Effect of electric and magnetic fields on impurity binding energy in zinc-blend symmetric InGaN/GaN multiple quantum dots
© Sadeghi and Naghdi; licensee Springer. 2014
Received: 3 November 2013
Accepted: 29 May 2014
Published: 3 September 2014
The binding energy of ground state for hydrogenic impurity in multiple quantum dots is calculated in the framework of effective-mass approximation and using a variational method. It is shown that the binding energy is a function of the size of dots, impurity position and external fields strength. The binding energy has a maximum value when the impurity is located on the center of dots and decreases for other impurity positions. The external electric and magnetic fields change the magnitude and the position of peaks.
PACS Codes 73.20.D; 71.21.La; 71.55.Eq
KeywordsBessel function Binding energy External field Multiple quantum dot Whittaker function
The study of confined quantum systems has been the interesting subject of investigation since the beginning of quantum theory. The interest in the study of the physical properties of confined quantum systems such as quantum wells, wires, and dots, has increased, with the recent progress in semiconductor nanotechnology –.
In recent years, theoretical and experimental investigations have been performed into the issue of the hydrogenic binding of an electron to a donor impurity which is confined within low-dimensional heterostructures ,. 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.
The wide-band gap GaN material systems have attracted much attention for their applications in optoelectronic devices . Built-in electric field is absent in zinc-blend (ZB) GaN structures because the spontaneous polarization does not exist in the ZB GaN due to the higher crystal symmetry. There has been a lot of work devoted to understanding of hydrogenic impurity states in ZB GaN quantum dots and quantum wire –. In all of those calculations, they are all base on single low-dimensional quantum structures. The impurity effects in ZB GaN-based multiple QDs have also been investigated theoretically ,. In theses systems, wave function would penetrate more to the adjacent quantum dots if the barrier height or the barrier thickness is reduced.
On the other hand, the application of an external electric field can provide much valuable information about the confined impurities. Recent theoretical investigations predicated both the field induced level shifts and the field dependence of the carrier lifetime. Therefore, the impurity and the applied electric field effects on the optical properties of QDs are of great interest for fundamental physics and device applications ,.
To our knowledge, there have not been theoretical investigations on impurity states in ZB symmetric multiple GaN QDs under external electric and magnetic fields. In this paper the variational method is used for calculating the impurity binding energy in symmetric I n G a N/G a N multiple quantum dots. In this regard, a trial wave function based on the carrier wave function in cylindrical quantum dot is introduced and the energy is calculated. In Section 2, the Hamiltonian and the calculation method are given. The numerical calculations and discussion on typical InGaN/GaN material are presented in Section 3.
where,,,. Matching the wave functions and their derivatives at the boundaries, the normalization constants and energy eigenvalues, E 0=E ||+E ⊥, are determined.
where α and β are the variational parameters and ρ i and z i are the position of the impurity.
3 Results and discussion
In this study, the numerical calculations are carried out on a typical G a N/I n x G a 1−x N/I n y G a 1−y N QDs. The following parameters are used in the calculations: m ∗=[0.1x+0.19(1−x)]m 0, E g =3.22(1−x)+1.9x−1.4x(1−x), x=0.15, and y=0.02.
The binding energy in a multiple cylindrical quantum dots using the variational method and appropriate wave function is calculated for ZB GaN structures in the presence of electric and magnetic fields. The results clearly showed that the binding energy has three peaks, that are around the center of dots, and decreases as the dot size increases. The electric field varies the value and the position of binding energy peaks according to impurity positions. The binding energy increases as magnetic field is applied for all impurity positions. The behavior of the binding energy is dependent on distribution of electron wave function and impurity position.
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