# Extract Device Model Parameters Across Geometry, Temperature and Voltage

Blog Post created by rajsodhi on Aug 25, 2017

A high-quality device model captures device behavior across geometry (W/L), temperature (T), drive voltage (Vdd), among numerous other input conditions. How much time do we spend trying to achieve a good fit across all these axes? What if we could easily bring up graphs of all key device targets such Vth (Threshold Voltage), Idsat (Drive Current), GM (Transconductance), and their variations across these dimensions?  We could then monitor them in one place, and tune or optimize model parameters while observing the agreement between measured and modeled data.  With Keysight’s Model Builder Program (MBP) 2017, we can achieve this goal. In this note, we are going to go through a couple of examples to show how MBP Script makes it possible to monitor device targets across the entire matrix of input conditions.

First, let’s look at the Threshold Voltage (Vth) variation as we vary device width (W) and length (L) on 4 sides of the W/L matrix, as shown below. Figure 1. Four sides of the W/L matrix for evaluation of Vth variation

The 4 sides of W/L space define the boundaries of modeled device sizes provided by a given semiconductor technology. A customer may use a geometry outside of this space, but will then need to re-target the model parameters for this unusual device.

Vth is the key device parameter of any transistor device, be it BULK, SOI or FinFET.  It defines when a transistor transitions from off to on.  If the Vth has been well modeled along the 4 sides of the W/L space, then we have good confidence that the model will work over the entire W/L plane. Both short and narrow channel effects will be covered.

By placing Tasks in sequence, a user may define a real modeling flow to be executed automatically.  A “Task” is object to represent a step in a flow, and is represented by a blue icon in the flow panel, as shown below in figure 2.  With Tasks, a modeling engineer can group modeling building blocks to extract the next logical group of device parameters.  In MBP, we may create a new Task button, as shown below, called “Display_Vth_Scaling_4_sides.”  By  clicking on this button, we can define and display the related graphs. Figure 2. Display Vth W/L scaling plots by Task button clicking

In figure 2, we plot Vth in a 2x2 layout, where each quadrant represents one side of the W and L scaling space.  The solid represents simulated data and the square represent measurements.  The MBP tool is now ready for model tuning or optimization.

To create this beautiful matrix of graphs, we need to create a new Task from MBP Script window and name it “Display_Vth_Scaling_4_sides,” as shown in figure 3.  In the newly created Task, in its Plot Select tab, click the “Add Plot” button to add these 4 plots.  We may populate the “Plot Name” using 2 of the predefined plot groups “vth_l_vbs” and “vth_w_vbs.” In the “filter define” field, we may filter the data based on desired input conditions, like “w=max(w)”.  The filter definition is highlighted in green for the first plot where vds=abs(min(vds)) && w=max(w). In other words, we filter the data for the absolute minimum Vds, and maximum W input conditions.

Figure 3. Create a Task by grouping Vth W/L scaling plots

MBP provides the most commonly used device targets, including Vth, Gm, Idsat, Idlin, etc. as well as common plot templates like the scaling graphs over W, L, T and Vdd.

One powerful plot type shows how well the model has been fitted across input conditions like geometry.  This is called an “Error Data Grid” plot.  In figure 4, we present the RMS error of device targets Vth and Idsat in our 2-dimensional geometry plane. However, we can choose pairs of input conditions to study, for example:

• W and L
• W/L and T
• W/L and VDD

Figure 4. RMS Error plots of Vth and Idsat across W/L plane.

When tuning model parameters, we can observe the RMS errors update on the fly. For example, slightly different model parameter settings lead to the following Error Data Grid plots: Figure 5. another state of the RMS Error plot of Figure 4.

The numbers are color-coded for quick and easy reading.

In figure 6, we illustrate how to create these incredibly useful Error Data Grid plots. In MBP’s Script window, we choose our device target (Idsat), specify the X and Y axes as ‘w’ and ‘l’ below, coloring for various RMS error ranges, etc. We can even add more targets to our Error Data Grid plot. Figure 6. ErrorDataGrid plot creation

These newly created plots can be integrated in the Flow as another Task button, as shown below: Figure 7. Display RMS Error plots by Task button clicking

Every Task object has a few properties of which “button mode” is one.  When the task is in button mode, then when you click it, it executes just that code to do an action, like extracting a group of parameters.  When the task is not in button mode, clicking on it has no immediate effect.  Rather, it marks where the flow may resume.

By monitoring a model’s performance (RMS error) across all input conditions, MBP provides a high-level view of the model in real time.  Our modeling engineer may enjoy the peace of mind that the device model has been done thoroughly and accurately.

Please see the attachment below.  We have attached an example project that includes:

1. demo data files
2. demo model files, initial version and final version.
3. script file that defines the flow Tasks and ErrorDataGrid plots

For more details about how to customize device targets and plots and how to customize the flow, please refer to the MBP Script tutorial.  https://devicemodelingworks.net/mbpst

ShuangCai

MALong