Slow, fast, and typical process corners of semiconductor devices can be determined with just a number, such as Z-scores (Sigma from process target). This method ensures confirmation of target process corners and quick delivery of the dies to validate their functionality internally within NXP Semiconductors.
Process monitor ring oscillators (PMRO) are a set of 18 ring oscillators on each die. PMRO time delay results were correlated back to wafer acceptance Test (WAT) structures, using a JMP scatter plot. The most correlating parameters were used to build the model. Production variation data of a previous device from the same technology was used as the predictor variable. The Simulator tool in the JMP Prediction Profiler was used for Monte Carlo simulation to predict the lifetime variation of the rings. Model mean/standard deviation and individual die PMRO data was used to calculate the Z-score for each die.
The PMRO model was also used to simulate current (IDD) data, which, in turn, helped to predict the max power of the device in production, as well as setting the upper IDD limit in the ATE test program.
Hello. My name is Nivetha Shivan. I'm a Product Engineer in NXP Semiconductors. Today, I'm going to be showing how to do Monte Carlo simulation using JMP Profiler to evaluate silicon process.
A semiconductor wafer typically consists of about 4,000 semiconductor chips on a medium-sized chip. In wafer fab facilities, they use something called WAT, wafer acceptance test, to evaluate if a wafer is fast or slow against customer specifications. These WAT structures are typically located in between dies on a wafer. There are about 11 adjacent dies, and there are 9 sites on a wafer, so there are about 99 adjacent dies to these WAT structures.
In our most recent NXP devices, we've implemented something called PMRO, process monitor ring oscillators. These structures are on every single die on the wafer, so about 4,000 dies per wafer. While WAT is only available in wafer form, PMRO is available in wafer form, final test, and board level testing, so gives much more flexibility to look at the data.
The key objective here is to see and to evaluate how far off a certain semiconductor die is from the process target and to ensure quick delivery of these samples to our internal team members. For this purpose, we requested increased WAT sampling. From nine sites on the wafer, we increased it to all sites on the wafer. Then we did PMRO to WAT correlations. We did both die level and wafer level correlations. The die level correlations were not strong because of cross wafer variations, so we ended up using wafer level correlations. I'm going to be doing a JMP demo to show this.
This is a sample dataset, which has about 22 wafers with different process splits. This column right here is the PMRO wafer median and then WAT wafer median. The first order, I'm going to be checking if the data makes sense. I'm going to do Analyze, Fit Y by X to do a regression plot. PMRO on the Y, WAT on the X. Hit OK.
I'm going to do a roll legend on the splits. Just as a first pass, it looks like this. A slow wafer has a higher delay time compared to, say, something like a fast wafer that has a lower delay time, so the data makes sense.
I'm going to be doing a fit line, so red triangle and Fit Line. The RSquare is 0.97. That says the WAT and PMRO are pretty strongly correlated. Then the RMSE is around 0.11, so it's on the lower side.
Next, I'm going to be doing the Monte Carlo simulations for which I need to be in the Fit Model platform. I'm going to go to the Analyze, Fit Model, PMRO on Y, and WAT in Effects. I'm going to be using the standard least squares for personality, changing the emphasis to effect screening, and then hit Run.
This is the same regression plot we looked at before. I'm going to be scrolling down to the prediction profiler. The red triangle next to it has a Simulator option.
Here, I'm going to be changing the Fixed to Random to do Monte Carlo simulations. JMP gives us an option to enter mean standard deviation. I'm going to be using data from a device that's been in production for over 2 years now, so there is a lot of data. I remember this number for the sake of this demo. This is again a sample dataset, not real values.
Then I'm going to be adding the number of runs. I'm going to be simulating about 1,000 wafers. That's 4,000 dice per wafer and then 1,000 wafers. Next, I'm going to add RMSE back into the model and then hit Simulate.
JMP gives us a little histogram over here. That's the simulated PMRO model. I would need to extract the mean and standard deviation from the model. I'm going to use Simulator to Table function at the bottom, Make Table. JMP gave us this PMRO model for about 1,000 wafers.
I'm going to do a histogram on the PMRO. The mean is about 14.9, and then the standard deviation is about 0.38. The model looks pretty normally distributed. I'm going to be plugging this model mean, model standard deviation into the Z-Scores equation next.
We're going to be switching over to a different dataset. This dataset basically has about 1,200 different semiconductor dies. They are ID'ed here, and their process splits as I know of them today. The data here is the PMRO data from the individual dies, and then I have an equation for the Z-scores. Here, I have model mean minus the individual data over the model standard deviation.
Next, I'm going to be checking if the data makes sense. I'm going to do a one-way analysis, so Analyze, Fit Y by X, Z-Scores on the Y, Split on the X. Hit OK.
Next, I'm going to be doing quantiles. The median quantiles are located here. It says that the fast dies are about plus 3 Sigma from target, and the slow dies are about minus 3 Sigma from the target, and the typical dies are centered around 0.
The process corners for these semiconductor dies have been successfully evaluated. Multiple NXP devices use the same PMRO model, and it works across the board as expected. More importantly, similar function in JMP profiler was used to do Monte Carlo simulation successfully in a very fast and effective way. I highly recommend you use Monte Carlo feature in JMP for your projects as well. Thank you.
Presenter
Skill level
- Beginner
- Intermediate
- Advanced
