Summer School for Integrated Computational Materials Education 2015 Kinetics Module Review Katsuyo Thornton, 1 Edwin Garcia, 2 Larry Aagesen, 1 Mark Asta

Summer School for Integrated Computational Materials Education 2015

Kinetics Module Review

Katsuyo Thornton,1 Edwin Garcia,2 Larry Aagesen,1

Mark Asta3, Jonathan Guyer4

1. Department of Materials Science & Engineering, University of Michigan

2. Purdue University

3. University of California, Berkeley

4. National Institute of Standards and Technology

Purposes of Kinetics Module

• Develop deeper understanding of diffusive transport through hands-on exercises.

• Learn how computational tools can be used to determine concentration profiles during diffusion.

• Demonstrate the technological importance of diffusion through an application to a semiconductor processing problem.

Summer School for Integrated Computational Materials Education Ann Arbor, MI June 15-26, 2015

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Larry Aagesen

Delete the

Concepts Illustrated Through Kinetics Module

1. Diffusion– Driving Force – Fick’s Law– Mass Conservation

2. Semiconductor Processing

3. Computational Kinetics

4. FiPy


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Part 1

Part 2

Driving Force for Diffusion• Consider 1D diffusion.• The atoms are randomly hopping right and left.• Half the atoms are moving toward right, and the other

half is moving to left.• Below, left side has

more atoms than right.• Net flux toward the

low concentration.

• Driving force =


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Concentration

xHigh conc. Low conc.

Fick’s First Law

dc

dx

highconcentration

lowconcentration

J J

• The flux is proportional to the driving force.• The proportionality constant is the diffusion coefficient.

5Summer School for Integrated Computational Materials Education Ann Arbor, MI June 15-26, 2015

Larry Aagesen

Atomic

Solution to the Diffusion Equation

...Co = C(x, t=0)

Cs = C(x=0,t)

• For a fixed concentration on one end of semi-infinite domain, an analytical solution exists.

• Cs = the surface concentration

• C0 = initial condition


Mass Conservation• Mass must be conserved.• Difference in flux will lead to change in

concentration (accumulation or depletion).• Mass conservation equation:

• In 1D:


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Semiconductor Device Processing

• Manufacture millions of devices simultaneously on a “chip”

• Steps in manufacture (simplified)– Crystal growth and dicing to “chip”– Photolithography to locate regions for doping– Doping to create n-type regions (can in some cases be done during

growth)– Overlay to create junctions– Metallization to interconnect devices– Passivation to insulate and isolate devices– Higher level “packaging” to interconnect chips

active devices(transistors, etc.)

metallic conductorsoxide passivation

silicon chip


Based on figures from MSE 201 course notes of J. W. Morris, Jr., University of California, Berkeley

Photolithography

• Minimum feature size depends on wavelength of “light”– Visible light: ~ 1 µm– Ultraviolet light: ~ 0.1 µm– Electrons, x-rays 0.1-1 nm– New and exotic methods

• Must have photoresist suitable to the “light”– Or use “light” to cut through oxide directly



Doping

• Add electrically active species

• Simple method– Coat surface and diffuse– Expose surface to a vapor and allow interdiffusion– Diffusion field is electrically active

• More precise: Ion implantation – Accelerate ions of the electrically active species toward

surface– Ions embed to produce doped region

dopant distribution

dopant ions



Doping: The Chemical Distribution

• Initial distribution is inhomogeneous– Diffusion produces gradient from surface– Ion implantation produces concentration at depth beneath

surface

• Can homogenize by “laser annealing”– Use a laser to melt rapidly, locally– Rapid homogenization in melted region– Rapid re-solidification since rest of body is heat sink

diffusion

ion implantation

laser anneal

c

x

dopant distribution

laser light

Summer School for Integrated Computational Materials EducationAnn Arbor, MI June 15-26, 2015


Overlay to Create Junctions

• Once primary doping is complete– Re-coat– Re-mask– Re-pattern– Dope second specie to create desired distribution of junctions

p nn p

nn

Summer School for Integrated Computational Materials EducationAnn Arbor, MI June 15-26, 2015


Part 2. Introduction to Computational Kinetics


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What is FiPy?

• Simply put: – Is a set of python libraries to solve PDEs

• In more detail:– Provides a numerical framework to solve

for the finite-volumes equation– The emphasis is on microstructural

evolution


FiPy Resources

• FiPy Manual (tutorials and useful examples)• FiPy Reference (what every single

command does)• Mailing List: [email protected]• You can also email the coauthors:

• John Guyer: [email protected]• Dan Wheeler: [email protected]

• FiPy Website http://www.ctcms.nist.gov/fipy/


A PDE is Solved in Five Steps

• Variables Definitions• Equation(s) Definition(s)• Boundary Condition Specification• Viewer Creation• Problem Solving


Larry Aagesen

Five?

Step-By-Step Walk-Though Follows


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Documents

Summer School for Integrated Computational Materials Education 2015 Kinetics Module Review Katsuyo Thornton, 1 Edwin Garcia, 2 Larry Aagesen, 1 Mark Asta