ECE 230B, HW-1, Winter 2012
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 semic
ECE 222B, Winter 2010 Solutions for Homework Set 6 1. Assume that you are given a dielectric covered ground plane as shown in Figure 8-30 of Balanis. Assume that the height of the dielectric covering is h, the dielectric permittivity is d , and the permea
ECE230A Fall 2009
Solution for Quiz #3
1. A semiconductor is doped with acceptors (Na) and donors (Nd). (a) Assuming the degeneracy factor is 2 for donors and 4 for acceptors. Nd > Na, p0, and Nd is 75% ionized, find the approximate electron concentration
ECE 230B, HW-#4, Winter 2010 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
ECE230A Fall 2009
Solution for Homework #3
1. The intrinsic carrier concentration at room temperature (300K) for Ge and Si is 2.3x1013 cm-3and 1.1x1010 cm-1, respectively. The bandgap energy Eg,Ge=0.67 eV, Eg,Si = 1.1 eV. (a) Find the intrinsic concentrat
ihtJ
Final, ECE230B, Winter 2412
zo
Assume Si, room temperature, and complete ionization.
V4
.
(10 pts) Consider an MOS capacitor with SiOz on n-type Si of No = 3x1016 cm-3.
(a) Sketch the C-V curve (high frequency).
(b) lf the Si bands bend down by 0.1 V
ECE 230B, HW-1, Winter 2010 Solutions 1. 3-D Gauss law is obtained after a volume integration of 3-D Poissons equation and takes the form of Q S E dS = si , where the LHS is an integral of the normal electric field over a closed surface S, and Q is the ne
ECE 230B, HW#6, Winter 2012
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
Bipolar Fundamentals
VBE Emitter Base V CB Collector SC
1E-1
IC0
1E-2 1E-3
IB 0
IC
Ec Ev
IB
Current (A)
IC IB
Ec Ev x
1E-4 1E-5 1E-6 1E-7 1E-8 1E-9 0.4
-WE
0
W
B
Base current = holes injected current holes injected from base into emitter. Collector curre
ECE230A Fall 2009
Solution for Homework #1
1. Provide a photograph of yourself and a brief self-instruction (3~4 sentences about your background, current status and study/research interest) 2. Many III-V compound semiconductors such as GaAs and InP have t
ECE 230B, HW-#5, Winter 2012
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
ECE230A Fall 2009
Solution for Quiz #2
1. For the 1-D InGaAs/InAlAs superlattice, the effective mass for InGaAs and InAlAs are denoted as m1 and m2, respectively. (a) Find the general solution of the Schordinger equation in regions I and II. (b) Write the
ECE230A Fall 2009
Solution for Homework #2
1. For the Kronig Penny model, show that (a) v (b) 0 at the band edge.
d 2 a 2 cos(ka) = dk 2 cos( a ) cos( a ) a sin( a ) p a 2 where = 2mE = h 2m h
(c) Find the effective mass assuming P=3/2, ka=, and a=3/2. In
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, estima
ECE 230B, HW-3, Winter 2012
Solutions
+
1.
Sketch the C-V curve (high frequency) of an MOS capacitor consisting of n poly gate on
n-type Si doped to N d =1016 cm-3. Calculate and show the flatband voltage on the C-V.
Draw the band diagram for V g =0. Give
P-N Junctions/Diodes
p
n
I
V
log I
I
slope = 60 m V/decade
60
V
V
Static Properties
Ec
Ef
Ei
Ec
(a)
Ei
Ef
Ev
Ev
p-type
n-type
Ec
(b)
q bi
Ei
Ef
Ev
Ec
Ef
Ei
Ev
Jn
q
No net current
No net current
flow at thermal
equilibrium:
n
nE
E=
( E f Ei )/ kT
n nie
kT
ECE 230B, HW-#4, Winter 2010 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 scali
ECE 230B, HW-#3, Winter 2010 1. Consider an n-channel MOSFET with 20 nm thick gate oxide and uniform p-type substrate doping of 1017 cm-3. The gate work function is that of n+ Si. (a) What is the threshold voltage? Sketch the band diagram at threshold con
ECE 230B, HW-#3, Winter 2010 1. Consider an n-channel MOSFET with 20 nm thick gate oxide and uniform p-type substrate doping of 1017 cm-3. The gate work function is that of n+ Si. (a) What is the threshold voltage? Sketch the band diagram at threshold con
ECE 230B, HW-2, Winter 2010 Solutions 1. When the gate voltage greatly exceeds the threshold for strong inversion, a first-order solution of s(Vg) can be obtained from the coupled equations, Eqs. (2.195) and (2.182), by keeping only the inversion charge t
ECE 230B, HW-2, Winter 2010 1. When the gate voltage greatly exceeds the threshold for strong inversion, a first-order solution of s(Vg) can be obtained from the coupled equations, Eqs. (2.195) and (2.182), by keeping only the inversion charge term. Show
ECE 230B, HW-1, Winter 2010 1. 3-D Gauss law is obtained after a volume integration of 3-D Poissons equation and takes the form of Q S E dS = si , where the LHS is an integral of the normal electric field over a closed surface S, and Q is the net charge e
MOSFET Scaling
Device scaling: Simplified design goals/guidelines for shrinking device dimensions to achieve density and performance gains, and power reduction in VLSI. reduction in VLSI. Issues: Short-channel effect, Power density, Switching delay, Relia
ECE 222B, Winter 2010 Homework Set 6, Due March 11th 1. Assume that you are given a dielectric covered ground plane as shown in Figure 8-30 of Balanis. Assume that the height of the dielectric covering is h, the dielectric permittivity is d , and the perm
ECE 222B, Winter 2010 Solution to Homework Set 5 1. Problem 8-2, Balanis Solution: Calculate a number of guide parameters given the dimensions a = 0.02286 m and b = 0.1016 m, and relative permittivity r = 2.56. It follows that the speed of light in the wa
ECE 222B, Winter 2010 Homework Set 4 Solutions 1. We wish to determine what fraction of light in glass (for simplicity, let the permittivity of the glass be g = 20 ), incident from the left upon an air gap with width is transmitted across the gap into an
ECE 230B Midterm (Winter 2010)
Assume silicon, room temperature, complete ionization. 1. (20 pts) An abrupt p-n junction with Nd = 1018 cm-3 and Na = 1017 cm-3 is forward biased at 0.5 V. (a) Draw the band diagram. Label the Fermi levels and indicate wher
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
Solutions to Chapter 4 Exercises 4.1. Under the scaling transformation, W W/, L L/, tox tox/, Vds Vds/, Vg Vg/ , and Vt Vt/, Eq. (3.23) becomes I ds eff (Cox ) and Eq. (3.28) becomes W / 1 Vg Vt I ds I ds eff (Cox ) = . L / 2m Note that both m = 1 + 3tox/