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Nondestructive evaluation (NDE) is to materials and structures as CAT-scanning is to the human body--an attempt to look inside without opening it. As in CAT-scanning, modern NDE requires sophisticated mathematical software to perform the mathematical "inversion" operations that allow one to infer the internal state of a structure from external measurments. In this note we will show how VIC-3D® fulfills this need. In reading this example, keep in mind that the data could be taken with a conventional impedance analyzer, such as the HP4194A. For higher frequencies, up to 180MHz,or so, the HP4915A series can be used. There is nothing exotic about the instrumentation; the exotic stuff is in VIC-3D®.
Figure 1: Typical semiconductor workpiece

Statement of the Problem:

  • t0=t1 + t2 + t3, the total thickness of the package
  • sigmaAl=3.57&times:107 S/m, the conductivity of aluminum
  • sigmaEpi=10 S/m, the conductivity of the epi-layer
  • t2=10× 10-6 m, the thickness of the epi-layer
  • t1, the thickness of the aluminum layer
  • sigmaSi, the conductivity of the silicon substrate

The problem shown here is extremely important in fabricating semiconductor wafers. It is quite difficult to simultaneously measure aluminum film thicknesses of the order of 560Å and semiconductor substrate conductivities of the order of 20,000 S/m using conventional instruments. We have shown that eddy-currents can do this job, by applying VIC-3D®, together with the same inversion algorithm that was used in the first example. Indeed, we have shown that one can solve this problem using either multifrequency or multi-liftoff impedance measurments. The VIC-3D® module even allows one to compute sensitivity coefficients and correlation matrices, from which variances can be computed. These data are useful for determining the stability of the solution. Our inversion computations showed that one can determine the film thickness and substrate conductivity accurately, even in the presence of significant amounts of noise.