Dopant Profiling in Silicon Wafers by Fourier Transform Infrared Spectroscopy

Abstract

A novel non-destructive method for one-dimensional dopant profiling in silicon wafers is presented. The approach is based on the measurements of the infrared reflectivity of the sample, performed by a Fourier Transform Infrared Spectrometer (FTIR), so it can be used both for ex situ and in situ analysis. In this work, we introduce a formulation of the problem that permits to linearly relate the field intensity reflected by the wafer to the doping profile. In particular, starting from the integral relations of the optical tomography that permit to relate the reflected field intensity to the dielectric profile of the sample, we consider the first order approximation of the reflected field intensity about a reference profile. By means of the relationship (Drude-Lorentz model), which holds true at infrared wavelengths, between the free carriers concentration and the complex permittivity of the semiconductor material, we directly relate the infrared spectroscopy data to the dopant profile. From this formulation an iterative algorithm is developed, such as at each iteration step the problem is formulated as the minimization of a proper functional representing the error between the measured reflected intensity, at different wavelengths, and the model data. In the first step we can assume as reference profile either the homogeneous one or the expected profile, the recovered profile is then used as reference profile in the next step and so on until a negligible variation between two successive recovered profiles is achieved. The main advantage of this approach is that the unknown carriers concentration profile is not described by a „parametric“ expression of a known function as in, but an expansion in a finite series of basis function is used. In this way we do not need to fix a priori the functional form of the doping profile.