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Namangan Institute of Engineering and Technology
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Bog'liq ТўпламNamangan Institute of Engineering and Technology
nammti.uz
10.25.2023
Pg.235
For an area equal to one (L
x
L
y
=1) of formula (12), the following is calculated:
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
(
)
4
2
8
2
8
2
d
d
fz
fz
fz
F
c
n
n
n
N
H
N
H c
eH
H
m
md
mc
eH
md
md
(13)
Here
2
2
(
)
d
cN
H
eH
is the filling factor. This is the number of Landau levels, taking into
account their spin splitting, in a quantizing magnetic field, at absolute zero temperature, filled with
electrons. This dimensionless parameter is used to facilitate the discussion of quantum oscillatory
effects in 2D electron gases.
As can be seen from formula (13), the Fermi energies are quantized if the filling factor is an
integer, then the minimum energy quantum will be
1
8
c
, that is, formula (13) gives the exact value
of the energy for the first level corresponding to the
1
.
2
2
2
1
2
1
(
)
8
2
fz
c
n
H
md
(14)
For all other levels, the rigorous theory gives the expression
2
2
2
2
1
(
)
8
2
fz
c
n
H
md
(15)
Here, the filling factor is an integer
0,1, 2, 3...
In addition, in two-dimensional semiconductors, in the presence of a quantizing magnetic
field, the energy spectrum of electrons is purely discrete. A purely discrete energy spectrum, in this
case the Fermi energy, is usually characteristic of a quantum dot. In this case, the magnetic induction
vector will be directed along the Z axis and perpendicularly along the plane of the transverse two-
dimensional layer. In a transverse quantizing magnetic field, quantum wells become analogous to a
quantum dot, in which the motion is limited in all three directions.
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