Diamagnetic susceptibility of a donor in Ga x In 1-x N y As 1-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, 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. 1.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. 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 Ga x In 1-x N y As 1-y was calculated by using formula in Ref. [7], and the values of material parameters for Ga x In 1-x N y As 1-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, m o = 1 in a.u.) and is the mean square distance of the donor electron from the field axis through the ionized impurity atom. 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. References [1] M. Kondow, K. Uomi, A. Niwa, T. Kitatani, S. Watahiki, and Y. Yazawa, Jpn. J. Appl. Phys. Part 1 35 (1996) [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) [3] S. Tomic, E.P. O’Reilly, 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) [4] D. A. Livshits, A. Yu. Egorov, and H. Riechert, Electron. Lett. 36 (2000) [5] W. Zhou, K. Uesugi, and I. Suemune, Appl. Phys. Lett. 83 (2003) [6] J. Hader, S. W. Koch, and J. V. Moloney, Solid- State Electron. 47 (2003) [7] K. Ryczko, G. Sek, J. Misiewicz, Solid State Commun. 122, (2002) [8] T. Fujisawa, M. Arai, T. Yamanaka, Y. Kondo, and F. Kano, J. Appl. Phys. 105, (2009) [9] C. Kittel, Introduction to Solid State Physics, seventh ed., Wiley, New York, 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. 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 Ga x In 1-x N y As 1-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 Ga x In 1-x N y As 1-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 Ga x In 1- x N y As 1-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] In Fig. 2 we display the effects of the well size and nitrogen concentration on the diamagnetic susceptibility of a donor in the quantum Ga x In 1- x N y As 1-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 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 Ga x In 1-x As 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. Fig. 3 The variation of 1/2 as a function of the well width for two different magnetic field and the nitrogen concentration values.