# Research on Device Modeling Technique Based on MLP Neural Network for Model Parameter Extraction
## 4 Results and Discussion  
### Error and Performance Analysis  
The mean value \(\mu\) of the RE for the training data is 2.81%, and the standard deviation \(\sigma\) of the RE is 3.04%. The training data with an RE greater than \(\mu+3\sigma\) accounted for 0.89% of all training data. We performed an analysis on the training data with an RE greater than \(\mu+3\sigma\) and counted the distributions of temperature, gate width, and gate length. The statistical results are shown in Figures 4-6, respectively. According to Figure 4, it can be seen that for the training data with an RE greater than \(\mu+3\sigma\), the proportions of different bars are not very different. The proportion of the first bar in Figure 5 is lower than that of the other bars, which is because the gate width range of this bar is smaller. The overall distribution of the gate width is uniform when the gate width range is considered. From Figure 6, it can be observed that the proportion of data with a small gate length is very large, and the proportion almost decreases with the increase in the gate length. It indicates that the NN model fits less well to the data with a small gate length. Due to the short-channel effect, more complex device physics mathematics are involved around the minimum gate length [10], so it is reasonable that the error is slightly higher at the smaller gate length. Figure 4: Temperature distribution of the training data with an RE greater than \(\mu+3\sigma\). The training data with an RE greater than \(\mu+3\sigma\) accounted for 0.89% of all training data. The mean value \(\mu\) of RE for the test data is 3.89%, and the standard deviation \(\sigma\) of RE is 3.71%. The test data with an RE greater than \(\mu+3\sigma\) accounted for 1.50% of all test data. The distributions of temperature, gate width, and gate length for the test data with an RE greater than \(\mu+3\sigma\) are shown in Figures 7-9, respectively. According to Figures 7 and 8, it can be seen that for temperature and gate width, the proportions of different bars are not very different. According to Figure 9, it can be seen that the proportion of data with a small gate length is higher. The NN model fits less well to the training data for small gate lengths and, therefore, fits the test data for small gate lengths less well. A statistical analysis of the IV curves for the training data was performed. It was found that for the \(I_{ds}\)-\(V_{gs}\) curves, the error of \(V_{gs}\) from 0 to 0.2 V was slightly higher than the other regions of the curves. It is basically in the subthreshold region when \(V_{gs}\) is between 0 and 0.2 V. According to Equation (4), it is known that the relationship between current and voltage in the subthreshold region is exponential. The exponential relation has infinite order derivatives, and its Taylor series expansion is composed of infinite polynomials. According  
Figure 5: Gate width distribution of the training data with an RE greater than \(\mu+3\sigma\). The training data with an RE greater than \(\mu+3\sigma\) accounted for 0.89% of all training data. Figure 6: Gate length distribution of the training data with an RE greater than \(\mu+3\sigma\). The training data with an RE greater than \(\mu+3\sigma\) accounted for 0.89% of all training data. to Equation (5), the relationship between current and voltage in the non-subthreshold region is polynomial. When using the same NN model for subthreshold and non-subthreshold regions, the finite polynomial for the non-subthreshold region is easier to fit and, therefore, its modeling accuracy is higher. The errors were counted separately for the subthreshold and non-subthreshold data in the training data using Equation (3), with 4.77% for the subthreshold region and 3.83% for the non-subthreshold region. At the same time, the errors were counted separately for the subthreshold and non-subthreshold data in the test data using Equation (3), with 6.89% for the subthreshold region and 4.79% for the non-subthreshold region.