metal density calculation

[saha.123]

Hi.....
How can i calculate the metal density in a particular layout? Is there any formula to measure it?

thanks in advance

 

[dick_freebird]

The formula is {metal area}/{total area} but this is not
much help. You have to tabulate all of the in-layer
features to get the {metal area}. This is usually done
using DRC scripts since those tools are right for this kind
of thing.

 

[sat]

Use foundry provided Density rules - as freebird stated above.. these are kind of DRC rules..
Calibre, PVS, Assura can do a density check.

Back to Basics:
Metal Density - is a point function, and therefore various functional representations are possible, {there is nothing like absolute value of density}. That means - different functional representations & context, can result in different density numbers, in the same design, at some specific X,Y location on a specific layer.
Let us see what the above means...
For a design - for a particular metal layer , say metal-2, {sum-total metal-2 area} / {total design area} = overall density of metal-2 in the design.
However, that is too gross representation, that does not ascertain how uniformly metal2 {route & fills or floating metals} is distributed across the whole area - some part of the chip might still has too much of metal-2, and some other places too sparse, although achieving overall density.. In most cases, density is measured by sub-dividing design into multiple smaller tiles/windows and density is measured on a tile-by-tile basis. Most popular method of density measurement mechanisms are 'walking-window' and 'centre-weighted-average-window'.

"Walking window" also known as "Stepping Windows" : in which a window of specified dimension (say 100um by 100um) is used for measuring density - then the window is moved along X-axis by half window dimension (that is 50um) - and again density is measured in that window, and such thing goes on - till it reaches X-max of the design, then the window moves half of its Y-size along Y-axis, again started moving in X-axis - in a very similar way a scanner scans a document. So, any point in a design - is most likely fall in the overlap zone of 4 windows. 1/4th {a quadrant} of a window stores the average density of 4 overlapping windows.
"Center weighted average windows" : in this method, multiple different concentric windows(rectangles /or/ squares) [from smaller to bigger dimensions] are put around a point in the design and density is measured in each of the window, and then all the density numbers are added together with a weight-factor to each of them (normalized) - to represent the effective density number.

Which method to choose - and why?
For a given foundry & process-node, Foundry will dictate {in the DRM} - on what exact density measurement technique they want, with tile/window(s) dimensions and step dimensions and in case of weighted average - the weight factors and so on..