# The effect of magnetic field on the impurity binding energy of shallow donor impurities in a Ga_{1−x}In_{
x
}N_{
y
}As_{1−y}/GaAs quantum well

- Unal Yesilgul
^{1}Email author, - Fatih Ungan
^{1}, - Serpil Şakiroğlu
^{2}, - Carlos Duque
^{3}, - Miguel Mora-Ramos
^{3, 4}, - Esin Kasapoglu
^{1}, - Huseyin Sari
^{1}and - Ismail Sökmen
^{2}

**7**:586

**DOI: **10.1186/1556-276X-7-586

© Yesilgul et al.; licensee Springer. 2012

**Received: **16 July 2012

**Accepted: **28 September 2012

**Published: **24 October 2012

## Abstract

Using a variational approach, we have investigated the effects of the magnetic field, the impurity position, and the nitrogen and indium concentrations on impurity binding energy in a Ga_{1−x}In_{
x
}N_{
y
}As_{1−y}/GaAs quantum well. Our calculations have revealed the dependence of impurity binding on the applied magnetic field, the impurity position, and the nitrogen and indium concentrations.

### Keywords

Impurities Quantum well Dilute nitride## Review

### Background

Over the past decade, the GaInNAs-based quantum-well structures have emerged as a subject of considerable theoretical and experimental research interest due to their very unique physical properties and due to a wide range of possible device applications. GaInNAs exhibits interesting new properties and differs considerably from the conventional III to V alloys. Significant changes occur in the electronic band structure compare with GaInAs with incorporation of small amounts of nitrogen into GaInAs. These include a large redshift of the bandgap, a highly nonlinear pressure dependence of the bandgap, an increase in the electron effective mass, and the N-induced formation of new bands [1–10]. This new material has received considerable attention due to the growing interest in its basic physical properties. Shan et al. showed that interaction between the conduction band and narrow resonant band formed by nitrogen states in GaInNAs alloys leads to a splitting of conduction band into sub-bands and a reduction of the fundamental bandgap [11]. Fan et al. have investigated the electronic structures of strained Ga_{1−x}In_{
x
}N_{
y
}As_{1−y}/GaAs quantum wells [12]. Hetterrich et al. investigated the electronic states in strained Ga_{0.62}In_{0.38}N_{0.015}As_{0.985}/GaAs multiple quantum-well structures [13]. Pan et al. have investigated the optical transitions in Ga_{1−x}In_{
x
}N_{
y
}As_{1−y}/GaAs single and multiple quantum wells using photovoltaic measurements at room temperature [14]. Several studies have been done on detailed optical characterization of Ga_{1−x}In_{
x
}N_{
y
}As_{1−y}. These papers include the temperature dependence of photoluminescence, absorption spectrum, and low-temperature photoluminescence [15–19].

There are many studies associated with the hydrogenic binding of an electron to a donor impurity which is confined within low-dimensional heterostructures [20–25]. The understanding of the electronic and optical properties of impurities in such systems is important because the optical and transport properties of devices made from these materials are strongly affected by the presence of shallow impurities. Also, it is well known that a magnetic field considerably affects the optical and electronic properties of semiconductors. Thus, the effects of magnetic field on the impurity binding energy are a very important problem [26–28]. However, up to now, to the best of our knowledge, no theoretical studies have been focused on impurity binding energies in single GaInNAs/GaAs quantum well (QW) under the magnetic field.

In this paper, using a variational technique within the effective mass approximation, we have investigated the effects of the magnetic field, the impurity position, and the nitrogen (N) and indium (In) concentrations on impurity binding energy in a Ga_{1 − x}In_{
x
}N_{
y
}As_{1 − y}/GaAs QW.

#### Theoretical overview

*z*-axis and takes the magnetic field to be applied to the

*z*-axis, i.e.,

**B**= (0, 0,

*B*). We choose a vector potential

**A**in written form $\text{A=}\frac{1}{2}\left(\frac{-{B}_{y}}{2},\frac{{B}_{x}}{2},0\right)$ to describe the applied magnetic field. Within the framework of the effective mass approximation, the Hamiltonian of a hydrogenic donor impurity in a Ga

_{1 − x}In

_{ x }N

_{ y }As

_{1 − y}/GaAs quantum well in the presence of magnetic fields can be written as follows:

*m*

^{*}is the effective mass,

*e*is the elementary charge,

**p**

_{e}is the momentum of the electron,

*ε*

_{ o }is the dielectric constant of the system,

**r**

_{ e }and

**r**

_{ i }are the electron and impurity atom positions, and

*V*(

*z*) is the confinement potential of the electron in the

*z*-direction. Using cylindrical coordinates (

*x*=

*ρ*cos

*ϕ*,

*y*=

*ρ*cos

*ϕ z*=

*z*) , we obtain the Hamiltonian as follows:

*x*and

*y*) plane. The location of the hydrogenic donor in the structure is given as (0, 0,

*z*

_{ i }). The electron confining potential,

*V*(

*z*), is taken as follows:

with *L* as the well width, and *V*_{0} is the conduction band offset which is taken to be 80% of the total discontinuity between the bandgap of GaAs and Ga_{1 − x}In_{
x
}N_{
y
}As_{1 − y} grown on GaAs [13].

_{1 − x}In

_{ x }N

_{ y }As

_{1 − y}/GaAs is calculated using the band anti-crossing model (BAC). The electron effective mass of Ga

_{1 − x}In

_{ x }N

_{ y }As

_{1 − y}/GaAs as predicted by the BAC model is given by the following [29, 30]:

*E*in the BAC model is taken to be the fundamental bandgap energy (

*E*

_{ G }) for Ga

_{1 − x}In

_{ x }N

_{ y }As

_{1 − y}:

*y*is the N composition in Ga

_{1 − x}In

_{ x }N

_{ y }As

_{1 − y};

*E*

_{C0}is the energy in the absence of N;

*E*

_{ C },

*E*

_{ N }, and

*V*

_{ NC }are the bandgap energies of InGaAs at Г point, the energy of the isolated N level in the InGaAs host material, and the coefficient describing the coupling strength between

*E*

_{ N }and the InGaAs conduction band, respectively. The band structure parameters used in this study are listed in Table 1[31–36].

**Parameters of the binary compounds used for the calculation**

Material | GaAs | InAs | GaN | InN |
---|---|---|---|---|

Electron effective mass | 0.067 | 0.026 | 0.15 | 0.14 |

Dielectric constant | 12.53 | 14.55 | 10.69 | 7.46 |

Energy gap | 1.420 | 0.417 | 3.299 | 1.94 |

*ψ*(

*z*) is the wave function of the donor electron which is exactly obtained from the Schrödinger equation in the

*z*-direction without the impurity, and

*ϕ*(ρ,λ) is the wave function in the (

*x*and

*y*) plane, and it is given by the following:

where *E*_{
z
} is the confinement ground state energy of the electron.

## Results and discussion

In this paper, we have theoretically investigated the effects of the magnetic field, the impurity position, and the nitrogen and indium concentrations on impurity binding energy in a Ga_{1 − x}In_{
x
}N_{
y
}As_{1 − y}/GaAs QW.

*y*= 0,

*y*= 0.005, and

*y*= 0.01) is given in Figure 1. As seen in this figure, when the magnetic field increases, the binding energy also increases. Magnetic field strength gives an additional parabolic magnetic confinement term. Under this additional magnetic confinement, the probability of the electron and impurity atom being on the same plane increases, and therefore, the binding energy increases. In this figure, one sees that when the well width increases, the impurity binding energies increase until they reach a maximum value, and they bind to decrease. This behavior is related to the change of the electron and impurity atom confinement in the quantum well. It should be noted that the donor binding energy increases with nitrogen concentration. As the nitrogen concentration increases, both the electron effective mass and the band discontinuity increase, while dielectric constant decreases. In this case, the coulombic interaction between the electron and a donor impurity increases, and therefore, the impurity binding energy increases.

_{1−x}In

_{ x }N

_{ y }As

_{1−y}/GaAs quantum well as a function of the well width for different values of the magnetic field and for two different indium concentrations (× = 0.15 and × = 0.30). It is seen that the impurity binding energy decreases with the well width for the considered values of the indium concentration. This behavior can be explained as follows: the band discontinuity and the dielectric constant increase with the increasing indium concentration; on the other side, the electron effective mass decreases. Thus, by increasing the indium concentration, particles get to be more energetic and they can penetrate into the potential barriers easily where the wave functions of the particles reflect their three-dimensional character, and the probability of finding the electron and hole in the same plane weakens. This behavior weakens the Coulomb interaction between the electron and impurity atom, and the binding energy begins to decrease.

_{1−x}In

_{ x }N

_{ y }As

_{1−y}/GaAs quantum well as a function of the magnetic field (

*B*) is given in Figure 3 for different impurity positions (

*z*

_{i}) and well width (

*L*=100 Å). As expected, when the magnetic field increases, the binding energy also increases. It can be clearly seen that the impurity binding energy decreases as the position of the impurity approaches the potential barriers. This is because the electron impurity distance increases when the position of the impurity approaches the potential barriers. This leads to the weakening of the electrostatic interaction, therefore to the decreasing in value of impurity binding energy.

## Conclusions

As a summary, we have investigated the effects of the magnetic field, the impurity position, and the nitrogen and indium concentrations on the impurity binding energy in a Ga_{1−x}In_{
x
}N_{
y
}As_{1−y}/GaAs quantum well in this study. The calculations were performed within the effective mass approximation. We have found the impurity binding energy on the magnetic field, the impurity position, and the nitrogen and indium concentrations. This case gives a new degree of freedom in device applications, such as near-infrared electro-absorption modulators and quantum well infrared detectors, and all optical switches. We hope that our results will stimulate further investigations of the related physics as well as device applications of group III nitrides.

## Declarations

### Acknowledgments

This work supported by The Scientific and Technological Research Council of Turkey (TÜBİTAK) for a research grant COST 109T650 and was partially supported by the Scientific Research Project Fund of Cumhuriyet University under the project number F-360. MEMR acknowledges support from Mexican CONACYT through Research Grant CB-2008-101777 and 2011-2012 Sabbatical Grant No. 180636. He is also grateful to the Universidad de Antioquia for hospitality during his sabbatical stay. This research was partially supported by Colombian Agencies: CODI-Universidad de Antioquia (Estrategia de Sostenibilidad 2013-2014 de la Universidad de Antioquia) and Facultad de Ciencias Exactas y Naturales-Universidad de Antioquia (CAD-exclusive dedication project (2012-2013). The authors thank CONACYT (Mexico) and COLCIENCIAS (Colombia) for support under the 2012-2013 Bilateral Agreement "Estudio de propiedades opticas, electronicas y de transporte en sistemas de baja dimension basados en carbono y semiconductores III-V: efectos de campos externos,temperatura y presion hidrostatica". The work was developed with the help of CENAPAD-SP, Brazil.

## Authors’ Affiliations

## References

- Ribeiro F, Latge A: Impurities in a quantum dot: a comparative study.
*Phys Rev B*1994, 50: 4913. 10.1103/PhysRevB.50.4913View Article - Porras N, Perez S, Latge A: Binding energies and density of impurity states in spherical GaAs‐(Ga, Al)As quantum dots.
*J Appl Phys*1993, 74: 7624. 10.1063/1.354943View Article - Movilla J, Planelles J: Off-centering of hydrogenic impurities in quantum dots.
*Phys Rev B*2005, 71: 075319.View Article - Miller A, Chemla D, Schmitt S: Electroabsorption of highly confined systems: theory of the quantum–confined Franz–Keldysh effect in semiconductor quantum wires and dots.
*Appl Phys Lett*1988, 52: 2154. 10.1063/1.99562View Article - Nomura S, Kobayashi T: Clearly resolved exciton peaks in CdSxSe1−x microcrystallites by modulation spectroscopy.
*Solid State Commun*1990, 73: 425. 10.1016/0038-1098(90)90044-CView Article - Porras-Montenegro N, Perez-Merchancano S: Hydrogenic impurities in GaAs-(Ga, Al)As quantum dots.
*Phys Rev B*1992, 46: 9780. 10.1103/PhysRevB.46.9780View Article - Zhu J: Exact solutions for hydrogenic donor states in a spherically rectangular quantum well.
*Phys Rev B*1989, 39: 8780. 10.1103/PhysRevB.39.8780View Article - Zhu J, Xiong J, Gu B: Confined electron and hydrogenic donor states in a spherical quantum dot of GaAs-Ga
_{1−x}Al_{ x }As.*Phys Rev B*1990, 41: 6001. 10.1103/PhysRevB.41.6001View Article - Pozina G, Ivanov I, Monemar B, Thordson J, Andersson T: Properties of molecular-beam epitaxy-grown GaNAs from optical spectroscopy.
*J Appl Phys*1998, 84: 3830. 10.1063/1.368562View Article - Bi W, Tu C: Bowing parameter of the band-gap energy of GaN
_{ x }As_{1−x}.*Appl Phys Lett*1997, 70: 1608. 10.1063/1.118630View Article - Shan W, Walukiewicz W, Ager J, Haller E, Geisz J, Friedman D, Olson J, Kurtz S: Band anticrossing in GaInNAs alloys.
*Phys Rev Lett*1999, 82: 1221. 10.1103/PhysRevLett.82.1221View Article - Fan W, Yoon S: Electronic band structures of GaInNAs/GaAs compressive strained quantum wells.
*J Appl Phys*2001, 90: 843. 10.1063/1.1378336View Article - Hetterich M, Dawson M, Egorov A, Bernklau D, Riechert H: Electronic states and band alignment in GalnNAs/GaAs quantum-well structures with low nitrogen content.
*Applied Physics Lett*2000, 76: 1030. 10.1063/1.125928View Article - Pan Z, Li L, Lin Y, Sun B, Jiang D, Ge W: Conduction band offset and electron effective mass in GaInNAs/GaAs quantum-well structures with low nitrogen concentration.
*Appl Phys Lett*2001, 78: 2217. 10.1063/1.1362335View Article - Tournie E, Pinault M, Vezian S, Massies J, Tottereau O: Long wavelength GaInNAs/GaAs quantum-well heterostructures grown by solid-source molecular-beam epitaxy Appl.
*Phys Lett*2000, 77: 2189. - Polimeni A, Capizzi M, Geddo M, Fischer M, Reinhardt M, Forchel A: Effect of temperature on the optical properties of (InGa)(AsN)/GaAs single quantum wells.
*Appl Phys Lett*2000, 77: 2870. 10.1063/1.1320849View Article - Perlin P, Winiewski P, Skierbiszewski C, Suski T, Kaminska E, Subramanya S, Weber E, Mars D, Walukiewicz W: Solar cells with 1.0 eV band gap, lattice matched to GaAs.
*Appl Phys Lett*2000, 76: 1279. 10.1063/1.126008View Article - Pinault M, Tournie E: On the origin of carrier localization in Ga InNAs/GaAs quantum wells.
*Appl Phys Lett*2001, 78: 1562. 10.1063/1.1354153View Article - Shirakata S, Kondow M, Kitatani T: Photoluminescence and photoreflectance of GaInNAs single quantum wells.
*Appl Phys Lett*2001, 79: 54. 10.1063/1.1374221View Article - Ungan F, Kasapoglu E, Sari H, Somken I: Dependence of impurity binding energy on nitrogen and indium concentrations for shallow donors in a GaInNAs/GaAs quantum well under intense laser field.
*The European Physical Journal B*2011, 82: 313. 10.1140/epjb/e2011-20081-6View Article - Sali A, Fliyou M, Loumrhari H: Photoionization of shallow donor impurities in finite-barrier quantum-well wires.
*Physica B*1997, 233: 196. 10.1016/S0921-4526(97)00305-0View Article - Duque C, Kasapoglu E, Sakiroglu S, Sari H, Sökmen I: Intense laser effects on donor impurity in a cylindrical single and vertically coupled quantum dots under combined effects of hydrostatic pressure and applied electric field.
*Appl Surf Sci*2010, 256: 7406. 10.1016/j.apsusc.2010.05.081View Article - Ruihaoi W, Wenfang X: Optical absorption of a hydrogenic impurity in a disc-shaped quantum dot.
*Curr Appl Phys*2010, 10: 757. 10.1016/j.cap.2009.09.010View Article - Kasapoglu E, Yesilgul U, Sari H, Sökmen I: The effect of hydrostatic pressure on the photoionization cross-section and binding energy of impurities in quantum-well wire under the electric field.
*Physica B*2005, 368: 76. 10.1016/j.physb.2005.06.039View Article - Yesilgul U, Kasapoglu E, Sari H, Sökmen I: Photoionization cross-section and binding energy of shallow donor impurities in GaInNAs/GaAs quantum wires.
*Solid State Communications*2011, 151: 1175. 10.1016/j.ssc.2011.04.029View Article - Sari H, Sökmen I, Yesilgul U: Photoionization of donor impurities in quantum wires in a magnetic field.
*J Phys D: Appl Phys*2004, 37: 674. 10.1088/0022-3727/37/5/005View Article - Terzis A, Baskoutas S: Binding energy of donor states in a GaAs quantum dot: effect of electric and magnetic field.
*J Phys Conf Ser*2005, 10: 77.View Article - Kasapoglu E, Sari H, Sökmen I: Binding energy of impurity states in an inverse parabolic quantum well under magnetic field.
*Physica B*2007, 390: 216. 10.1016/j.physb.2006.08.016View Article - Wu J, Shan W, Walukiewicz W: Band anticrossing in highly mismatched III-V semiconductor alloys.
*Semicond Sci Technol*2002, 17: 860. 10.1088/0268-1242/17/8/315View Article - Skierbiszewski C: Experimental studies of the conduction-band structure of GaInNAs alloys.
*Semicond Sci Technol*2002, 17: 803. 10.1088/0268-1242/17/8/309View Article - Ng ST, Fan W, Dang Y, Yoon S: Comparison of electronic band structure and optical transparency conditions of In
_{ x }Ga_{1−x}As_{1−y}N_{ y }/GaAs quantum wells calculated by 10-band, 8-band, and 6-band k·p models.*Phys Rev B*2005, 72: 115341.View Article - Chuang SL:
*Physics of Optoelectronic Devices*. New York: Wiley; 1995. - Vurgaftman I, Meyer J, Ram-Mohan L: Band parameters for III–V compound semiconductors and their alloys.
*J Appl Phys*2001, 89: 5815. 10.1063/1.1368156View Article - Vurgaftman I, Meyer J: Band parameters for nitrogen-containing semiconductors.
*J Appl Phys*2003, 94: 3675. 10.1063/1.1600519View Article - Chow W, Wright A, Nelson J: Theoretical study of room temperature optical gain in GaN strained quantum wells.
*Appl Phys Lett*1996, 68: 296. 10.1063/1.116064View Article - Gavrilenko V, Wu R: Linear and nonlinear optical properties of group-III nitrides.
*Phys Rev B*2000, 61: 2632. 10.1103/PhysRevB.61.2632View Article

## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.