Modeling of Carbon Clustering and Associated Metal Gettering

Abstract

Carbon implantation has significant potential for reduction of dopant diffusion and proximity gettering for low thermal budgets and SOI structures. There are two major contributions of this paper: a carbon clustering/precipitation model and models for metal gettering by carbon clusters. We consider a range of small C/I clusters and a moment-based precipitation model to describe precipitation of larger C precipitates. The energetics of C/I clusters are based on DFT calculations. The model for carbon precipitation is similar to previously developed oxygen precipitation model. To get the formation energy of C clusters, we use two different but complementary methods. One is from bottom to top, DFT calculation of small clusters, the other is from top to bottom, based on the formation energy of SiC and SiC/Si interfaces. For the DFT calculation, we tried different configurations for each cluster. We find that for small clusters the most energetically favored structure is elongated along a chain. The calculation results are listed in the Table 1 (The formation energies use interstitial C, CI, as the reference). Table 1. Formation energy for C/I clustersConfigurationsC2I2C3I3C4I4C5I5Infinite Chain (8 CIs in 64 Cell)System energy (eV)-361.87-370.44-378.50-385.96-410.00Formation energy (eV)-2.671-5.484-7.784-9.481-16.252 Based on the calculation results, we determine an expression for the formation energy of small cluster by considering strain energy and surface energy. For larger clusters (precipitates), we utilize DFT calculations of bulk formation energy differences and Si/SiC interface energy (1.58 J/m2). Combining the two approaches, we choose the lower energy value at each size in our simulations.A major portion of the work is obtaining the binding energy to carbon precipitates for different metal species. We put a metal atom in different 1NN or 2NN tetrahedral sites to find the strongest binding sites. The final results can be found in Tables 2.1-2.5.Table 2.1 Energy for Metal in siliconconfigurationCu_SiFe_SiW_SiNi_SiTi_SiCr_SiMo_SiSystem energy (eV)-349.779-354.538-357.43-352.371-354.01-354.804-356.34 Table 2.2 Metal binding energy for C2I2ConfigurationCuC2I2FeC2I2WC2I2NiC2I2TiC2I2CrC2I2MoC2I2System energy (eV)-364.289-368.954-371.888-367.187-368.536-369.592-370.711Binding energy-0.3226-0.2281-0.2699-0.628-0.3377-0.5998-0.1824 Table 2.3 Metal binding energy for C3I3ConfigurationCuC3I3FeC3I3WC3I3NiC3I3TiC3I3CrC3I3MoC3I3System energy (eV)-373.207-378.078-380.774-376.211-377.503-378.81-379.264Binding energy-0.669-0.78-0.5845-1.0802-0.7333-1.2463-0.1642 Table 2.4 Metal binding energy for C4I4ConfigurationCuC4I4FeC4I4WC4I4NiC4I4TiC4I4CrC4I4MoC4I4System energy (eV)-381.894-386.115-389.107-383.931-386.444-387.385-387.89Binding energy (eV )-1.2963-0.7578-0.8584-0.7413-1.615-1.762-0.7314Corrected binding energy (eV)-0.6603-0.6048-0.6434-1.208-1.528-0.4034 Table 2.5 Metal binding energy for SiCConfigurationCuSiCFeSiCWSiCNiSiCTiSiCCrSiCMoSiCSystem energy (eV)-1143.5-1149.1-1152.19-1144.93-1147.99-1147.34-1150.96Binding energy-2.3232-3.1642-3.3621-1.1563-2.5822-1.1352-3.222 The resulting model is compared to experimental observations of C redistribution and gettering.