Effect of complex formation on diffusion of arsenic in silicon

When As diffuses into Si, only a fraction of the As remains electrically active. Because of the importance of As as an emitter dopant, it is necessary to understand the nature of the inactive As and how it affects the solubility and diffusion of As⁺ ions. A model is proposed in which As⁺ diffuses via a simple vacancy mechanism while in quasiequilibrium with [V_SiAs₂] complexes. The flux of mobile monatomic As⁺ is modified according to the extent of [V_SiAs₂] complex formation. The structure of this defect and its formation energy (≈ 1.8 eV) are discussed. An effective diffusion coefficient is derived using this model: $D_{\mathrm{As}}{\text{=2D}}_i{C}_A{\text{\hspace{0.17em}/(1+8 K}}_2{\mathrm{\prime \; C}}_A^3)$ where C_A is the As⁺ concentration and $K_2\prime$ is a collective parameter that depends upon As⁺ surface concentration and the diffusion temperature. Experimental verification of the correctness of this equation is given. The important results of this quantitative analysis show that D_As reaches a maximum value with increasing As concentration, and then decreases monotonically. The As concentration at which D_max occurs is dependent upon the total As surface doping and the diffusion temperature. The ratio of total As to electrically active As⁺ decreases to a value of unity at 1300 °C. At 1250 °C it is shown that the solubility of As⁺ reaches a maximum value of 1.5 × 10²¹ atoms/cm³ in p‐type Si and 1.2 × 10²¹ atoms/cm³ in n‐type Si.