UIUC ECE Title Bar ece444
Theory and Fabrication of Integrated Circuits University of Illinois at Urbana-Champaign logo

HOME · LECTURE · LAB · GT · CALCULATORS · Text Only

Lab photo

Drive Diffusion Equations

Gaussian Approximation

The exact drive diffusion solution is unnecessarily complicated. A simplified form can be obtained by changing the initial condition for Fick's Laws.

The predeposition diffusion has a very high surface concentration, but is very shallow. This distribution can be approximated by a Dirac delta function - Δ(x).

Redefine the intial condition to:
N₂(x,0) = Qδ(x)

Solution for Fick's Laws using the delta function:

Substituting

This becomes:

Surface concentration (N₀₂):

S&M Correction

The S&M correction is an empirical correction factor that improves the Gaussian approximation when D₂t₂ is not much greater than D₁t₁.

Define

where:
Δ₁ = D₁t₁
Δ₂ = D₂t₂
Δ₃ = D₃t₃

Substitute Δ* for Δ₂

And the surface concentration is

Processing Equations

· Four Point Probe

· Oxidation

· Photolithography

· Phase Diagrams

· Predeposition Diffusion

· Junctions

· Drive Diffusion

· CVD

· Ion Implantation

Answers provided by this service may not be relevant to the materials presented in this website.

Department of Electrical and Computer Engineering
College of Engineering
University of Illinois Urbana-Champaign

Contact ece444
Copyright © 2007, 2008 The Board of Trustees at the University of Illinois. All rights reserved.

archives: ©1999   ©2000   ©2004   ©2005   ©2006