Chapter 7: Diffusion

Chapter 7: Diffusion

ISSUES TO ADDRESS...
• How does diffusion occur?
• Why is it an important part of processing?
• How can the rate of diffusion be predicted for some simple cases?
• How does diffusion depend on structure and temperature?

AMSE 205 Spring ‘2016

Chapter 7 - 1

Diffusion
Diffusion - Mass transport by atomic motion
Mechanisms • Gases & Liquids – random (Brownian) motion • Solids – vacancy diffusion or interstitial diffusion

AMSE 205 Spring ‘2016

Chapter 7 - 2

Diffusion

• Interdiffusion: In an alloy, atoms tend to migrate
from regions of high conc. to regions of low conc.

Initially

After some time

Figs. 7.1 & 7.2, Callister & Rethwisch 9e.

AMSE 205 Spring ‘2016

Chapter 7 - 3

Diffusion

• Self-diffusion: In an elemental solid, atoms
also migrate.

Label some atoms
C

After some time
C

A

D

A

D

B

B

AMSE 205 Spring ‘2016

Chapter 7 - 4

Diffusion Mechanisms
Vacancy Diffusion:
• atoms exchange with vacancies • applies to substitutional impurities atoms • rate depends on:
-- number of vacancies -- activation energy to exchange.

increasing elapsed time
AMSE 205 Spring ‘2016

Chapter 7 - 5

Diffusion Mechanisms
• Interstitial diffusion – smaller atoms can diffuse between atoms.

Fig. 7.3 (b), Callister & Rethwisch 9e.
More rapid than vacancy diffusion
AMSE 205 Spring ‘2016

Chapter 7 - 6

Processing Using Diffusion

• Case Hardening:
-- Diffuse carbon atoms into the host iron atoms at the surface.
-- Example of interstitial diffusion is a case hardened gear.

Chapter-opening photograph, Chapter 7, Callister & Rethwisch 9e.
(Courtesy of Surface Division, Midland-Ross.)

• Result: The presence of C atoms makes iron (steel) harder.

AMSE 205 Spring ‘2016

Chapter 7 - 7

Processing Using Diffusion

• Doping silicon with phosphorus for n-type semiconductors:

• Process:

0.5 mm

1. Deposit P rich layers on surface.

magnified image of a computer chip

silicon

2. Heat it.
3. Result: Doped semiconductor regions.

light regions: Si atoms

silicon

light regions: Al atoms
Adapted from Figure 19.27, Callister & Rethwisch 9e. AMSE 205 Spring ‘2016

Chapter 7 - 8

Diffusion
• How do we quantify the amount or rate of diffusion?

• Measured empirically
– Make thin film (membrane) of known cross-sectional area – Impose concentration gradient – Measure how fast atoms or molecules diffuse through the
membrane

M= mass diffused

J  slope time

AMSE 205 Spring ‘2016

Chapter 7 - 9

Steady-State Diffusion
Rate of diffusion independent of time Flux proportional to concentration gradient =

C1 C1

Fickʼs first law of diffusion

C2 C2 x1 x2
x

D  diffusion coefficient

AMSE 205 Spring ‘2016

Chapter 7 - 10