title: CALCULATION OF OSCILLATIONS OF THE DENSITY OF ENERGY STATES IN TWO-DIMENSIONAL
text: |
  CALCULATION OF OSCILLATIONS OF THE DENSITY OF ENERGY STATES IN TWO-DIMENSIONAL Pdf ko'rish
  |
  bet | 230/693 | Sana | 13.05.2024 | Hajmi | 15,56 Mb. | | #228860 |
  Bog'liq ТўпламCALCULATION OF OSCILLATIONS OF THE DENSITY OF ENERGY STATES IN TWO-DIMENSIONAL
  MATERIALS IN THE PRESENCE OF A LONGITUDINAL AND TRANSVERSE STRONG MAGNETIC FIELD
  U.I.Erkaboev, R.G.Rakhimov
  Namangan Institute of Engineering and Technology
  Annotation. In this article, we investigated the effect of temperature and a quantizing
  magnetic field on oscillations of the density of energy states in the conduction band of nanoscale
  semiconductor structures. A new mathematical model has been developed for calculating the
  temperature dependence of the oscillations of the density of states in a rectangular quantum well
  under the influence of a transverse quantizing magnetic field. Using the proposed model, the
  experimental results were explained at different temperatures and magnetic fields.
  Keywords: semiconductor, nanoscale semiconductor structures, quantizing magnetic field,
  quantum well, oscillation, density of energy states
  According to the band theory of a solid, the wave function of a free electron, in the presence
  of an external field, is a solution of the stationary Schrödinger equation with a parabolic dispersion
  law:
  2
  2
  *
  ( )
  ( )
  ( )
  2
  V r
  r
  E
  r
  m
  (1)
  Here, V(r) is the energy of free electrons in the presence of an external field, E is the energy
  of charge carriers in the absence of an external field,
  ( )
  r
  is the wave function. The dependence of
  the quantizing magnetic field on the wave function of electrons and the energy spectra of charge
  carriers in two-dimensional electron gases is determined using equation (1), in which the
  momentum operator should be replaced by the generalized momentum operator in a quantizing
  magnetic field:
  2
  *
  1
  ( )
  ( )
  ( )
  2
  i
  eA
  V z
  r
  E
  r
  m
  (2)
  Here,
  A
  is the vector potential of the induction of a strong magnetic field,
  ( )
  B
  rot A
  . To
  solve equation (2), the direction of the vector B is chosen in two different ways. In the first case, this
  vector will be directed along the plane of the two-dimensional layer (along the X-axis) and
  perpendicular to the Z-axis. For a longitudinal quantizing magnetic field, vector potential A can be
  chosen in the form of
  0,
  , 0
  A
  Bz
  .
  k m
  from the Schrödinger equation (2), for a deep
  rectangular quantum well, takes the following form:
  |
  | |