For the model parameter extraction problems, there are some empirical knowledge can be applied to accelerate the parameter extraction process. These empirical knowledge plays an important role in the parameter extraction, and lack of the experience usually make the extraction task more difficult. In general, the empirical rules are resulted from the characteristics of the model and the physical or mathematical meanings of the parameters.
Based on our experience and the investigation of the models, some empirical extraction strategies are proposed.
According the physical point of view, the parameters can be divided into several cate-gories, which include threshold voltage, mobility model, drain current, subthreshold region, drain-source resistance, channel geometry, output resistance, capacitance, process related and temperature modeling. Sensitivity of the parameters to be extracted is one of important issues for assisting parameter extraction. The sensitivity examination of parameters can point out what kind of parameters affects behavior of convergence significantly. According to this information, we firstly extract those most sensitive parameters. When these para-meters are firstly decided, all parapara-meters will be extracted simultaneously. To perform the sensitivity analysis, the developed system extracts single parameters category meanwhile
Figure 5.3: The sensitivities examination of the parameters to be extracted in the compact model.
locks other parameters. The expected result should show that varying certain parameters category would make notable progress while some others would not. Figure 5.3 shows the sensitivities examination of the extracted parameters in the compact model and reveals that the parameters related to the threshold voltage would make the most improvement.
The parameters in each category can be further divided into three types: parameters with physical meaning, global parameters and local parameters. For example, the parameters with physical meaning in category of threshold voltage include Vth0 and VBM. The global parameters are K1, K2, DVT1 and DSUB. The local parameters includes K3, K3B, W0, ... etc. The parameters with physical meaning can be decided firstly, and then adjust the
VDS (V)
Figure 5.4: The BSIM-4 extracted (solid-line) and measured (dot-lines) IDS − VDS and IDS− VGS curves of the 90 nm MOSFET (width = 10.0 µm), where VBS = 0 V and VGS varies from 0.4 to 1.4 V, and VDS = 0.1 V and VBS varies is 0 to -1.5 V.
global and local parameters to fit the targets. In some category, the parameters with phys-ical meaning can be can be obtained from measurement data, such as the Vsat in the drain current category. For some categories, they may have only one or two types of parame-ters. In the channel geometry category, there are only local parameters, but it still can have some rules for parameter extraction. To extract the parameters in the channel geometry category, the parameters Wint and Lint should be extracted until the extracted results has better shape, then start to extract other parameters.
VGS (V)
Figure 5.5: The EKV extracted (solid-line) and measured (dot-lines) IDS − VDS and IDS − VGScurves are of the 0.18 µm MOSFET, where VBS = -0.6V and, VGSmigrates from 0.4 to 1.4 V, and VDS = 1.3V and VBS migrates is 0 to -0.9 V.
5.4 The Achieved Results and Discussion
The achieved accuracies of the extracted model parameters are given in Figs. 5.4 and 5.5 for both BSIM-4 and EKV models. In Fig. 5.4a represents the IDS − VDS curves and Fig.
5.4b stands for IDS− VGScurves; the width and channel length of the target device is equal to 10 µm and 90 nm. On the other hand, the width and channel length of the target device is equal to 10 µm and 180 nm in Fig. 5.5;similarly, Fig. 5.5a represents the IDS− VDS curves and Fig. 5.5b stands for IDS− VGScurves. The errors between measured and extracted I-V curves are less than 3%. All figures shown above have demonstrated the accuracy of the proposed method. In the next part, the efficiency of the proposed method is discussed.
Figure 5.6 is a fitness score comparison with different extraction methods for BSIM-4 model. As shown in Fig. 5.6, without the guidance of NN, the methods of GA only and GA+LM spent a lot of time to reduce the fitness score down to 0.5, while the ones with NN can easily shot this problem. Comparing the GA+LM and GA+NN+LM method in Fig.
5.6, the NN detects the differences between measured and extracted curves, and suggest a better extraction direction to GA to perform the fine tune task among the curves and its corresponding relative parameters. The results indicate that the evolutionary process with the guidance of NN really shows the better convergence behavior, and they confirm the great efficiency of the method. The result confirms the efficiency of the method. Fig. 5.7 shows a comparison of the score convergence behavior of our proposed method with pure GA for different two compact models. The EKV compact model can more quickly achieve a lower score than the BSIM-4 model due to less parameters, but it’s final results are not better than the results of BSIM-4 model after lots of generations. This figure shows our method has superiority and robustness for both BSIM-4 and EKV compact models. We note that, shown in Figs. 5.6 and 5.7, when the other methods appear to be saturated, our method can continuously improve the fitness score. Experiments in this work preliminarily confirm that the proposed method solves complicated multidimensional optimization prob-lem effectively and provides an alternative for deep-submicron and nanoscale device model parameter extraction.
Figure 5.6: (a) the score convergence of different extraction methods, and (b)the score convergence behavior w/ and w/o applying NN as a director during the evolutionary process, where the testing is with BSIM-4 model applying to four 0.13 µm MOSFETs.
Figure 5.7: The score convergence behavior of our proposed method and pure GA for different compact models.