Introduction

 

 

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.