Silicon Oxidation Model



Deal and Grove’s model describes the kinematics of silicon oxidation. The model is generally valid for temperatures between 700 and 1300°C, partial pressures between 0.2 and 1 atmosphere, and for oxide thickness between 300 and 20,000°A for oxygen and water ambients.


Flux is the number of atoms or molecules crossing a unit area in unit time.



                  Fig. 2 Basic model for thermal oxidation of silicon [2]


Basic model for thermal oxidation of silicon [2]


The oxidizing species:





Under steady state, all the fluxes are equal, F1=F2=F3



F1=hG(CG-CS) -----------------(1)


          Where hG is the gas phase mass-transfer coefficient. [1] [4]



C0=HpS and C*=HpG



C0 is the equilibrium concentration in the oxide at the outer surface.

C* is the equilibrium bulk concentration in the oxide.

pS is the partial pressure in the gas adjacent to the oxide surface.

pG is partial pressure in the bulk of gas

H is Henry’s law constant.



C0=HpS=HkTCS where pS=kTCS   and 


C*=HpG=HkTCG where pG=kTCG


Substituting, C0 and C*, into equation (1), we get the following:


F1=h(C*-C0) where h=hG/HkT




F2 = D(C0-Ci)/d0



D is the diffusion coefficient

Ci is the oxidizing species concentration in the oxide adjacent to the oxide-silicon interface.

d0 is the oxide thickness.





Where kS is the rate constant of chemical surface reaction for silicon oxidation.



F1=F2=F3  and solving simultaneous equations we can find Ci and C0.





d02 + A d0 = B(t+t)


Where t represents a shift in the time axis to account for the presence of the initial oxide layer di.






N1 is the number of oxidant molecules incorporated into a unit volume of the oxide layer.