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ECE 535 (Fall 2013) HW #1
1. The dispersion relation for a diatomic chain is given by:
(
(
)
)
(
)
where, a = 0.6 nm, M1 = 2M2 = 50 mp is the mass of a proton .
(a) Given that the speed of sound in this material is s = 5 x 105 cm/s. Compute the force cons
ECE 535 (Fall 2012) HW #7
Due: Friday, October 19.
1. Consider a SiO2 /Si interface perpendicular to the [100] direction in Si. Derive the
expression for the density of state of a two-dimensional electron gas in each sub-band
for electrons sitting in the
ECE 535 (Fall 2012) HW #1 Solution
1. By using Hamiltonian canonical equations (1.1) & (1.2) in Prof. Hesss
book, derive the expression of the Lorentz force for a particle of charge
e
F =e E + B
v
(1)
from the following Hamiltonian:
H (, ) =
pr
e()
p
Ar
cfw_
Error that all of us did (me as well): when we integrate over angle, remember that we are doing
integration in the same direction for both k< and k> - either counter clock wise or clock wise but both.
So for k> from pi/2 to +pi/2 for k< from pi/2 t
ECE 535 (Fall 2013) HW #12
Due Dec. 6
1. The book derives jLR expression Eq. (10.6), for 3-D. Derive it for 1-D system and
compare with Eq. (8.64). Discuss the physical reason for the difference.
2. Problem 11.4 from the textbook.
3. Derive Eq. 11.41 expl
CHAPTER
13
DIODES
We have already discussed simple diodes (two-terminal devices) in Chapters 11
and 12, and have developed some of the theoretical concepts that are important for their understanding. In this chapter we discuss several types of diodes,
whi
CHAPTER
15
TRANSISTORS
Transistors (transfer resistors) are the most important of all solid-state devices
and distinguish themselves from the diodes by having a third terminal. In 1947,
John Bardeen and Walter Brattain identified minority carrier injectio
CHAPTER
16
FUTURE SEMICONDUCTOR
DEVICES AND THEIR
SIMULATION
16.1
NEW TYPES OF DEVICES
Semiconductor devices havebeen developed and proposed in the firsthalf of the
twentieth century with the declared goalto replacethe vacuum tubesand devices
of gaseous e
ECE 535 (Fall 2013) HW#8
Due: Friday, Oct. 25th
1. A Silicon sample is doped with Gallium concentration of 1017 cm-3 having a binding energy of
65 meV.
a) Find the analytical expression for the Fermi level with respect to the conduction band.
b) Find the
CHAPTER
14
LASER DIODES
Semiconductor laser diodes, and particularly those containing a quantum well as
the active region for light generation, form a prime example of the combination
of classical and quantum transport physics as well as electromagnetic t
CHAPTER
5
EQUILIBRIUM STATISTICS
FOR ELECTRONS AND
HOLES
Although we discussed the energy band structure (the electronic states) of a semiconductor in detail in the previous chapters, we did not include in our discussion
whether these states are actually
CHAPTER
12
NUMERICAL DEVICE
SIMULATIONS
12.1 GENERAL CONSIDERATIONS
It is clear from the previous chapters, that the simultaneous solution of the equations of Poisson and continuity for the electron and hole current densities requires
elaborate numerical
CHAPTER
3
THE THEORY OF ENERGY
BANDS IN CRYSTALS
3.1 COUPLING ATOMS
In Chapter 2 we hinted at a band structure for the E(k) relation from rather
formal arguments. We now introduce the bands from phenomenological considerations.
Consider a series of quantu
CHAPTER
11
THE DEVICE EQUATIONS
OF SHOCKLEY AND
STRATTON
To calculate the electronic current in a semiconductor device, we need to solve
the Boltzmann equation subject to (usually very complicated) boundary conditions. From the Boltzmann equation we can o
CHAPTER
7
SCATTERING THEORY
7.1 GENERAL CONSIDERATIONS-DRUDE THEORY
A precise knowledge of the motionand scattering of electrons is necessary to understand the conductivity of a solid. One wouldthink that scattering of electrons
by impurities impedes only
CHAPTER
9
GENERATIONRECOMBINATION
Generation-recombination (GR) processes are scattering processes similar to
those described in Chapter 7 and can usually be calculated in a similar fashion;
that is, by the use of the Golden Rule [3]. The reason another c
CHAPTER
6
SELF-CONSISTENT
POTENTIALS AND
DIELECTRIC PROPERTIES
OF SEMICONDUCTORS
As indicated at the end of Chapter 5, the calculation of electron and hole densities
becomes far more involved if the donor and acceptor densities are not constant
over space
ECE 535 (Fall 2013) HW #2
Due Friday September 13th
1. Harmonic Oscillator: A harmonic oscillator has the following potential:
( )
The wave function corresponding to this oscillator is given by:
( )
(
)
( )
Hn are the Hermite polynomials. The energy level
ECE 535 (Fall 2013) HW# 11
Due: Friday, Nov. 15
1. The steady-state distribution function for a one dimensional non-degenerate
semiconductor under non-equilibrium conditions is written as
u, and C are constant. If F is the electric field and T,
where
the
ECE 535 (Fall 2013) HW #10
Due Friday Nov. 8
1. Show that the scattering by optical phonon deformation potential with:
(
)
(
) (
)
satisfies the detailed balance equation:
( )(
( )
(
)
( )(
( )
(
)
Where feq is the equilibrium distribution function and is
ECE 535 HW # 7
Due Friday Oct. 18, 2013
1. Consider a SiO2/Si interface perpendicular to the [100] direction in Si. Derive the expression for the
density of state of a two-dimensional electron gas in each sub-band for electrons sitting in the(100), (010),
ECE 535 (Fall 2013) HW #8
Due: Friday, Nov. 1
1.
a ) Calculate the scattering probability S(k , k`) for a scattering potential:
= 0
()
for a 2D system.
b) Use the result from part (1a) to calculate the total scattering rate
1
()
= (, ).
Plot schematicall