Contactless characterization of doping profiles in silicon

A non-destructive and contactless method for the characterization, both ex situ and in situ, of one-dimensional doping profiles in semiconductor wafers is presented. Using the integral equations of the optical diffraction tomography, and the Drude-Lorentz model, which relate at infrared wavelengths the free carriers concentration to the complex permittivity of the semiconductor material, we have developed an iterative algorithm allowing to reconstruct one dimensional profiles in semiconductor samples starting from infrared spectroscopy data. In our approach, the unknown carriers concentration profile is not constrained to a given functional form (Gaussian, erfc,etc.), but an expansion in a finite series of basis function is used. This allows to recover the ``true'' profile without increasing too much the number of unknowns. Numerical simulations confirm the validity of the approach.