Download Effect of nitrogen on the diamagnetic

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 İzmir-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.
Introduction
3. Results and discussion
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.
References
In Fig. 1 we have presented the variation of the
donor diamagnetic susceptibility
as a function of
 dia
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
2. Theory
In Fig. 2 we display the effects of the well size
and nitrogen concentration on the diamagnetic
susceptibility of a donor in the quantum GaxIn1xNyAs1-y/GaAs well for B = 0 and B = 20 T. It is
observed that for B = 20 T, the quantum well width
dependence of the diamagnetic susceptibility is not
significant, whereas in the absence of the magnetic
field case the diamagnetic susceptibility decreases
with quantum well width L. In order to explain this
behavior we give the variation of the square root
mean of the relative distance between the electron
and impurity ion as a function of the well width in
Fig. 3. As seen in this figure, in the presence of the
magnetic field, B = 20 T, the separation between the
electron and impurity remains almost constant as
quantum well width increases, but as expected for B
= 0 case, the separation between the electron and
impurity increases with well width L. Also we have
2
observed that <  > decreases as the nitrogen
concentration increases, in the investigated range of
well width. Since as mentioned above, incorporation
of several percent of nitrogen in GaxIn1-xAs alloy
causes larger band gap difference between well and
barrier and therefore deeper quantum well, resulting
in the stronger confinement of the donor electron
and hence in the smaller separation between the
electron and impurity atom.
L = 100
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
2
8
-6
y = 0.05
(1)
y = 0.01
y = 0.02
y = 0.03
y = 0.04
y = 0.05
-8
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
P(Ga x In1-x N y As1-y )  xyP(GaN)  (1  x)(1  y)P(InAs) 
(1  x)yP(InN)  x(1  y)P(GaAs)
5
10
15
B ( Tesla )
20
25
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.
5
4
100
200
300
L( )
400
500
600
2

Fig. 3 The variation of < >1/2 as a function of the

 (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.
well width for two different magnetic field and
the nitrogen concentration values.
y = 0.02
y = 0.05
-4
Susceptibility (a.u)
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,
e2
2
dia  

4 mc2
6
(2)
0
 2 (z  z ) 2
i
(,z; , )  N(z)Exp   2 
2



7
_ B=0
----- B = 20 T
-10
0
y = 0.02
1/2
1  e
e

H
p  A(r)  
 V(z)
* 
2m  c
 o r  ri
-4
Susceptibility (a.u)
2
9
2

(a.u.)
1.
-8
-12
-16
_ B=0
- - - - B = 20 T
-20
100
200
300 L ( ) 400
500
600
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.
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 GaxIn1alloys which are important for
xNyAs1-y
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 F249]
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