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docs(palace): compare electrostatic cmim against IHP PDK compact model #169

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381 changes: 142 additions & 239 deletions nbs/_palace_electrostatic.ipynb
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207 changes: 63 additions & 144 deletions nbs/_palace_electrostatic.py
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Original file line number Diff line number Diff line change
Expand Up @@ -15,15 +15,26 @@
# %% [markdown]
# # Electrostatic Capacitance Extraction with Palace
#
# This notebook demonstrates electrostatic simulation using `gsim.palace.ElectrostaticSim` to extract the capacitance matrix between conductor terminals.
# We use `gsim.palace.ElectrostaticSim` to extract the **plate-to-plate (mutual)
# capacitance** of the IHP `cmim` (MIM capacitor) cell and compare it against the IHP
# PDK compact model. The bottom plate is on Metal5
# (terminal `T1` = SPICE `MINUS`), the top plate on TopMetal1 (`T2` = `PLUS`), joined
# by a 10x10 array of Vmim vias through a 0.19 um SiO2 MIM dielectric.
#
# We use the IHP `cmim` (MIM capacitor) cell. The bottom plate is on Metal5 and the top plate on TopMetal1, connected by a 10x10 array of Vmim vias through a thin MIM dielectric (0.19 um SiO2).
# Palace writes two matrices: `terminal-C.csv` (Maxwell — self-cap on the diagonal,
# negative induced charge off-diagonal) and `terminal-Cm.csv` (mutual/"SPICE" — its
# off-diagonal `Cm[i,j] = -C[i,j]` is the physical two-terminal capacitor). The MIM cap
# value is `Cm[1,2]`, which is exactly what the PDK `cap_cmim` model describes.
#
# **Limitation:** The current terminal system assigns one terminal per layer. Structures with multiple electrodes on the same layer (e.g., interdigitated capacitors) are not yet supported.
# The IHP `cap_cmim` is a 2-terminal model with an area + perimeter law (plate-to-plate
# only; substrate parasitics are left to extraction). See
# [`capacitors_mod.lib`](https://github.com/IHP-GmbH/IHP-Open-PDK/blob/main/ihp-sg13g2/libs.tech/ngspice/models/capacitors_mod.lib).
#
# **Requirements:**
# - IHP PDK: `uv pip install ihp-gdsfactory`
# - [GDSFactory+](https://gdsfactory.com) account for cloud simulation
# **Limitation:** one terminal per layer — multiple electrodes on the same layer (e.g.
# interdigitated caps) are not yet supported.
#
# **Requirements:** IHP PDK (`uv pip install ihp-gdsfactory`) and a
# [GDSFactory+](https://gdsfactory.com) account for cloud simulation.

# %% [markdown]
# ### Load IHP MIM capacitor
Expand Down Expand Up @@ -76,81 +87,43 @@
# %%
# sim.plot_mesh(show_groups=["metal", "topmetal", "via", "dielectric", "SiO2__vmim"])

# sim.plot_mesh(show_groups=["metal5", "topmetal1", "vmim", "SiO2__vmim"])
sim.plot_mesh(show_groups=["metal5", "topmetal1", "vmim", "SiO2__vmim"])

sim.plot_mesh(
style="solid",
transparent_groups=["air__None", "sio2__None", "air__sio2", "air__passive"],
interactive=True,
)
# sim.plot_mesh(
# style="solid",
# transparent_groups=["air__None", "sio2__None", "air__sio2", "air__passive"],
# interactive=True,
# )

# %% [markdown]
# ### Analytical estimate
#
# For the MIM capacitor: C = epsilon_0 * epsilon_r * A / d
# ### IHP PDK compact-model reference
#
# In this estimate, epsilon_r is read from the active PDK-derived stack material table for SiO2, the MIM drawing dimensions are read from the geometry `MIMdrawing` polygon bounding box, and we report two spacings:
# - d_topmetal1 = topmetal1_bottom - metal5_top
# - d_vmim = vmim_bottom - metal5_top
# This is the value the IHP `cap_cmim` SPICE device would report for the same
# geometry. We evaluate the PDK's own area+perimeter law using the process constants
# from the active techParams (`caspec` [F/m^2], `cpspec` [F/m], `lwd` [m]), so the
# reference is authoritative rather than hand-tuned. This is the number to compare the
# Palace mutual capacitance `Cm[1,2]` against.

# %%
import scipy.constants as const

# Pull SiO2 epsilon_r and plate spacings from the active stack derived from the current PDK.
stack = sim._resolve_stack()
sio2_props = stack.materials.get("sio2") or stack.materials.get("SiO2")
if sio2_props is None or sio2_props.get("permittivity") is None:
raise ValueError("Could not find SiO2 permittivity in active stack materials")
eps_r = float(sio2_props["permittivity"])

metal5 = stack.layers.get("metal5")
topmetal1 = stack.layers.get("topmetal1")
vmim = stack.layers.get("vmim")
if metal5 is None or topmetal1 is None or vmim is None:
raise ValueError("Could not find metal5/topmetal1/vmim in active stack layers")

metal5_top = metal5.zmin + metal5.thickness
topmetal1_bottom = topmetal1.zmin
vmim_bottom = vmim.zmin

d_topmetal1_um = topmetal1_bottom - metal5_top
d_vmim_um = vmim_bottom - metal5_top
if d_topmetal1_um <= 0:
raise ValueError(f"Non-physical topmetal1 spacing: {d_topmetal1_um} um")
if d_vmim_um <= 0:
raise ValueError(f"Non-physical vmim spacing: {d_vmim_um} um")

d_topmetal1 = d_topmetal1_um * 1e-6 # m
d_vmim = d_vmim_um * 1e-6 # m

# Read MIM drawing dimensions from geometry.
geom_component = sim.geometry.component
mim_polys = geom_component.get_polygons(by="name").get("MIMdrawing", [])
if not mim_polys:
raise ValueError("Could not find MIMdrawing polygons in geometry")

dbu = geom_component.kcl.dbu
left = min(poly.bbox().left for poly in mim_polys)
right = max(poly.bbox().right for poly in mim_polys)
bottom = min(poly.bbox().bottom for poly in mim_polys)
top = max(poly.bbox().top for poly in mim_polys)

mim_width_um = (right - left) * dbu
mim_length_um = (top - bottom) * dbu
A_mim = (mim_width_um * 1e-6) * (mim_length_um * 1e-6) # m^2

C_analytical_topmetal1 = const.epsilon_0 * eps_r * A_mim / d_topmetal1
C_analytical_vmim = const.epsilon_0 * eps_r * A_mim / d_vmim
C_analytical = C_analytical_topmetal1

print(f"eps_r(SiO2) = {eps_r}")
print(f"MIM drawing from geometry: {mim_width_um:.3f} x {mim_length_um:.3f} um")
print(
f"Analytical (d=topmetal1_bottom-metal5_top={d_topmetal1_um:.3f} um): {C_analytical_topmetal1 * 1e15:.1f} fF"
)
print(
f"Analytical (d=vmim_bottom-metal5_top={d_vmim_um:.3f} um): {C_analytical_vmim * 1e15:.1f} fF"
)
from ihp.cells2.ihp_pycell.utility_functions import Numeric
from ihp.tech import techParams

caspec = Numeric(techParams["cmim_caspec"]) # F/m^2 area-specific capacitance
cpspec = Numeric(techParams["cmim_cpspec"]) # F/m perimeter-specific capacitance
lwd = Numeric(techParams["cmim_lwd"]) # m line-width delta

# Use the device w/l (what the SPICE model is parameterized by), in meters.
leff = cap_width * 1e-6 + lwd
weff = cap_length * 1e-6 + lwd

C_pdk_area = caspec * leff * weff
C_pdk_perim = cpspec * 2.0 * (leff + weff)
C_pdk = C_pdk_area + C_pdk_perim

print(f"IHP model '{techParams['cmim_model']}' for {cap_width} x {cap_length} um cmim:")
print(f" area term = {C_pdk_area * 1e15:7.2f} fF")
print(f" perimeter term = {C_pdk_perim * 1e15:7.2f} fF")
print(f" C_pdk (total) = {C_pdk * 1e15:7.2f} fF <- reference for Palace Cm[1,2]")

# %% [markdown]
# ### Run on cloud
Expand Down Expand Up @@ -181,17 +154,19 @@ def read_palace_csv(path):
return [h.strip() for h in header], data


# Capacitance matrix
# Maxwell capacitance matrix (terminal-C.csv): diagonal = self-capacitance,
# off-diagonal = negative induced charge on the grounded neighbor.
header, C_matrix = read_palace_csv(results_dir / "terminal-C.csv")
print("Capacitance matrix (F):")
print("Maxwell capacitance matrix (F):")
print(f" C[1,1] = {C_matrix[0, 1]:+.4e} F ({C_matrix[0, 1] * 1e15:+.3f} fF)")
print(f" C[1,2] = {C_matrix[0, 2]:+.4e} F ({C_matrix[0, 2] * 1e15:+.3f} fF)")
print(f" C[2,1] = {C_matrix[1, 1]:+.4e} F ({C_matrix[1, 1] * 1e15:+.3f} fF)")
print(f" C[2,2] = {C_matrix[1, 2]:+.4e} F ({C_matrix[1, 2] * 1e15:+.3f} fF)")

# Mutual capacitance
# Mutual (lumped "SPICE") matrix (terminal-Cm.csv): off-diagonal is the physical
# plate-to-plate capacitor. Cm[1,2] is the device capacitance the PDK models.
_, Cm = read_palace_csv(results_dir / "terminal-Cm.csv")
print(f"\nMutual capacitance C_m[1,2] = {Cm[0, 2] * 1e15:.3f} fF")
print(f"\nMutual (plate-to-plate) capacitance Cm[1,2] = {Cm[0, 2] * 1e15:.3f} fF")

# Domain energy
_, E = read_palace_csv(results_dir / "domain-E.csv")
Expand All @@ -200,72 +175,16 @@ def read_palace_csv(path):
)

# %% [markdown]
# ### Compare with analytical estimate
# ### Compare: Palace vs IHP PDK model
#
# The Palace plate-to-plate capacitance is `Cm[1,2]` (equivalently `|C[1,2]|`),
# compared against the IHP `cap_cmim` compact-model value `C_pdk`.

# %%
import scipy.constants as const

C_palace = abs(C_matrix[0, 1])

stack = sim._resolve_stack()
sio2_props = stack.materials.get("sio2") or stack.materials.get("SiO2")
if sio2_props is None or sio2_props.get("permittivity") is None:
raise ValueError("Could not find SiO2 permittivity in active stack materials")
eps_r = float(sio2_props["permittivity"])

metal5 = stack.layers.get("metal5")
topmetal1 = stack.layers.get("topmetal1")
vmim = stack.layers.get("vmim")
if metal5 is None or topmetal1 is None or vmim is None:
raise ValueError("Could not find metal5/topmetal1/vmim in active stack layers")

metal5_top = metal5.zmin + metal5.thickness
topmetal1_bottom = topmetal1.zmin
vmim_bottom = vmim.zmin

d_topmetal1_um = topmetal1_bottom - metal5_top
d_vmim_um = vmim_bottom - metal5_top
if d_topmetal1_um <= 0:
raise ValueError(f"Non-physical topmetal1 spacing: {d_topmetal1_um} um")
if d_vmim_um <= 0:
raise ValueError(f"Non-physical vmim spacing: {d_vmim_um} um")

d_topmetal1 = d_topmetal1_um * 1e-6
d_vmim = d_vmim_um * 1e-6

geom_component = sim.geometry.component
mim_polys = geom_component.get_polygons(by="name").get("MIMdrawing", [])
if not mim_polys:
raise ValueError("Could not find MIMdrawing polygons in geometry")

dbu = geom_component.kcl.dbu
left = min(poly.bbox().left for poly in mim_polys)
right = max(poly.bbox().right for poly in mim_polys)
bottom = min(poly.bbox().bottom for poly in mim_polys)
top = max(poly.bbox().top for poly in mim_polys)

mim_width_um = (right - left) * dbu
mim_length_um = (top - bottom) * dbu
A_mim = (mim_width_um * 1e-6) * (mim_length_um * 1e-6)

C_analytical_topmetal1 = const.epsilon_0 * eps_r * A_mim / d_topmetal1
C_analytical_vmim = const.epsilon_0 * eps_r * A_mim / d_vmim
C_analytical = C_analytical_topmetal1

print(f"Palace result: {C_palace * 1e15:.3f} fF")
print(
f"Analytical (d=topmetal1_bottom-metal5_top): {C_analytical_topmetal1 * 1e15:.1f} fF"
)
print(
f"Analytical (d=vmim_bottom-metal5_top): {C_analytical_vmim * 1e15:.1f} fF"
)
print(
f"Ratio Palace / topmetal1-based analytical: {C_palace / C_analytical_topmetal1:.3f}"
)
print(
f"Ratio Palace / vmim-based analytical: {C_palace / C_analytical_vmim:.3f}"
)
print(f"Using A_mim = {mim_width_um:.3f} x {mim_length_um:.3f} um^2 from MIMdrawing")
print(f"d_topmetal1 = {d_topmetal1_um:.3f} um, d_vmim = {d_vmim_um:.3f} um")
# Palace device (mutual) capacitance — the quantity the PDK models.
C_palace = abs(Cm[0, 2])

print(f"Palace mutual Cm[1,2]: {C_palace * 1e15:.3f} fF")
print(f"IHP PDK model (cap_cmim): {C_pdk * 1e15:.3f} fF")

# %%
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