Diffusion
has been the primary method of introducing impurities such as boron,
phosphorous, and antimony into silicon to control the majority-carrier type and
resistivity of layers formed in the wafer. Diffusion is used to form bases,
emitters, and resistors in bipolar device technology, to form source and drain
regions and to dope polysilicon in MOS device technology.
The most common methods of diffusion are
·
Diffusion from a
chemical source in a vapor form at high temperature.
·
Diffusion from a
doped-oxide source
·
Diffusion and
annealing from an ion-implanted layer
Diffusion theories have been
developed from two major approaches
·
The continuum theory
of Fick's simple diffusion equation.
·
The atomistic theory,
which involves interactions between point defects (vacancies and interstitial
atoms) and impurity atoms.
Notes:
·
In silicon when
impurity concentrations are low, the measured diffusion profiles are well
behaved and agree with Fick's diffusion equation with a constant diffusivity,
which can be calculated readily.
·
When impurity
concentrations are high, however, the diffusion profiles deviate from the
predictions of the simple diffusion theory and impurity diffusion is affected
by factors not considered in Fick's simple diffusion laws.
·
Since the diffusion
profile measurements reveal concentration-dependent diffusion effects, Fick's
diffusion equation with concentration
dependent diffusivities is applied to the high concentration diffusions.[2]
·
A Boltzmann-Matano
analysis or other formulations of profile analysis determine the
concentration-dependent diffusivities.