ECE 441
Problem Set #2
Due: Wednesday, February 4
Professor E. Rosenbaum
Spring Semester 2015
Reading Assignment: Sections 4.1, 3.1-3.2
1.
Calculate the magnitude of the built-in field in the quasi-neutral region of an exponential impurity
distribution:
e
ECE 441 Spring 2015 TCAD Assignment 1 Solution
1.
(a)
As explained in the tutorial, you should define a fine mesh near the junction and a coarse
mesh for the rest of the device. Also, since the device is uniform in the y-direction, only
the mesh size in t
ECE 441
Midterm Exam #2
April 6, 2015
Name: :3 Ol 00S
Problem 1 (30)
Problem 2 (20)
Problem 3 (20)
Problem / (30)
Total (100 points)
Read careﬂlly:
This is a 50 minute exam. You must stop work and turn in your exam when the instructor
announces that the
ECE 441 Spring 2015 - Homework 3 Solution
1.
The exponential impurity distribution is
() = 0 ( )
Use the quasi neutral approximation, it can be derived:
|()| = |
1
()
()
25.9
| = | | = 0.32
= 8.09 102
For the abrupt junction with Nd = 1017 3, Na = 5 101
ECE 441 Spring 2015 Homework 4 Solution
1.
(a)
From = and = we have =
=
=
. Therefore, from =
d
From = dt , we can derive
d
= dt
The general solution for this differential equation is
() = C exp ( )
Assume the initial charge distribution is (, , , 0),
ECE 441 Spring 2015 - HW1 Solution
1.
(a)
Since total charge in the region < 2 is zero, from Gausss Law it is obvious that
= 0 for > 2 . Similarly, we also have = 0 for < 0.
The negative sheet charge located on the metal side at = 0 is equal to the total
1. In the circuit shown below, an unspecied semiconductor device is represented by a box.
The applied voltage is unknown; it may be zero or non-zero, positive or negative.
However, the band diagram (E vs. x) is available, and it is also shown below.
Bas
ECE 441 Spring 2015 - HW1 Solution
1.
(a)
Since total charge in the region < 2 is zero, from Gausss Law it is obvious that
= 0 for > 2 . Similarly, we also have = 0 for < 0.
The negative sheet charge located on the metal side at = 0 is equal to the total
ECE 441 Spring 2015 - HW #14 Solution
1.
a)
The short channel PMOS drain current equations are:
For VGS < VTP, VDS > VDSAT:
ID =
W
L
eff Cox (VGS VT )VDS 2 VDS 2 )
1
V
1 DS
Esat L
For VGS < VTP, VDS VDSAT:
ID =
Weff Esat Cox
(E
(VGS VT )2
) (1
VDS VDSAT
ECE 441 Spring 2015 - HW #13 Solution
1. (postponed from HW #12)
The off-state leakage current of a long channel MOSFET can be expressed as
IOFF = exp (
),
Cd
where n = 1 +
In order to reduce the leakage current by one order of magnitude, we need to i
ECE 441
Problem Set #13
Due: Wednesday, May 6
Professor E. Rosenbaum
Spring Semester 2015
Reading Assignment: Sections 10.1-10.2
1.
The ID model equations for an n-channel MOSFET are listed below. You are to write the
corresponding set of equations for a
ECE 441 Spring 2015 - Homework 12 Solution
1. (P 8.4); postponed from HW #11.
Since Si = 2 cm, from Figure 1.6 we get Na = 7.5 1015 3.
In depletion, the gate voltage and surface potential is related by
1
VG = VFB + (s p ) + C 2qNa s (s p )
ox
2s (s p )
Al
ECE 441 Spring 2016 - HW1 Solution
1.
According to Eqn. (1.1.23) and (1.1.24), the effective density of states is
3/2
,
2,
= 2(
)
2
From Table 1.3, the density of states effective mass for electrons and holes are
= 1.080 ; = 0.810
Thus
(a)
At 77K,
2 3/
ECE 441 Spring 2016 HW2 Solution
1.
(a)
Since the only current carrier in a metal is electron, the conductivity is
=
Thus
n =
= 0.375 2 1 1
This number is much smaller compared with the electron mobility in Si and Ge.
(b)
The drift velocity is related w
ECE 441
TCAD Assignment #2
Due: May 1, 2015
In this exercise, you will use TCAD to simulate an NMOS transistor. You will learn how to
simulate a quasi-static C-V characteristic and an I-V characteristic. You will investigate the
subthreshold behavior of a
ECE 441
Formula Sheet: Midterm #2
Monday, April 6, 2015
Professor E. Rosenbaum
Spring Semester 2015
1
1
exp
,
,
exp
exp
Abrupt PN junction:
,
ln
Avalanche multiplication:
, VJ is the reverse bias on the junction
Debye length:
, where N is the net doping c
ECE 441
TCAD Assignment #1
Due: Friday, March 13*
In this exercise, you will use TCAD to simulate a silicon PN junction diode. You will learn how
to (i) create a device structure using the TCAD script, (ii) simulate the (static) I-V characteristic,
and (i
ECE 441
Formula Sheet: Midterm #1
Friday, February 20, 2015
Professor E. Rosenbaum
Spring Semester 2015
1
1
exp
,
,
exp
exp
Abrupt PN junction:
,
ln
Avalanche multiplication:
, VJ is the reverse bias on the junction
Debye length:
, where N is the net dopi
ECE 441 Spring 2016 HW6 Solution
1. M&K P 5.12
Assume the diode has a long base on both the p-side and the n-side. The minority carrier
currents can be expressed as
( < ) = (
( > ) = (
+
)
) = 2 (
)
Since the net recombination rate in the space ch
ECE 441 Spring 2016 HW4 Solution
1.
The E-field is lowest near the center of the device. This is because the doping level near the
center of the device is highest. Since the resistor is biased at Vab=10V, there is significant current
flowing through the r
ECE 441 Spring 2016 HW5 Solution
1. M&K P 4.9
Assume we have an abrupt p+n diode. The capacitance of the diode can be expressed as
Cd =
=
2( )
Where is the junction area. Thus,
1
2( )
=
2
2
a)
The slope of the curve for 1V < Va < 0 is
d 1
2
1.5 1026
ECE 441 Spring 2016 HW3 Solution
1. (M&K P. A1.2 with modifications)
(a)
Since total integrated charge in the region < 2 is zero, from Gausss Law it is
obvious that = 0 for > 2 . Similarly, we also have = 0 for < 0.
The negative sheet charge located on th
ECE441
Spring 2016
Assignment # 6
Date: February 26, 2016
Due: March 4, 2016
1.)
M&K P 5.12
2.)
Derive equation (5.2.9a) from (5.2.8) using (5.2.1), (5.2.2), (5.2.5), and (5.2.6).
3.)
An n-type silicon sample contains recombination centers with their ener
ECE441
Spring 2016
Assignment # 4
Date: February 12, 2016
Due: February 19, 2016
1.)
For the silicon slab resistor we simulated in the TCAD tutorial, plot the E-field
along the x-axis when Vab=10V. Explain the physical reason for the particular
shape of t
ECE441
Spring 2016
Assignment # 2
Date: January 29, 2016
1.)
Due: February 5, 2016
The conductivity of copper is approximately 6 x 105 -1m-1 at room temperature
and is due to the mobility of electrons (one per atom) free to move under the
influence of an
ECE441
Spring 2016
Assignment # 1
Date: January 22, 2016
1.)
Due: January 29, 2016
Consider the expressions (M&K 1.1.23, 1.1.24) for effective densities of states at
the conduction and valence band edges, Nc and Nv respectively. Compute them
for Si at the
ECE441
Spring 2016
Assignment # 3
Date: February 5, 2016
1.)
Due: February 12, 2016
M&K, P A1.2 (pp. 50, from the appendix problems), with the following
modifications:
The charge density between xd1 < x < xd2 is 1 /2 instead of 21 .
M&K, P A1.3, (a)-(c),
ECE 441
Problem Set #13
Due: Wednesday, April 29
Professor E. Rosenbaum
Spring Semester 2015
Reading Assignment: Section 9.2
1.
Postponed from Problem Set #12. An NMOS transistor has body doping NA = 1017cm-3 and oxide
thickness Tox = 10nm. The desired th