Question # 1 / 17
In quantum mechanics an
unlocalized
electron moving in a
flat 1D world
of length L is represented by the plane wave:
where
is the wave radial frequency and k the wave vector.
Identify the following quantities:
average electron momentum
average electron energy
electron probability-density of presence at x
uncertainty on the momentum
uncertainty on the position
average electron momentum
average electron energy
electron probability-density of presence at x
uncertainty on the momentum
uncertainty on the position
average electron momentum
averge electron energy
electron probability-density of presence at x
uncertainty on the momentum
uncertainty on the position
1/L
average electron momentum
average electron energy
electron probability-density of presence at x
uncertainty on the momentum
uncertainty on the position
0
average electron momentum
average electron energy
electron probability-density of presence at x
uncertainty on the momentum
uncertainty on the position
~L
hydrogen.t
Question # 2 / 17
The energy levels in the hydrogen atom are:
Assume that 0 eV is the minimum energy for an electron not to be binded to the atom. Note that R=13.6 eV is the Rydberg constant.
quantwell.t
Question # 3 / 17
The energy levels in a deep quantum well are (with A a constant):
Sibonds.t
Question # 4 / 17
Give the number of covalent bonds formed by a Si atom in a Si crystal:
3 bonds
4 bonds
5 bonds
hybrid.t
Question # 5 / 17
Give the number of electron(s) involved in a single covalent bond in semiconductor crystal:
1 electron
2 electrons
1/2 electron
impurities.t
Question # 6 / 17
Using the scrolling menu select the correct choice give the electronic structure of a:
s2p1
s2p2
s2p3
donor atom in a silicon crystal
s2p1
s2p2
s2p3
a IV column element (C,Si,Ge...)
s2p1
s2p2
s2p3
acceptor atom in a silicon crystal
miller.t
Question # 7 / 17
Consider the three planes shown below.
Select the correct Miller indices.
1
2
3
(212)
1
2
3
(221)
1
2
3
(122)
[221] is the direction perpendicular to the plane:
1
2
3
band.t
Question # 8 / 17
Consider the three energy dispersion plots shown below.
Select the correct physical system associated with each system.
parabolic
linear
periodic
a photon in free space
parabolic
linear
periodic
a free electron in a flat world
parabolic
linear
periodic
a electron in a crystal
cubic.t
Question # 9 / 17
Consider the three Bravais cells shown below.
Select the correct type of cubic crystal these Bravais cells generate.
1
2
3
4
simple cubic
1
2
3
4
body centered cubic (for example Si in k or indirect space)
1
2
3
4
face centered cubic (for example Si in real or direct space)
1
2
3
4
not cubic (missing some symmetries)
Surface.t
Question # 10 / 17
Consider the 1D band diagram of the surface of a semiconductor at a temperature of 0 K.
Match the energy levels listed below with one of the labels 1 to 5.
1
2
3
4
5
Vacuum level
1
2
3
4
5
Deep core energy levels
1
2
3
4
5
Bottom of the valance band
1
2
3
4
5
Top of the valance band
1
2
3
4
5
Bottom of the conduction band
MetalorIns.t
Question # 11 / 17
Consider the 3 band diagrams below where the temperature is 0 K.
Identify the type of material they represent.
1
2
3
Insulator
1
2
3
Conductor
1
2
3
Semiconductor
FermiD.t
Question # 12 / 17
Consider the three Fermi Dirac distributions plotted below.
Select the correct temperature.
Figure
1
2
3
is for T1=0.
Figure
1
2
3
is for T2 = 300 K.
Figure
1
2
3
is for T3 = 3000 K respectively.
FermiL.t
Question # 13 / 17
Consider the band diagrams below.
Specify the doping type.
1
2
3
P-type semiconductor
1
2
3
N-type semiconductor
1
2
3
Intrinsic semiconductor
kspace.t
Question # 14 / 17
Select the correct definition.
k space
x space
is momentum space (also called indirect space).
k space
x space
is real space (also called direct space or position space).
A band diagram is the representation of the energy of an electron in
k space
x space
The band structure is the representation of the energy of an electron in
k space
x space
direct.t
Question # 15 / 17
Consider the energy bands shown below.
Select the correct type of bands for the material specified.
direct band
indirect band
Semiconductor with the band structure in Figure 1
direct band
indirect band
Semiconductor with the band structure in Figure 2
direct band
indirect band
Silicon, Germanium, and AlAs crystals
direct band
indirect band
GaAs and InP crystals
The gap 1 is
not the thermal bandgap.
the thermal bandgap.
The gap 2 is
not the thermal bandgap.
the thermal bandgap.
The gap 3 is
not the thermal bandgap.
the thermal bandgap.
current1.t
Question # 16 / 17
Consider the band structure shown below of a bulk semiconductor under an electric field.
could you identify the following electrons and holes:
1
2
3
4
5
electrons contributing to the conduction band current
1
2
3
4
5
electrons
not
contributing to the conduction band current
1
2
3
4
5
electrons contributing to the valence band current
1
2
3
4
5
electrons
not
contributing to the valence band current
1
2
3
4
5
holes associated with the valence band current
The velocity of the electrons 2 is directed toward the
left
right
The velocity of the holes 3 is directed toward the
left
right
The velocity of the electrons 5 is directed toward the
left
right
The electric field is directed toward the
left
right
The electrostatic potential is higher (more positive) on the
left
right
current2.t
Question # 17 / 17
Consider the band diagram below.
This band diagram shows the trajectory of a
ballistic
electron in the conduction band accelerated by an uniform electric field.
Could you identify the following quantities:
E_A
E_B
K
0
-qV(x)
is the total energy of the electron at x_A
E_A
E_B
K
0
-qV(x)
is the total energy of the electron at x_B
E_A
E_B
K
0
-qV(x)
is the kinetic energy of the electron at x_A
E_A
E_B
K
0
-qV(x)
is the kinetic energy of the electron at x_B
E_A
E_B
K
0
-qV(x)
is the potential energy of the electron at x
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