u00d7 10 16 atoms cm u2212 3 consequently in carbon doped crystals there is no or an extremely reduced need to increase l c by reducing the axial oxygen variation increasing the oxygen concentration toward the crystal tail upon review of the graph shown in fig5 it is seen that there is established a simple method to estimate the oxygen concentration needed over a range of carbon co doping levels the data points u201c a u201d u201c b u201d and u201c c u201d in fig4 and corresponding data points u201c d u201d u201c e u201d and u201c f u201d in fig5 were derived from tests comparing three heavily arsenic doped crystals of 100 mm diameter the arsenic concentration in these crystals was targeted to increase from 1 8 u00d7 10 19 atoms cm u2212 3 crystal seed to 3 8 u00d7 10 19 atoms cm u2212 3 crystal tail the corresponding amount of arsenic dopant was added to 30 kg charges of poly silicon after melting the silicon charge the first crystal was grown without intentionally adding carbon data points u201c a u201d and u201c d u201d respectively in fig4 and 5 the second crystal was grown after adding only 50 mg high purity carbon to the melt data points u201c b u201d and u201c e u201d respectively in fig4 and 5 and for the third crystal 150 mg high purity carbon was added data points u201c c u201d and u201c f u201d respectively in fig4 and 5 no additional countermeasures for homogenizing the axial oxygen profile were applied as a result the three crystals with varying carbon levels have a comparable axial oxygen profile the oxygen concentration falls from 8 3 u00d7 10 17 atoms cm u2212 3 at.