4.4.2 Segregation Model

  At the early stage of a diffusion process equilibrium at the material interface is not reached, hence, we have to define a diffusion flux across the interface box area which accounts for the segregation kinetics, as given by (4.4-4), where denotes the transport coefficient.

 

determines how fast any disturbance of the equilibrium conditions at the interface is compensated by the dopant flux across the interface. After thermal equilibrium is reached the ratio of the concentrations on each side of the boundary are given by the according segregation coefficient m.

Generally, segregation coefficients are extracted form experiments under certain process conditions. It is possible to trace the dopant concentration across the interface with SIMS analysis, followed by the extraction of the segregation data to obtain good simulation results. Unfortunately, segregation behavior is influenced by other process conditions like local hydrogen or florine content in the material layers. Advanced process technologies are even able to control the segregation process. During the fabrication of the gate oxide it is common to blow in nitrogen at the end of the oxidation process for several seconds. This short term nitridation affects the segregation conditions at the gate oxide interface significantly. Thus the oxide layer represents a stable diffusion barrier for dopants [Mat93].

Generally, the silicon/silicon dioxide interface is of vital importance for process development. The most commonly used p-type dopant, boron, exhibits strong tendencies to accumulate in the oxide (m ;SPMlt; 1), where phosphorus shows the opposite segregation behavior (m ;SPMgt; 1). Segregation data [Plu86] for several dopants at the silicon/silicon dioxide interface are given in Table 4.4-1.