Understanding and controlling the impurity behavior are important for low-cost and high-efficiency of multi-crystalline silicon solar cells. We employ the infrared spectroscopy to study the change of oxygen and carbon concentrations after thermal treatment in different parts of multi-crystalline silicon ingots grown by directional solidification technology. In correlation with the solar cell performances such as the minority carrier lifetime, photoelectric conversion efficiency and internal quantum efficiency, we investigate the physical mechanism of the effects of various concentrations of oxygen and carbon on cell performance. We propose an oxygen precipitation growth model considering the influence of carbon to simulate the size distribution and concentration of oxygen precipitation after the thermal treatment. It is found that carbon not only deteriorates the efficiency of the cells made from the silicon from the top part of the ingot, but also plays an important role in the effect of oxygen precipitation: enhancing the size and the quantity of oxygen precipitation in the silicon from the middle part of the ingot, which induces the defect and increases the recombination; while resulting in the small size and low quantity of oxygen precipitation in the silicon from the bottom part due to the low carbon content, thereby improving the cell efficiency through gettering impurities. We further demonstrate the complex behaviors of oxygen and carbon by a two-step thermal treatment technique, from which we point out that the two-step thermal treatment is applicable only to the improvement of the efficiency of solar cells from the bottom part of multi-crystalline silicon ingots.