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Diamagnetic susceptibility of a donor in
GaxIn1-xNyAs1-y/GaAs quantum well under the
magnetic field E. Kilicarslan , F. Ungan, S.
Sakiroglu , C. A. Duque, E. Kasapoglu , H.
Sari , I. Sökmen Cumhuriyet University,
Physics Department, 58140 Sivas-Turkey Dokuz
Eylül University, Physics Department
Izmir-Turkey Instituto de Fisica, Universidad
de Antioquia, AA 1226, Medellin, Colombia
Abstract Diamagnetic susceptibility of a
hydrogenic donor in a quantum well are
investigated in the presence of the magnetic
field by using a trial wave function in the
framework of the effective mass approximation.
The results show that the diamagnetic
susceptibility donor in the quantum well
increases with the nitrogen mole fraction. Also
it has been observed that, the nitrogen effect on
the diamagnetic susceptibility is not significant
in the range of the large magnetic field values
where the additional geometric confinement is
predominant.
References 1 M. Kondow, K. Uomi, A. Niwa, T.
Kitatani, S. Watahiki, and Y. Yazawa, Jpn. J.
Appl. Phys. Part 1 35 (1996) 1273-1275. 2 M.
Kondow, T. Kitatani, S. Nakatsuka, M. C. Larson,
K. Nakahara, Y. Yazawa, M. Okai, and K. Uomi,
IEEE J. Sel. Top. Quantum Electron. 3 (1997)
719-730. 3 S. Tomic, E.P. OReilly, R. Fehse,
S. J. Sweeney, A. R. Adams, A. D. Andreev, S. A.
Choulis, T. J. C. Hoesa, and H. Riechert, IEEE J.
Sel. Top. Quantum Electron. 9 (2003)
1228-1238. 4 D. A. Livshits, A. Yu. Egorov, and
H. Riechert, Electron. Lett. 36 (2000)
1381-1382. 5 W. Zhou, K. Uesugi, and I.
Suemune, Appl. Phys. Lett. 83 (2003)
1992-1994. 6 J. Hader, S. W. Koch, and J. V.
Moloney, Solid-State Electron. 47 (2003)
513-521. 7 K. Ryczko, G. Sek, J. Misiewicz,
Solid State Commun. 122, (2002) 323-327. 8 T.
Fujisawa, M. Arai, T. Yamanaka, Y. Kondo, and F.
Kano, J. Appl. Phys. 105, (2009)
113114-113121. 9 C. Kittel, Introduction to
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• Introduction
• The semiconductor materials containing a small
  mole fraction of the nitrogen such as GaInNAs has
  become the focus of a considerable recent
  research activity because of their potential
  application in long wavelength lasers on GaAs
  substrates 1-7. By adding a small amount of N
  into the GaInAs material, the band gap of the
  material is dramatically reduced. This feature
  makes it useful for high-temperature operation
  compared with conventional lasers grown on InP
  substrate 8. This fact enables usage of these
  materials for the realization of 1.3 and 1.55 ?m
  quantum well lasers which are important for data
  communications systems 9 -12. This new material
  exhibits very different properties, enhancement
  of electron and hole effective mass and
  dielectric constant by the incorporation a small
  amount of nitrogen atom 7, 8. To our knowledge,
  this is the first investigation diamagnetic
  susceptibility of a donor in quantum wells under
  the magnetic field. The investigation on the
  effects of impurities and external applied fields
  on the electronic and optical properties of these
  low dimensional structures is one of great
  relevance for their potential application in
  optoelectronic technology based on the low
  dimensional semiconductor heterostructures.

3. Results and discussion In Fig. 1 we
have presented the variation of the donor
diamagnetic susceptibility as a function
of the magnetic field for different nitrogen
concentrations and L 100 Å. It is seen that
diamagnetic susceptibility increases with
magnetic field for a given nitrogen concentration
y. Since it is known that in the presence of the
magnetic field the donor electron has an
additional geometric confinement in the (x-y)
plane, the electron wave function is more
concentrated around the impurity ion and the
separation between the electron and impurity atom
decreases with magnetic field. We have observed
that, as expected the effect of nitrogen enhances
the diamagnetic susceptibility. Also it is seen
that, the effect of the nitrogen concentration on
diamagnetic susceptibility decreases with
magnetic field. This is because of increase of
the additional geometric confinement due to the
presence of the magnetic field, the cyclotron
length for electron relative to the well size
decreases as the magnetic field increases. Due to
this feature the effect of the nitrogen on the
diamagnetic susceptibility is more dominant for
small magnetic field values and this effect is
not significant especially for large magnetic
field values.
2. Theory In the effective mass
approximation the Hamiltonian describing the
interaction of an electron with a hydrogenic
impurity placed at (0, 0, zi) in a quantum well
with a uniform magnetic field applied parallel to
the growth direction, i.e. perpendicular to the
layers, is given by
(1) Compositional dependence of the band
energy in the bulk GaxIn1-xNyAs1-y was calculated
by using formula in Ref. 7, and the values of
material parameters for GaxIn1-xNyAs1-y were
obtained using a linear interpolation between
parameters of relevant binary semiconductors


(2) Since an
exact solution of the Hamiltonian in Eq. (1) is
not possible, a variational approach has been
adopted. For the ground state of an electron in
the Coulombic interaction with impurity in a
quantum well we use the following
three-dimensional trial wave function,


(3) where N is the normalization constant,
and are the variational parameters, is the
ground state wave function of the square quantum
well in the z-direction. The variational
parameters and can be determined by minimizing
the expectation value of the Hamiltonian in Eq.
(1). The diamagnetic susceptibility of the
hydrogenic donor, in atomic units, is given by
9 (4) where c is
the velocity of light (c 137 and e 1, mo 1
in a.u.) and is the mean square distance of the
donor electron from the field axis through the
ionized impurity atom.
Fig. 1 The variation of the diamagnetic
susceptibility as a function of the magnetic
field for L 100 Å, and for several values of
the nitrogen concentration.
In this study, the effects of the nitrogen
concentration and magnetic field on diamagnetic
susceptibility of a hydrogenic donor placed in
GaxIn1-xNyAs1-y/GaAs a quantum well are
investigated in the framework of the effective
mass approximation by using a trial wave function
with two parameters. It is observed that the
diamagnetic susceptibility of the donor in the
GaxIn1-xNyAs1-y/GaAs quantum well increases with
nitrogen mole fraction. Also it should be noted
that nitrogen mole fraction dependence of
diamagnetic susceptibility is not significant in
the range of the magnetic field values where the
additional geometric confinement is dominant. As
a result, the obtained results of the effect of
the nitrogen on the diamagnetic susceptibility of
the donor in the presence of the magnetic field
may will be motivate experimental determination
of the magnetic and electronic properties of low
dimensional semiconductors based on
GaxIn1-xNyAs1-y alloys which are important for
optoelectronic devices such as semiconductor
lasers, detectors, filters, and optical
amplifiers operating in the 1.25 to 1.7
µm. Acknowledgemten- We are grateful to
Cumhuriyet University for supporting the work
CUBAP F-249
Fig 2. The variation of the diamagnetic
susceptibility as a function of the well width
for two different magnetic field and the nitrogen
concentration values.