Modeling of Carbon Clustering and Associated Metal Gettering
Authors: Jin Yu , Dunham Scott T. 
Published: February 2020

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.