PHYSICO-MATHEMATICAL MODELING OF SEMICONDUCTOR NANODEVICES

The article presents a physico-mathematical model of two-stage diffusion of donor and acceptor impurities in silicon semiconductors for the formationof two p - n - junctions in nanoscale structures. The model takes into account the temperature dependence of diffusion coefficients and activation energy,duration of diffusion cycles, impurity concentration in the initial silicon, surface concentrations, and the solubility limit of dopants. Onedimensionalconcentration profiles were simulated numerically, with identification of conductivity type inversion points. The depths of the emitter and collector junctions and the base width were calculated, considering secondary redistribution of dopants. The simulation was carried out using the MathCAD environment. Doping profiles were constructed for each stage of thermal treatment. The influence of technological parameters on the formation of the electric field in the base region was evaluated. The dependence of the junction positions on the time and temperature of individual diffusion stages was demonstrated. A series of simulations was conducted for various geometric scales: 100 nm, 50nm and 20nm . The change in base width under different pre-deposition and drive-in regimes was determined. Concentration distribution curves were plotted for each case. The current gain in a common-emitter configuration was evaluated. Numerical data were presented for typical technological parameters. The proposed model can be used to predict transistor parameters prior to fabrication and to justify the choice of optimal conditions for base region formation in micro- and nanoelectronic structures.