Si molecular beam Epitaxy: A model for temperature dependent incorporation probabilities and depth distributions of dopants exhibiting strong surface segregation

A model describing the incorporation of thermal dopants into single crystal films grown by molecular beam epitaxy (MBE) is presented. The model is general, accounts for dopant surface segregation during deposition, and allows dopant incorporation probabilities and depth profiles to be calculated as a function of film growth conditions (e.g. deposition rate, dopant beam flux, and growth temperature T_s). Input data to the model include thermodynamic parameters such as the free energy of segregation and dopant-surface binding energies together with kinetic parameters such as incident fluxes and dopant diffusivities. The model is applied here to Si MBE in which common dopants are typically characterized by strong surface segregation and temperature-dependent incorporation probabilities σ. Calculated values of σ(T_s) and calculated depth profiles were found to agree very well with available experimental data for both group-III acceptors and group-V donors in Si. In addition, the model predicts, in agreement with limited experimental data, that a growth parameter range exists in which abrupt doping profiles can be obtained, even for dopants which exhibit strong surface segregation. Finally, transition temperatures from equilibrium to kinetically-limited segregation are determined for several dopants.