Process Lab: Concentration-Dependent Diffusion

By Shuqing (Victor) Cao1, Yang Liu1, Peter Griffin1

1. Stanford University

This modules simulates both the standard diffusion and concentration-dependent diffusion.

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Version 1.1 - published on 30 Oct 2019

doi:10.21981/DJ6J-7953 cite this

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The diffusion process is one of the most important processes in VLSI fabrication. It is implemented in processes such as the drain and source doping, the quality of which is extremely important for the electrical properties and performance of today's integrated circuit technology. This simulation tool simulates the dopant diffusion process by solving the partial differential equations. The tool gives users the freedom to adjust critical parameters and conditions in the process, such as the initial doping profile, time, temperature, length, and so on. It also gives users opportunities to choose between the delta or box-shaped dopant source, concentration dependency, as well as the type of dopants among 6 commonly used dopant species.

A dopant concentration versus diffusion depth figure is plotted almost instantaneously after the users specify the necessary parameters and conditions. The entire diffusion process is simulated after one click on the web interface, while all the complicated details and PDE-solving procedures are hidden behind the scene. The interactive interface of the module and its simplicity of usage demonstrates the module's educational value in that it helps students and engineers build intuition into the diffusion process with minimum learning curve. Insightful comparison, such as one between concentration dependent and independent diffusion, can be done easily. Moreover, the module can be used as a handy and efficient "diffusion calculator".

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The numerical kernel, PROPHET, was developed by C. Rafferty and R.K. Smith at Bell Labs. GUI Interface powered by Rappture, developed by Michael McLennan, Purdue University.


Developed by Shuqing Cao, Yang Liu and Peter Griffin, Stanford University, 2006

Silicon VLSI Technology advisors: James Plummer, Michael Deal, and Peter Griffin, Stanford University

Technology CAD advisor: Robert Dutton, Stanford University


  • J. D. Plummer, M. D. Deal, and P. B. Griffin, Silicon VLSI Technology, Fundamentals, Practice and Modeling, Prentice Hall, 2000.

Cite this work

Researchers should cite this work as follows:

  • Shuqing (Victor) Cao, Yang Liu, Peter Griffin (2019), "Process Lab: Concentration-Dependent Diffusion," (DOI: 10.21981/DJ6J-7953).

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