Direct Extraction of MOS Transistor Current Model Parameters
Doctoral thesis, 1994
This thesis presents a study of MOS transistor model parameter extraction. The objective of this study was to develop an efficient, accurate, robust extraction strategy which determines physically reasonable parameter values. The direct parameter extraction approach was chosen to meet these requirements. The basic idea in this approach is to determine the parameters from a small number of data points using analytical expressions. Ideally, only one data point is needed for each parameter. The parameters are determined sequentially in the region of operation where they have their most significant influence on the model characteristics. All interactions between parameters are taken into account during a subsequent iterative improvement procedure.
Direct extraction algorithms for two popular and commonly used SPICE MOS transistor models, level 3 (MOS3) and level 4 (BSIM), are proposed. For the MOS3 and the BSIM models, all current parameters are extracted from 15 and 25 data points, respectively. Even if only a small number of data points are used, good agreement between measured and simulated device characteristics is obtained for both models. The influence of measurement noise on the data points taken in the linear region was studied using sensitivity analysis. The model accuracy was investigated through repeated extraction in the linear region using different combinations of data points. These two studies resulted in a recommendation for the selection of data points.
A method of extracting the series resistance and series resistance independent model parameters for MOS3 is presented. During the experimental verification of this method different external resistors were connected to the transistors. When extracting transistor parameters according to the model, which did not include the series resistance explicitly, the values of three of the parameters were found to depend strongly on the connected external resistors. These were the mobility reduction factor due to the transverse electric field, the maximum drift velocity, and the saturation field factor. These results are in good agreement with results obtained from extractions using synthetic data as input to the extraction algorithm. From the simulations it was also found that the static feedback factor depends weakly on the series resistance but this was never confirmed experimentally. When the series resistance was included in the model, constant parameter values were obtained which were independent of the connected external resistors.
A novel linear region four-point technique was developed for extraction of the threshold voltage, the gain, and the first and second order mobility reduction factors due to the transverse electric field for the BSIM2 transistor model developed for submicron transistors. This method shows that direct extraction is not limited by the transistor model. Instead, the strategy adopted in this study is applicable for a number of different models.
This study also emphasises the similarity between direct extraction and least square fitting of the parameters and shows that least square fitting is a natural extension of direct extraction: similar analytical techniques are used to determine the parameters in both cases. An extraction algorithm based on least square fitting techniques which can be used for extracting the linear region parameters as well as the effective geometries is suggested. This algorithm together with algorithms for the saturation and subthreshold regions comprise a complete extraction scheme based on least square fitting techniques for the BSIM transistor model.
Finally, a novel interpretation of the channel width dependence of the mobility reduction factor due to the transverse electric field is proposed. The electrical broadening of the channel is shown to have a similar influence on the drain current as the mobility reduction factor. A method for separating these two effects is presented.