INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line...
Transcript of INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line...
![Page 2: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/2.jpg)
Outline
Systematic vs. random mismatch Hand calculation of random mismatch Sources of random mismatch Offset and calibration
![Page 3: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/3.jpg)
MatchingPreviously we have discussed systematic mismatch. Systematic mismatch can be minimized by careful layout or trimming. Binning is also used. When "identical" devices are manufactured, random fluctuations cause electrical parameters of devices on the same die to have a statistical distribution. (Random mismatch)
![Page 4: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/4.jpg)
MatchingNeed good matching between devices in input pair. And devices in current mirror.
Both systematic and random. Trimming can help both. Typically want to minimize inherent effect of both.
![Page 5: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/5.jpg)
Systematic mismatchDesired mean value Systematic mismatch
![Page 6: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/6.jpg)
Random mismatchBetter = more devices will be closer
to the desired (mean) value
Better
Worse
![Page 7: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/7.jpg)
Worst-case analysisAssuming a normal distribution (reasonable assumption from central limit theorem). Worst case minimum value: μ - 3σWorst case maximum value: μ + 3σ 3σ would capture 99.73 %6σ would capture 99.9999998 %
![Page 8: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/8.jpg)
Monte-carlo simulationFab provides statistical parameters for device models.
Run a large number of simulations with different permutations of parameters. Does not neccessarily give insight into which devices are causing problems, or how to improve yield.
![Page 9: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/9.jpg)
Hand calculation
A systematic study of mismatch
between parameters of two identical
MOSFETs.
Manufacturing devices with different W/L, distance, orientation to see how this affects matching.
![Page 10: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/10.jpg)
Hand calculation
Area proportionality constant
Size
Matching of parameter, P, between two identically drawn devices
Distance
Variation with spacing
SpDx can be made small with good layout
![Page 11: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/11.jpg)
Hand calculationMismatch between two identically drawn transistors. Will do hand calculation to find ΔVth and Δß/ß. Use this to find ΔId/Id, Vos, etc.
![Page 12: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/12.jpg)
Sources of randomness● Line edge roughness (LER)● Random dopand fluctuation (RDF)● Gate oxide thickness● ... Some effects due to the manufacturing process may not be truly random, but will appear random to us as designers, because it's outside our control. We will count this as "random".
![Page 13: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/13.jpg)
Line edge roughness"LER is caused by a number of statistically fluctuating effects at these small dimensions such as shot noise (photon flux variations), statistical distributions of chemical species in the resist such as photoacid generators, the random walk nature of acid diffusion during chemical amplification, and the nonzero size of resist polymers being dissolved during development. It is unclear which process or processes dominate in their contribution to LER." [http://spie.org/x32401.xml]
![Page 14: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/14.jpg)
Random dopant fluctuationAs features scale, fewer dopant atoms in the channel. The relative contribution of one atom increases. Single atom affects electrical parameters.
![Page 15: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/15.jpg)
Basic rule of matching
Big devices match better. Randomness averages out more over a larger area. Big devices, more capacitance, more area. Reducing random mismatch comes at a cost. Important to know how much mismatch we can live with to avoid costly overdesign.
![Page 16: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/16.jpg)
Threshold voltageImportant contributions are tox and dopant concentration in channel region
Improves with scaling in tox
Best guess
Technology parameter
![Page 17: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/17.jpg)
Beta variabilityRelative current factor mismatch, Δß/ß [%]
Best guess for Aß is 2 % µm
![Page 18: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/18.jpg)
Drain current mismatch
![Page 19: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/19.jpg)
ΔId/Id vs Vgs
![Page 20: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/20.jpg)
Current mirror example
One standard deviation!
![Page 21: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/21.jpg)
Input referred offset
![Page 22: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/22.jpg)
Digital offset calibration
![Page 23: INF4420 - Universitetet i oslo · Use this to find ΔId/Id, Vos, etc. Sources of randomness Line edge roughness (LER) Random dopand fluctuation (RDF) Gate oxide thickness ... Some](https://reader030.fdocuments.in/reader030/viewer/2022040822/5e6bf3872b15f21f8d3fd468/html5/thumbnails/23.jpg)
ReferencesOrshansky, et al., Design for Manufacturability and Statistical Design, Springer, 2008 Pelgrom, Component matching: best practices and fundamental limits, IDESA. Pastre and Kayal, Methodology for the Digital Calibration of Analog Circuits and Systems, Springer, 2006