devices = ['sg13_lv_nmos', 'sg13_lv_pmos']
choice = 0 # select which device to plot, start from 0Copyright 2024 Boris Murmann and Harald Pretl
Licensed under the Apache License, Version 2.0 (the “License”); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
This notebook displays various important metrics for the SG13G2 CMOS technology. The corresponding Xschem testbenches are named techsweep_sg13g2_lv_nmos.sch and techsweep_sg13g2_lv_pmos.sch (to be found in the xschem folder).
In [1]:
In [2]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
# widths used for characterization
w = np.array([5, 5])In [3]:
# read ngspice data
df_raw = pd.read_csv('./techsweep_'+devices[choice]+'.txt', sep=r'\s+')
par_names = df_raw.columns.to_list()
par_prefix = par_names[1].split('[')[0]
# remove extra headers in file body and unwanted columns
#df_raw = df_raw[~df_raw['v-sweep'].str.contains('v-sweep')]
df = df_raw.drop(['frequency', 'frequency.1'], axis=1)
df = df.apply(pd.to_numeric)
# rename columns for readability
df.columns = df.columns.str.removeprefix(par_prefix+'[')
df.columns = df.columns.str.replace(par_prefix[1:], '')
df.columns = df.columns.str.removesuffix(']')
# round sweep vectors to easily addressable values
df['l'] = df['l'].apply(lambda x: round(x/1e-6, 3))
df['vgs'] = df['vgs'].apply(lambda x: round(x, 3))
df['vds'] = df['vds'].apply(lambda x: round(x, 3))
df['vsb'] = df['vsb'].apply(lambda x: round(x, 3))
print(df.columns)
# Note on noise data:
# 1.: sid, sfl are thermal and flicker noise current densities at 1 Hz in A^2/Hz from operating point dataIndex(['cdd', 'cgb', 'cgd', 'cgdol', 'cgg', 'cgs', 'cgsol', 'cjd', 'cjs',
'css', 'fug', 'gds', 'gm', 'gmb', 'ids', 'l', 'rg', 'sfl', 'sid', 'vds',
'vdss', 'vgs', 'vsb', 'vth'],
dtype='object')In [4]:
# sweep variable vectors
l = np.unique(abs(df['l']))
vgs = np.unique(abs(df['vgs']))
vds = np.unique(abs(df['vds']))
vsb = np.unique(abs(df['vsb']))In [5]:
# plot gm/ID and fT versus gate bias
#| label: fig-nmos-gmid-ft-vs-vgs
#| fig-cap: $g_m/I_D$ and $f_T$ as a function of the gate-source voltage.
L1 = min(l); VDS1=0.75; VSB1=0
df1 = df.loc[(df['l'] == L1) & (abs(df['vds']) == VDS1) & (abs(df['vsb']) == VSB1)]
gm_id1 = df1['gm'].values/df1['ids'].values
cgg1 = df1['cgg'].values + df1['cgdol'].values+df1['cgsol'].values
ft1 = df1['gm'].values/cgg1/2/np.pi
ft2 = df1['fug'].values
fig, ax1 = plt.subplots()
ax1.grid(axis='x')
ax1.set_xlabel(r'$V_\mathrm{GS}$ (V)')
color = 'tab:blue'
ax1.set_ylabel(r'$g_\mathrm{m}/I_\mathrm{D}$ (S/A)', color=color)
ax1.plot(vgs, gm_id1, color=color)
ax1.tick_params(axis='y', labelcolor=color)
ax2 = ax1.twinx()
color = 'tab:red'
ax2.set_ylabel(r'$f_\mathrm{T}$ (GHz)', color=color)
ax2.plot(vgs, ft1/1e9, color=color)
ax2.plot(vgs, ft2/1e9, color=color)
ax2.tick_params(axis='y', labelcolor=color)
fig.tight_layout()
plt.title(devices[choice]+', $L$='+str(L1)+r'µm, $V_\mathrm{DS}$='+str(VDS1)+r'V, $V_\mathrm{SB}$='+str(VSB1)+'V')
plt.xlim(0, 1.5)
plt.axvline(x = df1['vth'].values[0], color='k', linestyle='--')
plt.show()
In [6]:
# plot product of gm/ID and fT versus gm/ID
plt.plot(gm_id1, gm_id1*ft1/1e9)
plt.xlim(2, 26)
plt.xlabel(r'$g_\mathrm{m}/I_\mathrm{D}$ (S/A)')
plt.ylabel(r'$f_\mathrm{T} \cdot g_\mathrm{m}/I_\mathrm{D}$ (GHz $\cdot$ S/A)')
plt.title(devices[choice]+', $L$='+str(L1)+r'µm, $V_\mathrm{DS}$='+str(VDS1)+r'V, $V_\mathrm{SB}$='+str(VSB1)+'V')
plt.grid()
plt.show()
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# plot fT versus gm/ID
#| label: fig-nmos-ft-vs-gmid
#| fig-cap: $f_T$ vs. $g_m/I_D$.
plt.plot(gm_id1, ft1/1e9)
plt.xlim(2, 26)
plt.xlabel(r'$g_\mathrm{m}/I_\mathrm{D}$ (S/A)')
plt.ylabel(r'$f_\mathrm{T}$ (GHz)')
plt.title(devices[choice]+', $L$='+str(L1)+r'µm, $V_\mathrm{DS}$='+str(VDS1)+r'V, $V_\mathrm{SB}$='+str(VSB1)+'V')
plt.grid()
plt.show()
In [8]:
# plot fT versus gm/ID for all L
#| label: fig-nmos-ft-vs-gmid-vs-l
#| fig-cap: $f_T$ vs. $g_m/I_D$ as a function of $L$.
VDS2=0.75; VSB2=0
df2 = df.loc[(abs(df['vds']) == VDS2) & (abs(df['vsb']) == VSB2)]
gm_id2 = df2['gm'].values/df2['ids'].values
gm_id2 = np.reshape(gm_id2, (len(vgs), -1), order='F')
ft2 = df2['gm'].values/(df2['cgg'].values+df2['cgdol'].values+df2['cgsol'].values)/2/np.pi
ft2 = np.reshape(ft2, (len(vgs), -1), order='F')
fig, ax = plt.subplots()
ax.plot(gm_id2, ft2/1e9)
ax.legend(loc='center right', bbox_to_anchor=(1.2, 0.5), title='L (µm)', labels=l.tolist())
plt.xlim(2, 26)
plt.xlabel(r'$g_\mathrm{m}/I_\mathrm{D}$ (S/A)')
plt.ylabel(r'$f_\mathrm{T}$ (GHz)')
plt.title(devices[choice]+r', $V_\mathrm{DS}$='+str(VDS1)+r'V, $V_\mathrm{SB}$='+str(VSB1)+'V')
plt.grid()
plt.show()
In [9]:
# plot gm/gds versus gm/ID for all L
#| label: fig-nmos-gmgds-vs-gmid-vs-l
#| fig-cap: $g_m/g_{ds}$ vs. $g_m/I_D$ as a function of $L$.
gm_gds2 = df2['gm'].values/df2['gds'].values
gm_gds2 = np.reshape(gm_gds2, (len(vgs), -1), order='F')
fig, ax = plt.subplots()
ax.plot(gm_id2, gm_gds2)
ax.legend(loc='center right', bbox_to_anchor=(1.2, 0.5), title='L (µm)', labels=l.tolist())
plt.xlim(2, 26)
plt.ylim(0, 200)
plt.xlabel(r'$g_\mathrm{m}/I_\mathrm{D}$ (S/A)')
plt.ylabel(r'$g_\mathrm{m}/g_\mathrm{ds}$ (V/V)')
plt.title(devices[choice]+r', $V_\mathrm{DS}$='+str(VDS1)+r'V, $V_\mathrm{SB}$='+str(VSB1)+'V')
plt.grid()
plt.show()
In [10]:
# plot Id/W (Jd) versus gm/ID for all L
#| label: fig-nmos-jd-vs-gmid-vs-l
#| fig-cap: $I_D/W$ vs. $g_m/I_D$ as a function of $L$.
jd2 = df2['ids'].values/w[choice]/1e-6
jd2 = np.reshape(jd2, (len(vgs), -1), order='F')
fig, ax = plt.subplots()
ax.semilogy(gm_id2, jd2)
ax.legend(loc='center right', bbox_to_anchor=(1.2, 0.5), title='L (µm)', labels=l.tolist())
plt.xlim(2, 26)
if choice == 0:
plt.ylim(1e-2, 1e3)
else:
plt.ylim(1e-2,1e3)
plt.xlabel(r'$g_\mathrm{m}/I_\mathrm{D}$ (S/A)')
plt.ylabel(r'$I_\mathrm{D}/W$ ($\mu$A/$\mu$m)')
plt.grid(which='minor')
plt.grid(which='major')
plt.title(devices[choice]+r', $V_\mathrm{DS}$='+str(VDS1)+r'V, $V_\mathrm{SB}$='+str(VSB1)+'V')
plt.show()
In [11]:
# plot Vdss versus gm/ID for all L
#| label: fig-nmos-vdsat-vs-gmid-vs-l
#| fig-cap: $V_{ds,sat}$ vs. $g_m/I_D$ as a function of $L$.
vdss2 = df2['vdss']
vdss2 = np.reshape(vdss2, (len(vgs), -1), order='F')
fig, ax = plt.subplots()
ax.plot(gm_id2, vdss2)
ax.legend(loc='center right', bbox_to_anchor=(1.2, 0.5), title='L (µm)', labels=l.tolist())
plt.xlim(2, 26)
plt.ylim(0, 1)
plt.xlabel(r'$g_\mathrm{m}/I_\mathrm{D}$ (S/A)')
plt.ylabel(r'$V_\mathrm{ds,sat}$ (V)')
plt.grid(which='minor')
plt.grid(which='major')
plt.title(devices[choice]+r', $V_\mathrm{DS}$='+str(VDS1)+r'V, $V_\mathrm{SB}$='+str(VSB1)+'V')
plt.show()
In [12]:
# plot gamm versus gm/ID for all L
#| label: fig-nmos-gamma-vs-gmid-vs-l
#| fig-cap: $\gamma$ vs. $g_m/I_D$ as a function of $L$.
sid2 = df2['sid'].values
gm2 = df2['gm'].values
sid2 = np.reshape(sid2, (len(vgs), -1), order='F')
gm2 = np.reshape(gm2, (len(vgs), -1), order='F')
gamma2 = sid2/4/1.38e-23/300/gm2
fig, ax = plt.subplots()
ax.plot(gm_id2, gamma2)
ax.legend(loc='center right', bbox_to_anchor=(1.2, 0.5), title='L (µm)', labels=l.tolist())
plt.xlim(2, 26)
if choice == 0:
plt.ylim(0.6,1.2)
else:
plt.ylim(1,2.5)
plt.xlabel(r'$g_\mathrm{m}/I_\mathrm{D}$ (S/A)')
plt.ylabel(r'Noise factor $\gamma$ (1)')
plt.grid(which='minor')
plt.grid(which='major')
plt.title(devices[choice]+r', $V_\mathrm{DS}$='+str(VDS1)+r'V, $V_\mathrm{SB}$='+str(VSB1)+'V')
plt.show()
In [13]:
# plot fco versus gm/ID for all L
#| label: fig-nmos-fco-vs-gmid-vs-l
#| fig-cap: Flicker-noise corner frequency vs. $g_m/I_D$ as a function of $L$.
sfl2 = df2['sfl'].values
sfl2 = np.reshape(sfl2, (len(vgs), -1), order='F')
fco = sfl2/sid2
fig, ax = plt.subplots()
ax.semilogy(gm_id2, fco)
ax.legend(loc='center right', bbox_to_anchor=(1.2, 0.5), title='L (µm)', labels=l.tolist())
plt.xlim(2, 26)
plt.ylim(1e2, 1e8)
plt.xlabel(r'$g_\mathrm{m}/I_\mathrm{D}$ (S/A)')
plt.ylabel(r'$f_\mathrm{co}$ (Hz)')
plt.grid(which='minor')
plt.grid(which='major')
plt.title(devices[choice]+r', $V_\mathrm{DS}$='+str(VDS1)+r'V, $V_\mathrm{SB}$='+str(VSB1)+'V')
plt.show()