Mathematical modeling of the heat and mass transport during laser processing of silicon

The incorporation of phosphorus dopant into the front side of a silicon wafer is important for making high efficiency photovoltaics. These types of photovoltaics require structures known as selective emitters, which are characterized by heavily doped, highly conductive areas directly beneath the metallized contacts and lightly doped regions in between the contacts that enhance light collection at lower wavelengths. Laser doping offers an appealing way to form selective emitters because the incorporation of dopant can be done in the liquid state. A three-dimensional mathematical model, which solves for temperature, dopant, and fluid velocity fields, is used to investigate the role of fluid flow on the final dopant distribution profile during the laser doping process with a continuous-wave laser operating with a 532 nm wavelength. The output power and scanning velocity were varied from 10 to 20 W and 0.5 to 5.0 m/s, respectively. Instantaneous and final dopant profiles under different doping conditions are compared.