ECE 230B, HW-#4, Winter 2016
1.
Under the charge sheet model, the channel pinches off when the surface potential
reaches a maximum for a high enough Vds. Express the s,max in terms of Vgs Vfb, Cox,
and Na. At approximately what Vds is this maximum surface

ECE 230B, HW-#5, Winter 2016
1.
Apply constant-field scaling rules to the long-channel currents, Eq. (3.19) for the
linear region, and Eq. (3.23) for the saturation region, and show that they behave as
indicated in Table 4.1.
Solution:
Under the scaling t

Final, ECE230B, Sample
Assume Si, room temperature, and complete ionization.
Consider an MOS capacitor with SiO2 on n-type Si of Nd = 3x1016 cm-3.
(a) Sketch the C-V curve (high frequency).
(b) If the Si bands bend down by 0.1 V at the surface, what are t

ECE 230B, HW#6, Winter 2016
1.
Carrier transit time is defined as tr Q/I, where Q is the total inversion charge
and I is the total conduction current of the device. For a MOSFET device biased in the
linear region (low drain voltage), use Eq. (3.23) and th

ECE 230B, HW-#4, Winter 2016
1.
Under the charge sheet model, the channel pinches off when the surface potential
reaches a maximum for a high enough Vds. Express the s,max in terms of Vgs Vfb, Cox,
and Na. At approximately what Vds is this maximum surface

ECE 230B, HW-3, Winter 2016
Solutions
+
1.
Sketch the C-V curve (high frequency) of an MOS capacitor consisting of n poly gate on
n-type Si doped to Nd=1016 cm-3. Calculate and show the flatband voltage on the C-V. Draw
the band diagram for Vg=0. Given to

ECE 230B Quiz-2 (Winter 2010)
Assume silicon, room temperature, complete ionization.
Consider the design of a 100 nm (channel length) nMOSFET. Assume a gate
oxide thickness of 3 nm.
(a) What substrate doping (assume uniform) is needed for control of short

ECE 230B, HW#6, Winter 2016
1.
Carrier transit time is defined as tr Q/I, where Q is the total inversion charge
and I is the total conduction current of the device. For a MOSFET device biased in the
linear region (low drain voltage), use Eq. (3.23) and th

ECE 230B Quiz-1 (Winter 2010)
Assume silicon, room temperature, complete ionization.
Consider an abrupt n+-p junction with p-type doping of Na = 1017 cm-3.
(a)
What is the built-in potential?
(b)
If both contacts are 0.1 cm away from the junction, estimat

ECE 230B, HW#5, Winter 2016
1.
Apply constant-field scaling rules to the long-channel currents, Eq. (3.23) for the
linear region, and Eq. (3.28) for the saturation region, and show that they behave as
indicated in Table 4.1.
2.
Apply constant-field scalin

P-N Junctions/Diodes
p
n
I
V
log I
I
slope = 60 m V/decade
V
V
Static Properties
No net current
flow at thermal
equilibrium:
kT dn
= 0
J n = q n nE +
q dx
dE f
= 0
dx
d i
E=
dx
( E fEi )/ kT
n = nie
q(i f )/ kT
= nie
Built-in Potential
Fermi level Ef

MOSFET Scaling
Device scaling: Simplified design goals/guidelines for shrinking device
dimensions to achieve density and performance gains, and power
reduction in VLSI.
Issues: Short-channel effect, Power density, Switching delay, Reliability.
The princip

Bipolar Fundamentals
VCB
VBE
1E-1
IC0
Emitter
Collector
Base
IB0
1E-2
SC
Ec
IC
Ev
Ec
IB
Ev
x
-WE
0
W
B
Base current = holes injected
from base into emitter.
Collector current = electrons
j
from emitter into base.
injected
3/16/2014
Current Gain
=IC/IB
C

ECE 230B, HW-1, Winter 2016
1.
Use the density of states, N(E), derived in Section 2.1.1.2 to evaluate the average kinetic
energy of electrons in the conduction band:
K.E.
=
( E Ec ) N ( E ) f ( E )dE
Ec
Ec
.
N ( E ) f ( E )dE
(a) For a non-degenerate sem

ECE 230B, HW-2, Winter 2016
1.
Assume silicon, room temperature, complete ionization. An abrupt p-n junction with Na =
Nd = 1017 cm-3 is reversed biased at 2.0 V.
(a) Draw the band diagram. Label the Fermi levels and indicate where the voltage
appears.
(b

ECE 230B, HW-1, Winter 2016
1.
Use the density of states, N(E), derived in Section 2.1.1.2 to evaluate the average kinetic
energy of electrons in the conduction band:
K.E.
=
Ec
( E Ec ) N ( E ) f ( E )dE
Ec
.
N ( E ) f ( E )dE
(a) For a non-degenerate sem

ECE 230B, HW-2, Winter 2016
1.
Assume silicon, room temperature, complete ionization. An abrupt p-n junction with Na =
Nd = 1017 cm-3 is reversed biased at 2.0 V.
(a) Draw the band diagram. Label the Fermi levels and indicate where the voltage
appears.
(b

ECE 230B, HW-3, Winter 2016
+
1.
Sketch the C-V curve (high frequency) of an MOS capacitor consisting of n poly gate on
n-type Si doped to Nd=1016 cm-3. Calculate and show the flatband voltage on the C-V. Draw
the band diagram for Vg=0. Given tox=10 nm, w