Document Type : Reasearch Paper

**Authors**

Department of Physics, An-Najah National University, Nablus,West Bank, Jordan.

**Abstract**

In the present work, the exact diagonalization method had been implemented to calculate the ground state energy of shallow donor impurity located at finite distance along the growth axis in GaAs/AlGaAs heterostructure in the presence of a magnetic field taken to be along z direction. The impurity binding energy of the ground state had been calculated as a function of confining frequency and magnetic field strength. We found that the ground state donor binding energy (BE) calculated at =2 and , decreases from BE=7.59822 to BE=2.85165 , as we change the impurity position from d=0.0 to d=0.5 ,respectively .In addition, the combined effects of pressure and temperature on the binding energy, as a function of magnetic field strength and impurity position, had been shown using the effective-mass approximation. The numerical results show that the donor impurity binding energy enhances with increasing the pressure while it decreases as the temperature decreases.

**Keywords**

**Main Subjects**

[1] Bastard G., (1981), Hydrogenic impurity states in a quantum well: A simple model. *Phys. Rev. B***. **24: 4714-4718.

[2] Poonam V., Sanjiv K. M., (2019), Applications of silver nanoparticles in diverse scctors. *Int. J. Nano. Dimens.*10: 18-36.

[3] Porras-Montenegro N., Perez-Merchancano S., latge A., (1993), Binding energies and density of impurity states in spherical GaAs‐(Ga, Al)As quantum dots. *J. Appl. Phys. *74: 7624-7628.

[4] Ciftja O., (2013), Understanding electronic systems in semiconductor quantum dots, *Phys. Scrip.* 88: 058302-058306.

[5] Liang S., Xie W. F., (2011), The hydrostatic pressure and temperature effects on a hydrogenic impurity in a spherical quantum dot. *Eur. Phys. J. B***. **81: 79-84.

[6] Holtz O., Qing Xiang Zh., (2004), Impurities confined in quantum structures, 1st ed, (*Springer*), 5-10.

[7] Dingle R., Stormer H. L., Gossard A. C.,Wiegmann W., (1978), Electron mobilities in modulation‐doped semiconductor heterojunction superlattices. *Appl. Phys. Lett.* 33: 665-671.

[8] Zhu J.-L., (1989), Exact solutions for hydrogenic donor states in a spherically rectangular quantum well. *Phys. Rev. B.* 39: 8780-8786.

[9] Yuan J.-H., Liu Ch., (2008)*, *Binding energy of an off-center hydrogenic donor in a spherical quantum dot with strong parabolic confinement. *Phys. E.* 41: 41-44.

[10] Rezaei G., Shojaeian Kish S., (2012), Effects of external electric and magnetic fields, hydrostatic pressure and temperature on the binding energy of a hydrogenic impurity confined in a two-dimensional quantum dot. *Phys. E: Low-dimens. Sys. Nanostruc***. **45: 56-60.

[11] Zhu J., Cheng Y., Xiong J., (1990), Exact solutions for two-dimensional hydrogenic donor states in a magnetic field.* Phys. Lett. A.* 145: 358-362.

[12] Mmadi A., Ahmani K. R, Zorkani I., Jorio A., (2013), Diamagnetic susceptibility of a magneto-donor in Inhomogeneous Quantum Dots. *Superlat. Microstruct.* 57: 27-36.

[13] Miller D. A. B., Chemla D. S., Schmitt-Rink S., (1987), Relation between electroabsorption in bulk semiconductors and in quantum wells: The quantum-confined Franz-Keldysh effect. *Phys. Rev. B*. 33: 6976-6980.

[14] Chen H., Li X., Zhou Sh, (1991), Stark shift of hydrogenic impurity states in a quantum well*. Phys. Rev. B***. **4: 6220-6226.

[15] MacDonald A. H., Ritchie D. S., (1986), Hydrogenic energy levels in two dimensions at arbitrary magnetic fields. *Phys. Rev. B*. 33: 8336-8341.

[16] Chuu D. S, Hsiao C. M., Mei W. N., (1992), Hydrogenic impurity states in quantum dots and quantum wires. *Phys. Rev. B***. **46: 3898-3904.

[17] Zhu K. D., Gu S. W., (1993), Shallow donors in a harmonic quantum dot in high magnetic fields. *Phys. Lett. A*. 172: 296-298.

[18] Khordad R., Fathizadeh N., (2012), Simultaneous effects of temperature and pressure on diamagnetic susceptibility of a shallow donor in a quantum antidote. *Physica. B.* 407: 1301-1305.

[19] John P. A., (2008), Simultaneous effects of pressure and magnetic field on donors in a parabolic quantum dot. *Solid State Commun.* 147: 296-300.

[20] Perez-Merchancano S. T., Paredes-Gutierrez H., Silva-Valencia J., (2006), Hydrostatic-pressure effects on the donor binding energy in GaAs–(Ga, Al)As quantum dots*. J. Phys: Condens. Matter*. 19: 026225-026230.

[21] Kassim H. A., (2007), Study of shallow donor level binding energies confined in a GaAs–Ga1−xAlxAs spherical quantum dot. *J. Phys: Condens. Matter***. **19: 036204-036209.

[22] Bzour F., Shaer A., Elsaid Mohammad K., (2017), The effects of pressure and temperature on the exchange energy of a parabolic quantum dot under a magnetic field. *J. Taibah Univ. Sci. *11: 1122-1134.

[23] Schwarz M. P., Grundler D., Wilde D. M., Heyn M. Ch., Heitmann D. J., (2002), Magnetization of semiconductor quantum dots. *J. Appl. Phys.* 91: 6875–6877.

[24] Hijaz E., Elsaid M. K., Elhassan M., (2017), Magnetization of coupled double quantum dot in magnetic fields. *J. Comput. Theor. Nanosc. *14: 1700-1705.

[25] Bzour F., Elsaid M. K., Ilaiwi K. F., (2018), The effects of pressure and temperature on the energy levels of a parabolic two-electron quantum dot in a magnetic field. *J. King Saud. Univ.* 30: 83-90.

[26] Bzour F., Elsaid M. K., Shaer A., (2017), The effects of pressure and temperature on the magnetic susceptibility of semiconductor quantum dot in a magnetic field. *App. Phys. Res.* 9: 77-82.

[27] Elsaid M., Hijaz E., (2017), Magnetic susceptibility of coupled double GaAs quantum dot in magnetic fields. *Acta Phys. Pol. A*. 131: 1491-1496.

[28] Elsaid M., Hjaz E., (2017), Energy states and exchange energy of coupled double quantum dot in a magnetic field. *Int. J. Nano Dimens.* 8: 1-8.

[29] Shaer A., Elsaid M., Elhasan M., (2016), The magnetic properties of a quantum dot in a magnetic field. *Turk. J. Phys.* 40: 209-218.

[30] Shaer A., Elsaid M., Elhasan M., (2016), Variational calculations of the heat capacity of a semiconductor quantum dot in magnetic fields. *Chin. J. Phys .*54: 391-397.

[31] Shaer A., Elsaid M., Elhasan M., (2016), Variational calculations of the exchange energy of a two-electron quantum dot in a magnetic field. *Jord. J. Phys.* 9: 87-93.

[32] Shaer A., Elsaid M., Elhasan M., (2016), Magnetization of GaAs parabolic quantum dot by variation method.* J. Phys. Sci. App.* 6: 39-46.

[33] Bruno-Alfonso A., Candido L., Hai G-Q., (2010), Two-dimensional electron states bound to an off-plane donor in a magnetic field. *J. Phys: Condens. Matter*. 22: 125801-125806.

[34] Khajeh Salehani H., Shakouri Kh., Esmaeilzadeh M., Majlesara M. H., (2012), Effects of on-center impurity on energy levels of low-lying states in concentric double quantum rings*. Int. J. Nano Dimens. *3: 43-51.

[35] El-Said M., (1994), Effects of applied magnetic field on the energy Levels of shallow donors in a parabolic quantum dot. *Phys. B: Condens. Matter***. **202: 202-206.

Autumn 2019

Pages 375-390