With the scaling of MOSFET's dimensions into the submicron regime, the influence of the distribution of dopants on short channel device characteristics increases dramatically. The complex multi-dimensional fields created by the doping profile become one of the most important factors in determining the electrical behavior of MOSFETs. One-dimensional (1D) profiling tools such as spreading resistance (SRP) and secondary ion mass spectrometry (SIMS) are available. However, due to the shallow vertical and lateral junctions, the proximity effects, and the interaction between dopants species, 1D profiles are less indicative of actual two-dimensional (2D) profiles. Attempts to extend the 1D profiling tools to higher dimensions (e.g. 2D SRP, 2D SIMS) have met with limited success when applied to state-of-the-art CMOS technology [98][58][32]. Newer techniques aimed at addressing these shortcomings are still in the early development stage [72][23][2].
Scientists in other fields, such as in geophysics, facing a similar lack of direct experimental measurements resort to inverse modeling [100][73]. The use of inverse modeling techniques for doping profiling have been suggested first in [77]. Two methods were proposed. The first method parameterizes the profile using analytical expressions. This presumes a priori knowledge of the general form of the profile functional variation. The second method discretizes the profile and employs a dedicated iterative linear least squares solver to determine the doping at all the grid points. The resulting large number of parameters in this formulation could cause the least-squares problem to become ill-conditionned. The use of singular value decomposition was proposed as a solution in this case. Different one-dimensional (1D) examples were presented as well as a two-dimensional (2D) profile extraction of a junction charge-coupled device.
In [55][53][54][52], inverse modeling techniques for the determination of one- and two-dimensional MOSFET doping profiles from electrical C-V measurements are described. The implementation is based on similar principles, namely the inference of the continuous variation of the doping profile from the solution of Poisson's equation and appropriate capacitance measurements. Two major new contributions are: