Theoretical calculations of Debye length, built-in potential and depletion layer width versus dopant density in a heavily doped p-n junction diode

Theoretical calculations of Debye length, built-in potential, depletion layer width and capacitance as a function of dopant density in a heavily doped p-n junction diode are described in this paper. The heavy doping effects such as carrier degeneracy, dopant density-dependent dielectric constant and bandgap narrowing are accounted for by using the empirical approximation for the reduced Fermi-energy given by[1] and the dopant density dependent dielectric constant given by[2], as well as the bandgap narrowing model proposed by[3]. The results show that: (1) bandgap narrowing and carrier degeneracy have important effects on the junction built-in potential; (2) carrier degeneracy and dopant density-dependent dielectric constant are important to Debye length for the abrupt junction case, and (3) the dopant density-dependent dielectric constant is a key parameter which strongly affects the values of depletion layer width and depletion capacitance. These findings are important for modeling of heavily doped p-n junction devices in the VLSI applications.