The dopant distribution coefficient and equilibrium growth

A different application of chemical equilibrium leads to an explanation of how the incorporation of defects and dopants depends on the growth conditions (Winer and Street 1989). Section S.l describes the unexpected rf power and gas concentration dependence of the dopant distribution coefficient, particularly for arsenic doping. A schematic diagram of the growth process is shown in Fig. 6.19, in which three-fold and four-fold silicon and dopants are deposited from the gas phase. The deposition reactions proposed for arsenic doping are 

The subscripts denote the coordination in the a-Si H film, e is an electron, C is the gas-phase mole fraction of the species, and the 

The approximations are valid because the concentration of band tail electrons is small and most of the arsenic and silicon atoms are threefold and four-fold coordinated, respectively. 

69) and (6.70) are the doping reactions related to the gas-phase and solid-phase concentrations of silicon and phosphorus. The square root law applies to the gas-phase arsenic concentration provided that and are regular (i.e. independent of arsenic concentration). However, the law only applies to the solid-phase concentrations (Eq. (6.70)) if, in addition, is also constant. The variation of the arsenic distribution coefficient with rf power and gas concentration (Fig. 5.4) explains the deviations from the doping law for the solid phase which are shown in Fig. 5.17. The phosphorus distribution coefficient has a much weaker dependence on the rf power and gas concentration, so 

The distribution coefficient can be expressed in terms of the relative deposition rates for silicon and arsenic, and r  

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