Next: 4.4 Model Overview with Up: 4. Oxidation of Doped Previous: 4.2 Five-Stream Dunham Diffusion

4.3 Segregation Interface Condition

If at the Si/SiO interface there is a dopant concentration $C_{I,O}$ and $C_{I,Si}$ on the oxide and silicon side, respectively, as illustrated in Fig. 4.1, the segregation coefficient can be written as [83]

$\displaystyle m=\frac{C_{I,Si}}{C_{I,O}}$

(4.23)

If it is assumed that $C_{I,O}>C_{I,Si}$ the flux of dopants from the SiO

segment to the silicon segment through the interface is [83]

$\displaystyle J_S=k_O C_{I,O}-k_{Si} C_{I,Si}=k_O\Big(C_{I,O}-\frac{k_{Si}}{k_O}\Big)=h\Big(C_{I,O}-\frac{C_{I,Si}}{m}\Big),$

(4.24)

where

and $k_{Si}$ are the reaction rate coefficients in SiO

and silicon, respectively.

is the interface transfer coefficien which has units of velocity.

In the steady state the interface flux and (4.24) can be transformed to the relationship

$\displaystyle \frac{C_{I,O}}{C_{I,Si}}=\frac{k_{O}}{k_{Si}}.$

(4.25)

Next: 4.4 Model Overview with Up: 4. Oxidation of Doped Previous: 4.2 Five-Stream Dunham Diffusion

Ch. Hollauer: Modeling of Thermal Oxidation and Stress Effects