4.5.2 Results



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4.5.2 Results

To illustrate the failure of simple knot placement strategies, Fig. 4.1 compares the analytically extracted profile with profiles determined using 10 and 15 equally spaced knots. It is clear that the oscillations between 0.6 and 1.3 are an artifact of the extraction   procedure. In essence, the range and the number of available measurement voltages, the doping level, and the number of coefficients make such an extraction ill-conditionned.

The use of the self-adaptive scheme described in the previous section   resolves these problems. New knots are only inserted where they are needed as determined from the capacitance fit errors. In this case, only six knots are sufficient to reach a good fit. Fig. 4.2 shows the extracted doping using the proposed algorithm with the analytical extracted profile. As seen, the failure of the deep depletion approximation near the interface and in rapidly changing profile regions, results in large one-dimensional profile errors in the analytical profile. The performance of the knot placement strategy is depicted in Fig. 4.3 which compares the decrease in the residual sum of squares as a function of the number of knots when using the new algorithm to the case of equally spaced knots. Finally, the excellent capacitance fit achieved is shown in Fig. 4.4.

 
Figure 4.1: Comparison of Analytically Extracted Profile (solid-symbols) with Profile Extracted using 10 (dashed) and 15 (dotted) equally spaced knots for a MOS Capacitor with 70 oxide and 4000 area.  

 
Figure 4.2: Inverse Modeling (solid) and Analytical (dashed) extracted profiles for a MOS Capacitor with 70 oxide and 4000 area.  

 
Figure 4.3: Residuals Sum of Squares (SSQ) as a function of number of knots for the new placement algorithm (solid) and equally spaced knots (dashed).  

 
Figure 4.4: Simulated (solid) and experimental (symbols) deep depletion C-V of a MOS Capacitor with 70 oxide and area.  



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Next: 4.6 One-Dimensional Source/Drain Doping Up: 4.5 One-Dimensional MOS Doping Previous: 4.5.1 An Algorithm for



Martin Stiftinger
Tue Aug 1 19:07:20 MET DST 1995