The Importance of Pairing Reactions for the Modeling of Defect-Dopant Interactions in Silicon
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demanded by processes like TEOS or nitride deposition often requiring temperatures between 600'C and 800'C. When such processes directly follow an ion implantation step (e.g. for spacer formation immediately after S/D extension implantation), models based on local pair equilibrium fail to predict TED even if interstitial clustering is taken into account. DIFFUSION MODELS In order to investigate the influence of pairing reactions, two diffusion models are compared. One is the model labeled 'pda.full' of TSUPREM4[8] which is based on the assumption of local pair equilibrium, the other is a self coded model allowing for full dynamic pairing of dopants and point defects. The latter model was implemented in the equation solver PROMIS[9]. Throughout this study, phosphorus will be used as the diffusing species but as already indicated above, the results principally hold for boron as well. Dopant-Defect Reactions Both models take into account the following dopant-defect reactions: Ji +Vj A+ + P
(-i -j)e-
(1)
API+1
(2)
29 Mat. Res. Soc. Symp. Proc. Vol. 532 01998 Materials Research Society
A+ + V'
APi+
Vi
- AV+ 1
AV' + Py•
A+ + (I - i - j)eA+ + (1 - i - j)e-
(3) (4) (5)
Eq. (1) represents the bulk recombination of interstitials I and vacancies V. The reaction of substitutional dopants A with point defects to form dopant-interstitial pairs AI and dopant-vacancy pairs AV is described by Eqs. (2-3), respectively, while Eqs. (4-5) describe the recombination of pairs with the opposite type of point defect. Superscripts denote the charge states of the species, so A is a donor in the above reactions. The substitutional donor always has the charge state +1. But point defects and pairs can change their charge states by exchange of electrons with the thermal electron gas. As far as the charging reactions X1 - e XiT(6) are concerned, local equilibrium is assumed in both models. The validity of this approximation is supported by an estimation of the time constant of charging given in reference
[I].
The model in TSUPREM4 is based not only on the assumption of local equilibrium of the charging reactions Eq. (6) but also on local equilibrium of the pairing reactions Eqs. (2-5). Therefore the system of differential equations to be solved for the diffusion of species A reduces to three equations for the total concentrations I = I + AI, V = V + AV and A= A+AI+AV. The reference model implemented in PROMIS assumes local equilibrium of charging but not of pairing reactions. Consequently the full set of five differential equations for the species A, I, V, Al and AV has to be solved. Selection of Model Parameters The physical parameters used in both models have been taken from the literature[3, 4, 5]. With these parameters the models reproduce phosphorus diffusion experiments at 900'C and 1000°C with constant phosphorus surface concentrations ranging from intrinsic to solid-solubility very well. Using the same parameters both models give similar results for these experiments since pairing reactions can be assumed to be in local equ
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