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# 5. Three Terminal MOS VG Control and VCB Control¶

## 5.1. Notes¶

The downloader works now as intended. Not downloading current version of programs has caused a great deal of problem. It happened today with ruocan too, when she thinks she had the latest version, it turns out that she had the older version, which took a lot of time for us to figure out.

Give this program a try, and let me know how it works.

1. This one works now, I had the files saved in the c:root folder rather than the current folder during testing.

It now saves files under your working folder if you use the new version.

## 5.2. Homework 3 (Due Th class):¶

1. see slide 21

2. For first problem, just use the latest codes we used today.

try all 4 combinations of overlay and subplots, use a different tox, Na, or try different tox, Na.

save all PDFs (rename them in file system or in python program)

write down the points learned today on the graphs. Many adobe readers allow you to type on a PDF. If you have trouble finding one, let me know.

## 5.3. Homework 2 (Report due next class):¶

1. Practice the new interactive MOS codes. Take screenshots. Compare with equations, see if it makes sense to you.

2. Write a small program to graph out VTB and VTC as a function of doping from 1e16 to 1e18 for tox=1nm, 2nm, and 10nm. Explain your graphs.

3. Investigate the VCB control point of view by looking at how surface potential and charges vary with VCB when VGB is held constant. You can use the sample program provided below.

Explain why surface potential increases with increasing VCB, why ps eventually saturates, and how the saturated ps value relates to psa(Vgb), the depletion surface potential.

A sample program you can use / modify is given below:

#-------------------------------------------------------------------------------
# Name:        Vcb Control of Inversion Charge in 3-T MOS
# Purpose:     For teaching how Vcb controls inversion charge and the concept
#              of channel pinch-off.
# Author:      GuofuNiu
#
# Created:     08/02/2012, updated 2/16/2012
#-------------------------------------------------------------------------------

from myplot import *
from equisemi import Nmos, Metal, Psemi
import numpy as np
from matplotlib.pyplot import show, interactive
from matplotlib.backends.backend_pdf import PdfPages

'''
For teaching how Vcb controls inversion charge and the concept
Also serve as a demo for calculating surface potential vs Vcb for various Vg
You can modify this code for your own purpose

Examine the 'vcb_control_view.pdf' file for output graphics.

'''
fig_format = 'png'

pp = PdfPages('vcb_control_view.pdf')
nmos = Nmos()
vgs = np.linspace(0, 2.0, 5)

ps_from_vg = nmos.ps_from_vg_bisect
qinv_from_ps = nmos.qinv_from_ps

vcbs = np.linspace(0, 2, 50)
cols = colors[:]
ax = None
ax_qinv = None
fig = None
fig_qinv = None

ps = vcbs.copy()
qinv = vcbs.copy()

##interactive(True)
for vg in vgs:
nmos.vgb = vg
color = cols.pop(0)
for idx, vcb in enumerate(vcbs):
nmos.vcb = vcb
ps[idx] = ps_from_vg(vg)
qinv[idx] = qinv_from_ps(ps[idx])

line, ax, fig = myplot(ax=ax, x=vcbs, y=ps,
xlabel='$V_{cb} (V)$',
ylabel='$\phi_{s} (V)$',
label='Vgb=%4.1f' % (vg),
color=color, fig=fig)

pp.savefig(fig)

line2, ax_qinv, fig_qinv = myplot(ax=ax_qinv, x=vcbs, y=qinv,
xlabel='$V_{cb} (V)$',
ylabel='$Q_{inv} (C/cm^2)$',
label='vgb=%4.1f' % (vg),
color=color,
fig=fig_qinv)

cols.append(color)
pp.savefig(fig_qinv)

fig.savefig(nmos.name + '_ps_vcb.png', format=fig_format)
fig_qinv.savefig(nmos.name + '_qinv_vcb.png', format=fig_format)
show()

pp.close()

## 5.4. Homework 1 (Report Due 2/16 Class Time)¶

2. Read the 3-T MOS notes above, summarize the impact of VCB on the Qs-ps, Qs-ps, Qs-Vg curves.

3. Study the mos_vcb_demo() function. Make a copy in another program file, and change doping or oxide thickness, see if you can understand the resulting plots (see the PDF output) using the equations learned from the notes.

def mos_vcb_demo():
'''
Illustrates the effect of Vcb using
pss based MOS data (no bisect that is)

Note that the Vg range will
vary a lot as Vcb varies as
the internal surface potential array nmos.pss
varies with Vcb.

'''

metal = Metal('Npoly')
oxide = Oxide(2)
vcbs = np.array([0, 1, 2])
psemi = Psemi(5e15)

nmos_list = []

for vcb in vcbs:
nmos = Nmos(metal, oxide, psemi, vcb)
nmos_list.append(nmos)

plotter = NmosPlotter(nmos_list)
plotter.save_figs_as_pdf('gate_control_at_vcbs_from_ps.pdf')

4. Study the nmos_vg_plotter_demo() function and its PDF output. Explain results with equations in your own words.

PDF output

def nmos_vg_plotter_demo():
'''
Vg dependence of MOS physics from
using Bisect method.

This demo uses doping dependence for illustration.

:download:see sample output of Vg dependence with doping impact
<../../doping_impact_from_vg.pdf>
'''

# create a metal, an oxide and a ptype semi
metal = Metal('Npoly')
oxide = Oxide(2)
dopings = np.logspace(16, 18, 3)
nmos_list = []
vgs = np.linspace(-2,2,100)

for doping in dopings:
psemi = Psemi(doping)
nmos = Nmos(metal, oxide, psemi)
nmos_list.append(nmos)

plotter = NmosVgPlotter(nmos_list, vgs)

plotter.save_as_pdf('doping_impact_from_vg.pdf')
plotter.write_sphinx(prefix='doping_vg')

5. Study the nmos_vcb_plotter_demo() function and its PDF output. Explain results with equations in your own words.

PDF output

def nmos_vcb_plotter_demo():
'''
Vcb dependence of MOS physics from
using Bisect method.

This demo uses doping dependence for illustration.

:download:see sample output of Vcb dependence with doping impact
<../../vcb_dependence_from_vg.pdf>

'''
# create a metal, an oxide and a ptype semi
metal = Metal('Npoly')
oxide = Oxide(2)
dopings = np.logspace(16, 18, 1)
nmos_list = []
vgb = 1
vcbs = np.linspace(0,2,100)

for doping in dopings:
psemi = Psemi(doping)
nmos = Nmos(metal, oxide, psemi, vgb=vgb)
nmos_list.append(nmos)

plotter = NmosVcbPlotter(nmos_list, vcbs)
plotter.save_as_pdf('vcb_dependence_from_vg.pdf')
plotter.write_sphinx(prefix='doping_vcb')