In this study, line defects and point defects are introduced in a complete two-dimensional triangular lattice silicon. Using waveguide coupling and linear interference, an all-optical half-adder structure based on photonic crystal is proposed. The half-adder consists of waveguide beam splitters, an all-optical logic AND gate and an all-optical logic XOR gate. Using Rsoft software, combined with the plane-wave-expansion method and the finite-difference time-domain method, the proposed half-adder is simulated. Results show that the contrast ratios of the "carry" and "sum" ports of the proposed half-adder are 4.67 dB and 10.77 dB when the input-light wavelength is 1530 nm, and the response time is about 2.67 ps. In order to improve the contrast ratio of the "carry" port, the structure of the half-adder is optimized. The contrast ratios of the "carry" and "sum" ports of the optimized half-adder are 8.26 dB and 15.34 dB, respectively, and the response time is 3.67 ps. Theoretically, it can reach a data transmission rate of 0.273 Tbps. The proposed half-adder with optimized structure has the characteristic of high contrast ratio, and plays an important role in all-optical signal processing systems and integrated optical circuits.