Ion Implantation and Synthesis of Materials - Studium

146 11 Si Slicing and Layer Transfer: Ion-Cutapparent diffusivity is dependent on the method of hydrogen insertion. Hydrogencan be introduced into silicon through various processes – such as reactive ionetching,glow discharge, plasma hydrogenation, or H-ion implantation – andconsequently each method, with its distinct influence on defect or impuritygeneration in the silicon crystal, leads to a different behavior of hydrogen in thematerial. For example, hydrogen appears to diffuse more rapidly under conditionsof low hydrogen concentration than it does under conditions of high hydrogenconcentration. Furthermore, H diffusion is a function of the silicon conductivityand type.The earliest work on the behavior of hydrogen in crystalline silicon (c-Si)found that hydrogen is very mobile in c-Si and that, in the temperature regimebetween 900 and 1,200°C, the diffusion coefficient could be expressed asDH−3 ⎛−0.48eV⎞ 2 −1= 9.4 × 10 exp⎜ ⎟cm s ,⎝ kT ⎠(11.1)where k is the Boltzmann constant (Van Wieringen and Warmoltz 1956). At thesehigh temperatures the interaction of H atoms with defects and impurities is low.Studies performed with tritium diffusion in c-Si at lower temperatures, in therange of 400–550°C, found that the diffusion in c-Si could be described as(Ichimiya and Furuichi 1968)DT−5 ⎛−0.56eV⎞ 2 −1= 4.2 × 10 exp⎜ ⎟cm s .⎝ kT ⎠(11.2)Experimental and theoretical studies on H diffusion in silicon at lowertemperatures, where trapping of hydrogen at defects and impurities and H 2 -molecule formation are significant, discovered much lower effective diffusivities.Values for the H-diffusion coefficient in silicon expected from an extrapolation ofthe diffusion coefficient of (11.1) to lower temperatures are several orders ofmagnitude higher than experimentally obtained diffusivities. This is illustrated inFig. 11.2, which shows (11.1) and (11.2) extrapolated to low temperatures withexperimentally determined values from Johnson et al. (1986).Several processes have been invoked to explain the details of hydrogen profilesin silicon. These processes include reactions of hydrogen at dopant sites and withlattice defects, reactions between hydrogen atoms, and the dissociation of trappedhydrogen. Pseudopotential density functional calculations showed that atomichydrogen in silicon can appear in all three charge states: H + , H0, and H – (Van deWalle et al. 1989). The charge state depends on the position of the Fermi level.The positive charge state is more stable in p-type silicon and the negative chargestate more stable in highly n-type doped silicon. Therefore, charge state-dependentdiffusion coefficients have been incorporated into many kinetic studies.