capiche: A system for analyzing foundry metal stackups using FasterCap

Author: Tim Edwards
Initial version: January 6, 2023
Updates:
- January 12, 2023: Corrected some errors in FasterCap input files, including breaking out separate left and right segments for metal wires that have sidewall dielectric. Corrected the handling of TOPOX over metal 5 in sky130A, which was previously capturing the sidewall but not the dielectric above the metal.
- January 29, 2023: Additional errors in FasterCap intput files based on feedback from the FasterCap developer.
- December 2024: Automatically generate tech file for magic - Leo

Requirements:

python3
uv
FasterCap or FasterCap (updates)
- LinAlgebra or LinAlgebra (updates)
- Geometry
magic
open_pdks or ciel (installed for sky130, gf180mcu and/or ihp-sg13g2 processes)

Setup:

Using uv

You can run capiche directly using uv:

uv run capiche

Or you can install capiche in a virtual environment:

uv venv
source .venv/bin/activate
uv pip install -e .

After which you can just execute capiche. To deactivate the virtual environment, run deactivate.

Using pip

Create a virtual environment, enable it, and install capiche:

python3 -m venv .venv
source .venv/bin/activate
pip install -e .

After which you can just execute capiche. To deactivate the virtual environment, run deactivate.

Usage:

capiche sky130A/metal_stack_sky130A.py
capiche gf180mcuD/metal_stack_gf180mcuD.py
capiche ihp-sg13g2/metal_stack_ihp-sg13g2.py

[!NOTE] If FasterCap isn't in the standard execution path, set the environment variable FASTERCAP_EXEC to the full path of FasterCap.

[!NOTE] If magic isn't in the standard execution path, set the environment variable MAGIC_EXEC to the full path of magic.

[!NOTE] If PDK_ROOT is not set and the PDK is not installed in the default /usr/local/share/ or commonly used /usr/share/ or ~/.ciel or ~/.volare directories, then pass the location of the PDK .magicrc startup file as the 2nd argument to compute_coefficients.py (see the open_pdks installation instructions for more information).

Add option -verbose=1 for more output, or -verbose=2 for considerably more output.

This will run for a long time[^1], generating metal wire configurations and running them through FasterCap to generate coupling capacitance estimations for each geometry. Once the data files containing all of the coupling capacitance tables have been generated, capiche will solve for coefficients to analytic solutions of parasitic capacitance, and generate plots of the FasterCap results vs. results extracted using the program magic and the analytic expressions computed using the calculated coefficients.

[^1]: Around 12 hours on a modern 16-core processor, e.g., Intel core-i9 Results are saved, so that subsequent runs will not repeat the FasterCap runs if the output files exist. Most of the time is spent running FasterCap.

Most output is in the form of capacitance tables and SVG format plots.

The main output file is <pdk_name>/analysis/coefficients.txt listing the following coefficients:

areacap <metal> <conductor> <value>

The parallel plate capacitance in aF/um^2 between the bottom of metal layer <metal> and the top of conductor layer <conductor>, which may be a metal or a substrate type.
fringecap <metal> <conductor> <value>

The maximum fringe capacitance per edge length in aF/um between <metal> and <conductor>, where <conductor> may be another metal layer above or below <metal>, or a substrate type. The <conductor> is treated as an effectively infinite surface in all directions.
sidewall <metal> <value> <offset>

The value of sidewall coupling capacitance per unit length satisfying the analytical expression
```
 Ccoup = <value> / (separation + <offset>)
```
Where <value> is in aF/um and <offset> is in um.
fringeshield <metal> <conductor> <multiplier> <offset>

The fraction of fringe capacitance shielded by a nearby wire on the same plane as <metal> with both wires placed over a large plane of material <conductor>. The coefficients are used in the following analytic expression for fringe shielding:
```
 Cfrac = tanh(<multiplier> * (separation + <offset>))
```
Where <multiplier> is unitless and <offset> is in um. "separation" is the distance from the edge of <metal> to the edge of the nearby wire of the same metal type. Cfrac represents the unshielded portion of the fringe capacitance.
fringepartial <metal> <conductor> <multiplier> <offset>

The fraction of fringe capacitance of <metal> incident upon another layer <conductor> (which may be a metal layer or substrate type) from the edge of <metal> out to a given distance. The coefficients are used in the following analytic expression for the partial fringe:
```
 Cfrac = (2/pi)*arctan(<multiplier> * (distance + <offset>))
```
Where <multiplier> is unitless and <offset> is in um. Cfrac represents the portion of the maximum fringe capacitance (i.e., item (2) above) seen on <conductor> from the metal edge out to distance "distance".

Plots are made of the data taken for items (3), (4), and (5) above. Each plot has three components:

The measurements obtained from FasterCap analysis
The best-fit curve for the analytic expressions discussed above
The measurements obtained from extracted layout in magic

Plots can be found in:

<pdk_name>/plots/sidewall for item (3) above
<pdk_name>/plots/fringeshield for item (4) above
<pdk_name>/plots/fringepartial for item (5) above

Note that as of the first version of Capiche, magic encodes models of fringe shielding and partial fringing that are different from the analytical expressions described above. This is to be expected, as the purpose of Capiche is to improve the models used in magic (see "work to do", below).

Input file format:

The main input file to Capiche is a python script that describes a process metal and dielectric stack. The file

sky130A/metal_stack_sky130A.py

is provided as a complete example, and describes the metal stack of the SkyWater sky130 process with options as selected for the open_pdks process variant name "sky130A" (which is 6 metal layers; see open_pdks for more information). Any process can be described with a similar file, which needs to encode a number of values in Python variable form, as described below. The file is evaluated in Python line by line, so any valid Python syntax is allowed. However, Capiche Python scripts will only expect and use the following variables:

process = '<pdk_name>'

where <pdk_name> is a name given to the process (e.g., "sky130A"). This name will be used as the directory top level for all files and data generated by Capiche for the process. If the name matches an open_pdks technology variant name (e.g., "sky130A"), then it will also be used to automatically find the magic tech file for the process.

layers['<layer_name>'] = ['<type>', <values>. . .]

This is the main metal and dielectric stackup information. There are six types recognized by the single-letter <type>. The type of layer determines what the remaining <values> items in the list must be. The layer types are as follows:

'd':	Diffusion type, used for substrate, well, or diffusion
'f':	Field oxide type, which is directly above the substrate
'k':	Simple dielectric
'b':	Simple dielectric unrelated to any metal
'c':	Conformal dielectic
's':	Sidewall dielectric
'm':	Metal

Layers may be listed in any order, although obviously a bottom-to-top or top-to-bottom format will be easier to read and understand. Every layer stack must have one layer called 'air' representing the area above the highest manufactured layer in the process. All other layer names are arbitrary and should be chosen to be meaningful within the context of the process.

The list entries for each of the types above are as follows:

['d', <height>, <reference>]

where <height> is the height above the substrate (assumed to be at zero height), and <reference> is the name of the dielectric layer immediately above the layer (normally field oxide).

['f', <K_value>]

This entry is for the field oxide. This is like other dielectrics, but the field oxide is always referenced to the substrate, so it has only a single value, which is the dielectric K coefficient (a dimensionless unit which is multiplied by the permitivity of vacuum)

['k', <K_value>, <reference>]

This is a simple dielectric boundary. All planes in a fabrication process are assumed to be dictated by each metal layer, so dielectric boundaries do not need to define a layer hight. They are simply referenced to the dielectric layer name <reference> of the dielectric directly below the layer. The <K_value> is the dielectric K constant.

['c', <K_value>, <thick1>, <thick2>, <thick3>, <reference>]

This is a conformal dielectric which is formed around a metal layer and forms a layer above and around the metal. <K_value> is the dielectric K constant of the layer. <thick1> is the thickness of the dielectric over metal, while <thick2> is the thickness of the dielectric where the metal is not present. <thick3> is the sidewall thickness of the dielectric. The <reference> layer is always a metal.

['s', <K_value>, <thick1>, <thick2>, <reference>]

This is a sidewall dielectric which is formed around a metal layer but does not exist awa

Capiche

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