Modeling of Carbon Clustering and Associated Metal Gettering

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 clusters

Configurations	C2I2	C3I3	C4I4	C5I5	Infinite Chain    (8 CIs in 64 Cell)
System energy (eV)	-361.87	-370.44	-378.50	-385.96	-410.00
Formation 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 silicon

configuration	Cu_Si	Fe_Si	W_Si	Ni_Si	Ti_Si	Cr_Si	Mo_Si
System energy (eV)	-349.779	-354.538	-357.43	-352.371	-354.01	-354.804	-356.34

Table 2.2 Metal binding energy for C2I2

Configuration	CuC2I2	FeC2I2	WC2I2	NiC2I2	TiC2I2	CrC2I2	MoC2I2
System energy (eV)	-364.289	-368.954	-371.888	-367.187	-368.536	-369.592	-370.711
Binding energy	-0.3226	-0.2281	-0.2699	-0.628	-0.3377	-0.5998	-0.1824

Table 2.3 Metal binding energy for C3I3

Configuration	CuC3I3	FeC3I3	WC3I3	NiC3I3	TiC3I3	CrC3I3	MoC3I3
System energy (eV)	-373.207	-378.078	-380.774	-376.211	-377.503	-378.81	-379.264
Binding energy	-0.669	-0.78	-0.5845	-1.0802	-0.7333	-1.2463	-0.1642

Table 2.4 Metal binding energy for C4I4

Configuration	CuC4I4	FeC4I4	WC4I4	NiC4I4	TiC4I4	CrC4I4	MoC4I4
System energy (eV)	-381.894	-386.115	-389.107	-383.931	-386.444	-387.385	-387.89
Binding energy (eV )	-1.2963	-0.7578	-0.8584	-0.7413	-1.615	-1.762	-0.7314
Corrected binding energy (eV)	-0.6603	-0.6048	-0.6434		-1.208	-1.528	-0.4034

Table 2.5 Metal binding energy for SiC

Configuration	CuSiC	FeSiC	WSiC	NiSiC	TiSiC	CrSiC	MoSiC
System energy (eV)	-1143.5	-1149.1	-1152.19	-1144.93	-1147.99	-1147.34	-1150.96
Binding 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.