Impurity incorporation and doping efficiency in a-Si:H

A chemical equilibrium model of impurity incorporation in a-Si:H leads to a simple expression for the doping efficiency η of substitutional impurities I in terms of the impurity distribution coefficient, d(I), and the gas-phase impurity mole fraction, ${\mathit{X}}_{\mathit{I}}$; η==[${\mathit{I}}_4$]/[I]∝(d(I)${)}^{\mathrm{-}1}$${\mathit{X}}_{\mathit{I}}^{\mathrm{-}1/2}$. In order to test this model, the distribution coefficients of As and P were measured over a wide range of a-Si:H deposition conditions from which η and the impurity incorporation rate were determined. An approximate analytical expression for d(I) has been fitted to the data and various impurity-incorporation mechanisms are considered to account for its form. The resulting intuitive, analytical expressions for the incorporation rate and doping efficiency of substitutional impurities in a-Si:H are valid for most deposition conditions.