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standard deviation of the mismatch for two devices (Read 145 times)
polyam
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standard deviation of the mismatch for two devices
Jan 09th, 2023, 12:28pm
 
Hi,

According to Pelgram's rule the standard deviation of the mismatch for two devices is calculated by Delta_Vth = Avth / sqrt(WL). Obviously W and L is the device size and Avth is a technology dependent constant. Could you please anyone help me how to find/calculate/simulate that constant for a given MOS process?

Thanks
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smlogan
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Re:  standard deviation of the mismatch for two devices
Reply #1 - Jan 14th, 2023, 11:02am
 
Dear polyam,

> Could you please anyone help me how to find/calculate/simulate that constant
> for a given MOS process?


The constant has been documented in various forms in a number of papers. Marcel Pelgrom (note spelling) and others (see references 1,2) have devised a term "matching energy" defined as Cox*AVT^2 that has been documented to show how the term varies with process node. You might examine the figures in either of these two references to better understand the magnitude of the AVT^2 term. If you are getting models for simulation from a foundry that include mismatch parameters, you can probably simulate the mismatch for devices with different W/L to emprically estimate its value for that process.

Shawn

[1]. P. R. Kinget, "Device Mismatch: An Analog Design Perspective," 2007 IEEE International Symposium on Circuits and Systems, New Orleans, LA, USA, 2007, pp. 1245-1248, doi: 10.1109/ISCAS.2007.378336.
[2.] M. J. M. Pelgrom, H. P. Tuinhout and M. Vertregt, "Transistor matching in analog CMOS applications," International Electron Devices Meeting 1998. Technical Digest (Cat. No.98CH36217), San Francisco, CA, USA, 1998, pp. 915-918, doi: 10.1109/IEDM.1998.746503.
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Shawn
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A Kumar R
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Re:  standard deviation of the mismatch for two devices
Reply #2 - Jan 16th, 2023, 1:19am
 
Hi Polyam,

usually PDK document contains a plot of Vth mismatch voltage vs. 1/sqrt(WL), can we find this constant from the plot?.

Thanks.
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