Callister - An introduction - 8th edition

Summary • 143
Diffusion in Semiconducting Materials
• The two heat treatments that are used to diffuse impurities into silicon during
integrated circuit fabrication are predeposition and drive-in.
During predeposition, impurity atoms are diffused into the silicon, often from
a gas phase, the partial pressure of which is maintained constant.
For the drive-in step, impurity atoms are transported deeper into the silicon
so as to provide a more suitable concentration distribution without increasing
the overall impurity content.
• Integrated circuit interconnects are normally made of aluminum—instead of metals
such as copper, silver, and gold that have higher electrical conductivities—on
the basis of diffusion considerations. During high-temperature heat treatments,
interconnect metal atoms diffuse into the silicon; appreciable concentrations will
compromise the chip’s functionality.
Equation Summary
Equation
Page
Number Equation Solving for Number
5.1a J M At
Diffusion flux 126
5.3 J D dC Fick’s first law—diffusion flux for steady-state diffusion 127
dx
0C
5.4b D 02 C
Fick’s second law—for nonsteady-state diffusion 128
0t 0x 2
C x C 0
x
5.5 1erf a Solution to Fick’s second law—for constant surface composition 129
C s C 0 22Dt b
5.8 D D 0 exp a Q d
Temperature dependence of diffusion coefficient 133
RT b
List of Symbols
Symbol
Meaning
A Cross-sectional area perpendicular to direction of diffusion
C Concentration of diffusing species
C 0 Initial concentration of diffusing species prior to the onset of the diffusion process
C s Surface concentration of diffusing species
C x Concentration at position x after diffusion time t
D Diffusion coefficient
D 0 Temperature-independent constant
M Mass of material diffusing
Q d Activation energy for diffusion
R Gas constant (8.31 J/mol # K)
t Elapsed diffusion time
x Position coordinate (or distance) measured in the direction of diffusion,
normally from a solid surface