# Research on Device Modeling Technique Based on MLP Neural Network for Model Parameter Extraction
## 2 Data Preparation and Pre-Processing  
### Data Preparation  
This work uses current data for device modeling, defining the influence of the model parameters on the current as the sensitivity. Model parameters with non-zero sensitivity are taken as the inputs of the NN. The sensitivity calculation formulas are defined as follows:  
\[A0[i] = |\frac{\Delta I_{i}}{I_{i}}/\frac{\Delta P}{P}| \tag{1}\]  
\[S(A) = max(A0) \tag{2}\]  
where \(I_{i}\) is current when the model parameter \(A\) is set to \(P\), and \(\Delta I_{i}\) denotes the current difference when the model parameter \(A\) is set to \(P\) and \(P+\Delta P\) under the same working conditions. Array \(A0\) represents the sensitivity array containing all current data. \(S(A)\) represents the sensitivity of the model parameter \(A\), which is the maximum value of array \(A0\). In this work, we take the BSIM-SOI model as the source for the training set and testing set [13]. The sensitivity analysis results of the BSIM-SOI model show 128 model parameters with non-zero sensitivity, which are used as the NN inputs. Some of the model parameters with high sensitivity are listed in Table 1. It took 23.9 h to generate the data needed for the sensitivity analysis and 36 s for the sensitivity analysis itself. The extraction of device model parameters needs to take into account various working conditions (voltages, temperature) [14; 15] and use a MOSFET of different sizes [16; 17]. Therefore, the inputs of the NN need to contain six variables, namely, drain-source voltage (\(V_{ds}\)), gate-source voltage (\(V_{gs}\)), bulk-source voltage (\(V_{bs}\)), temperature (T), gate width (W), and gate length (L) in addition to the model parameters. Drain-source current (\(I_{ds}\)) is the output. The MLP neural network consists of an input layer, a few hidden layers, and an output layer, which are fully connected [18; 19]. The 45 nm SOI process [20] was used to build the circuit. The minimum gate length value of the nmosbc-type MOSFET used in this work is 56 nm, while the minimum value of the gate width is 654 nm. For the training set, the gate length ranges from 56 nm to 1000 nm, the gate width from 654 nm to 1200 nm, and the temperature from \(-40\)\({}^{\circ}\)C to 125 \({}^{\circ}\)C. The output characteristic (\(I_{ds}\)-\(V_{ds}\)) curves sweep from 0 to 1.0 V for the \(V_{ds}\) with a step of 0.05 V. The transfer characteristic (\(I_{ds}\)-\(V_{gs}\)) curves sweep from 0 to 1.0 V for the \(V_{gs}\) with a step of 0.05 V. The temperature, gate length, and gate width are scattered within the ranges. At the same time, the Latin hypercube sampling method was applied to the model parameters to ensure that their ranges were fully covered [21]. Tens of thousands of sets of IV curves were prepared as the training set. The time taken to generate the training set for the NN was 11.2 h.  
A good NN model must have good generalization ability, i.e., it is required that the NN model performs well on the test data, which is different from the training data [22; 23]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Model Parameters** & **Description** \\ \hline Bigc & Parameter for I\({}_{gs}\) and I\({}_{gcd}\) \\ Nrecr0 & Recombination non-ideality factor at reversed bias for source \\ Beta2 & Third V\({}_{ds}\) dependent parameter of impact ionization current \\ Vtun0 & Voltage dependent parameter for tunneling current for source \\ Ntun & Reverse tunneling non-ideality factor for source \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Some model parameters of BSIM-SOI. The inputs were extended to varying degrees when preparing the test set. W was taken from 654 nm to 1500 nm, L from 56 nm to 1200 nm, and T from \(-40\)\({}^{\circ}\)C to 125 \({}^{\circ}\)C. The range of model parameters was extended to 1 to 1.1 times the original range. The test set takes a minor step for voltage.