The Binding Energy of an Exciton-Donor Complex in a Quantum Dot

The Binding Energy of an Exciton-Donor Complex in a Quantum Dot

in a Magnetic Field

A.A.Avetisyan1, E.M.Kazaryan2 and K.Moulopoulos1

1University of Cyprus, Department of Physics, P.O.Box 20537,1678, Nicosia, Cyprus 2Yerevan State University, 1 A.Manoogian, 375025,Yerevan, Armenia. E-mail:

The theoretical investigation of magnetic field influence on the binding energy of the quasiparticle complexes in a quantum dot (QD) of A2B6 semiconductor is very interesting for study of the magnetooptical properties of QDs and for practical applications in new optoelectronic devices. We have developed a variational approach to study the influence of magnetic field on the ground state energy of an exciton-donor complex (EDC), which consists of exciton bound to an ionized donor impurity in a QD with parabolic confining potential. The impurity is taken to be fixed in the center of the spherical QD with the radius d. In the adiabatic approximation σ=me/mh<<1(me and mh are the effective masses of electron and hole) the trial wave function of the system is a product of the electronic g(ra,rb,R,θ1)and the holef(R,θ2)wave functions [1]. We have chosen g in the form that takes into account Coulomb interaction between the particles and also the spherical confining boundary of the

22QD: g=Nexp( δ(ra+rb)R)Jo(k1ra)exp( γrasin2θ γpra, whereδ is the first

variational parameter, ra and rb are the distances of the electron from the impurity and the hole correspondingly,R is the distance between the impurity and the hole; k1=α1d withα1 being the first root of the spherical Bessel functionJ0(k1ra), which vanishes on the QD surface;γp=hωp2R , ωp is the harmonic oscillator frequency of the parabolic confining

20≤r≤d. The factor exp( γra2sin2θ describes potential of the QD:Vc(r)=m ω2pr

the influence of the magnetic field [2,3], θ1 and θ2 are the angles between ra, R and the magnetic field B, applied along thez-direction, γ=hωB2R , ωB=eBmec. We use the

units of the length aB. The energy of the electronic =h2κ/mee2and the energy R =e2/2κaB

system V(R)=gHeg becomes the potential energy for the motion of the hole [1]. We have chosen the hole trial wave function with the second variational parameterλ, based on the results of [1] and on the solution of the system with Coulomb repulsive interaction in spherical QD with parabolic cofining potential [2]. The variation of the ground state total and binding energies of EDC with respect δandλwere performed for different values of d,σ and

B. The behavior of the binding energy of EDC with the increasing of the magnetic field and the features of the magnetooptical absorption in a QD are discussed. Both cases of finite and infinite potential barrier on the QD surface are considered.

This work is supported by Armenian Program “Semiconductor Nanoelectronics”.

[1] A. A. Avetisyan, A. P. Djotyan and E. M Kazaryan, Phys. Stat. Sol ( c), 0, 734 (2003)

[2] A. A. Avetisyan, K. Moulopoulos and A. P. Djotyan, The Abstracts of XXXIII

International School on the Physics of Semiconductor Compounds “Jaszowiec 2004”, Poland (2004)

[3] Z. Xiao, J. Zhu, and F. He, J.Appl. Phys., 79, 9181 (1996)