterization. Definition.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Diffusion #1' - chelsey


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
diffusion 1

Diffusion #1

ECE/ChE 4752: Microelectronics Processing Laboratory

Gary S. May

January 29, 2004

outline
Outline
  • Introduction
  • Apparatus & Chemistry
  • Fick’s Law
  • Profiles
  • Characterization
definition
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
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
outline5
Outline
  • Introduction
  • Apparatus & Chemistry
  • Fick’s Law
  • Profiles
  • Characterization
dopant sources
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
Solid Source

Example reaction: 2As2O3 + 3Si → 4As + 3SiO2

(forms an oxide layer on the surface)

liquid source
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
gas source
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
outline11
Outline
  • Introduction
  • Apparatus & Chemistry
  • Fick’s Law
  • Profiles
  • Characterization
diffusion mechanisms
Diffusion Mechanisms
  • Vacancy: atoms jump from one lattice site to the next.
  • Interstitial: atoms jump from one interstitial site to the next.
vacancy diffusion
Vacancy Diffusion
  • Also called “substitutional” diffusion
  • Must have vacancies available
  • High activation energy (Ea ~ 3 eV  hard)
interstitial diffusion
Interstitial Diffusion
  • “Interstitial” = between lattice sites
  • Ea = 0.5 - 1.5 eV  easier
first law of diffusion
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.
conservation of mass
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
Fick’s Law
  • When the concentration of dopant atoms is low, diffusion coefficient can be considered to be independent of doping concentration.
temperature effect
Temperature Effect
  • Diffusivity varies with temperature
  • D0 = diffusion coefficient (in cm2/s) extrapolated to infinite temperature
  • Ea = activation energy in eV
outline19
Outline
  • Introduction
  • Apparatus & Chemistry
  • Fick’s Law
  • Profiles
  • Characterization
solving fick s law
Solving Fick’s Law
  • 2nd order differential equation
  • Need one initial condition (in time)
  • Need two boundary conditions (in space)
constant surface concentration
Constant Surface Concentration
  • “Infinite source” diffusion
  • Initial condition: C(x,0) = 0
  • Boundary conditions:

C(0, t) = Cs

C(∞, t) = 0

  • Solution:
key parameters
Key Parameters
  • Complementary error function:
  • Cs = surface concentration (solid solubility)
total dopant
Total Dopant
  • Total dopant per unit area:
  • Represents area under diffusion profile
example
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
Example (cont.)

When C = 1015 cm–3, xj is given by

constant total dopant
Constant Total Dopant
  • “Limited source” diffusion
  • Initial condition: C(x,0) = 0
  • Boundary conditions:

C(∞, t) = 0

  • Solution:
example27
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 cont28
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).
pre deposition
Pre-Deposition
  • Pre-deposition = infinite source

xj = junction depth (where C(x)=Csub)

drive in
Drive-In
  • Drive-in = limited source
  • After subsequent heat cycles:
multiple heat cycles
Multiple Heat Cycles

where: (for n heat cycles)

outline33
Outline
  • Introduction
  • Apparatus & Chemistry
  • Fick’s Law
  • Profiles
  • Characterization
junction depth
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 depth35
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
4-Point Probe
  • Used to determine resistivity
4 point probe37
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
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)
sheet 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
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.