Generation of a New SPAYN Database from a Limited Data Set

SPAYN is a very comprehensive statistical tool designed specifically for semiconductor industry. One of the main features of SPAYN is the ability to perform analysis on the measured data collected from wafers. This generates information on dominant parameters and can be used for physically based worst case analysis.

However, sometimes collecting a large data base is not feasible for some applications. In this case it is possible to use the built-in simulator inside SPAYN to generate data based on our past experience about the model parameters. This can be useful for those characterization engineers who are developing a new technology or are not able to access a large measured database.

 

Generation of SPAYN Data Base By Simulation

First start VYPER in your working directory and then open the SPAYN application window inside VYPER. On the main SPAYN window go to File->Operations->DB From Stats.... This will pop up a Database Generation Setup Window. In this example we are going to generate a database including five parameters. We give them general names as Param_1, Param_2, Param_3, Param_4, Param_5. But these parameters could be any SPICE model parameters we think that are important and whose distribution is known based on experience. In the Database Generation Setup Window (see Figure 1.) we would first input the number of parameters to consider. In order to specify the joint distribution of those parameters you need to specify the mean and sigma for each parameter, and then possibly may specify the correlation matrix. In this example we consider all five parameters are independent of each other. Click on the Generation Window..., there should pop up a Database Generation window. Enter the Number of Simulation points on the first text field and click on Generate... button at the bottom of the window. We could also choose one of the two formats for the simulation data, one is standard Spayn Database the other is Comma Separated Values. Give a filename on the popup Destination Filename window and hit return or press the store button, the simulated data is then generated and stored in this file.

 

Figure 1. Database Generation Setup Window.

 

Worst Case Analysis On the Simulation Data

Use the File->Load/Import... to load the simulation data we just generated. Now we could first use the Analysis->Histogram feature to see how good our simulation data is. Since the simulation is to generate multidimensional Gaussian distribution, we would see that each parameter is fit by a one dimensional Gaussian distribution quite well. Now if the parameter data are correlated, i.e. the correlation matrix is not the identity matrix when we are doing the simulation, we may need to use the Groups/Equations->PCA/PFA feature to perform a Principal Component Analysis or Principal Factor Analysis to find independent dominant parameters and reduce the number of parameters for worst case analysis.

In our case, we start with five independent dominant parameters, so we could go directly to define our dominant parameters using four parameters out of the five parameters. Use Groups/Equations->User-defined->Dominant Parameters... feature to accomplish this definition. Now the Simulation Menu bar becomes active, so we could go to Simulation->All User Dominant..., this would give us a Simulation Interface window(see Figure 2.). Now use one of many methods available in this simulation window to generate corner models, and save them as a .lib file for circuit simulation. Or we could use VYPER to call a circuit simulator directly for worst case simulation. At this stage the operations are pretty much the same with measured data.

 

Figure 2. Simulation Interface Window.

 

Summary

In summary, when we do not have enough measured data, but have some knowledge of how the important parameters are distributed, we could use the built-in simulator in SPAYN to generate data according to our distribution knowledge of model parameters and perform worst case analysis on this simulation database and generate circuit performance spread.