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Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices

Hydrogenic impurity states in a parabolic quantum dot: Hydrostatic pressure and electric ﬁeld effects Jian-Hui Yuan ⇑, Yan Zhang, Meng Li, Zhi-Hui Wu, Hua Mo * The Department of Physics, Guangxi Medical University, Nanning, Guangxi 530021, China

a r t i c l e

i n f o

Article history: Received 26 April 2014 Received in revised form 8 June 2014 Accepted 15 June 2014 Available online 26 June 2014 Keywords: Quantum dot Hydrogenic impurity Hydrostatic pressure

a b s t r a c t The binding energy of hydrogenic impurity associated with the ground state and some low-lying states in a GaAs spherical parabolic quantum dot with taking into account hydrostatic pressure and electric ﬁeld are theoretically studied by using the conﬁguration–integration method. The binding energies of these low-lying states of the impurity depend sensitively on the hydrostatic pressure, electric ﬁeld and the strength of the parabolic conﬁnement. Based on the analysis of these impurity states, we propose a way for preparation of quantum bit (qubit) by using the strong quantum conﬁnement to the impurity in the quantum dot. Also we calculate the wave functions of some low-lying states to discuss the oscillator strength which is related to the electronic dipole-allowed transitions from 0s state to 0p state. The results show that the electronic dipole-allowed transitions mostly happen between the 0s state and 0p state, especially for the quantum conﬁnement large enough. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction The study of semiconductor quantum dots (QDs) holds a great interest in experimental and theoretical subject in recent years [1–24]. The semiconductor structures with quantum conﬁnement

⇑ Corresponding authors. Tel.: +86 150 7882 3937 (J.-H. Yuan). Tel.: +86 077 1535 8270 (H. Mo). E-mail addresses: [email protected] (J.-H. Yuan), [email protected] (H. Mo). http://dx.doi.org/10.1016/j.spmi.2014.06.006 0749-6036/Ó 2014 Elsevier Ltd. All rights reserved.

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show interesting physical properties which is not depend only on the strength of the conﬁnement but also on the external electric ﬁeld. With the development of modern technology, it is now possible to produce QDs by using these techniques such as etching and molecular beam epitaxy [2]. QDs have been fabricated in different shapes, such as disk-like (cylindrical) shape and spherical shape. The new, unusual properties of the low-dimensional nanometer-sized semiconductor (the three dimensional nanoscale conﬁnement of the charge carriers) give rise to a full quantum nature to these structures. Thus increasing attention has been focused on energy quantized states of charge carriers mainly because of their potential applications in the optical devices [2]. The impurities in semiconductors can affect electrical, the optical and transport properties [3–5]. Thus, impurities play an essential role in semiconductor devices. All semiconductor devices factually incorporate dopants as a crucial ingredient for their proper functioning. Thus an understanding of the nature of impurity states in semiconductor structures is one of the crucial problems in semiconductor physics. The study of the behavior of hydrogenic impurity states in semiconductor nanostructures dates back to the early 1980s through the pioneering work of Bastard [6]. In spite of growing interest in the topic of impurity doping in nanocrystallites, most theoretical work carried out on shallow donors in spherical quantum dots employs variational approaches, alternatively, perturbation methods limited to the strong conﬁnement regime and the method of numerical diagonalization [6–10]. Bose and Yuan et al. [7] calculated the binding energy of a shallow hydrogenic impurity in spherical quantum dot with a parabolic potential by using perturbation method, respectively. Li and Xia [8] calculated the electronic states of a hydrogenic donor impurity in low-dimensional semiconductor nanostructures in the framework of effective-mass envelope-function theory by using the plane wave method. Xie and Zhu et al. [9] investigate the binding energy of hydrogenic donor impurity in a parabolic quantum dot and in a rectangle spherical quantum dot using the method of numerical diagonalization, respectively. As far as we known, the electric ﬁeld will destroy the symmetry of the system. So, a considerable attention of the energy levels of shallow impurities in QDs may be drawn. The energy spectrum of the carriers will make respectable changes because the electric ﬁeld results in an energy Stark shift of the quantum states. Using the variational approaches [10], Murillo calculated the binding energy of an on-center donor impurity in a spherical GaAs-(Ga,Al)As QD with parabolic conﬁnement as a function of the dot radius and the applied electric ﬁeld. The quantum size, impurity position and electric ﬁeld affect on the energy of donor placed anywhere in a GaAs spherical quantum crystallite which embedded in Ga1xAlxAs matrix was discussed theoretically by Assaid et al. [11]. It is well known that hydrostatic pressure is a powerful tool to investigate and control the optical properties of low-dimensional semiconductor electronics-related systems. However, most of these studies were concerned with the ground-state electronic properties. Recently, the hydrostatic pressure has been attracted much attention for the impurity state. Within the framework of effective-mass approximation, Xia et al. [12] studied the hydrostatic pressure effects on the donor binding energy of a hydrogenic impurity in InAs/GaAs self-assembled quantum dot (QD) by means of a variational method. Yesilgul et al. [13] investigated effects of an intense laser ﬁeld and hydrostatic pressure on the intersubband transitions and binding energy of shallow donor impurities in a quantum well. Duque et al. [14] have studied theoretically the hydrostatic pressure effects on optical transitions in InAs/GaAs cylindrical QD. So far, the binding energy of the low-lying states of donor impurity with external electric ﬁeld in the presence of the hydrostatic pressure was rarely studied. And mostly all of study the binding energy of the ground state about this topic was carried out by the variational approaches [15] or in a two-dimensional QD [16]. It is more interesting for us, recently, the topic for the various conﬁned potential in the QD using potential morphing method (PMM) have been reported by Garoufalis et al. for investigating the lowing-lying state and optical properties [17]. In this work, we will investigate the binding energy of the ground state and some low-lying states of a spherical QD with parabolic conﬁnement in the presence of an external electric ﬁeld and hydrostatic pressure. The spherical QDs so far are formed from semiconductor nanocrystals embedded in either an insulating or a semiconducting matrix. An attempt is to study the inﬂuence of the external electric ﬁeld, hydrostatic pressure and parabolic conﬁnement strength to the shallow donor impurity using the conﬁguration–integration methods (CI) [18]. Our numerical calculations are carried out for one of the typical semiconducting materials, GaAs. We ﬁnd that the binding energies of these low-lying states of the impurity depend sensitively on the hydrostatic pressure, electric ﬁeld and

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the parabolic conﬁnement strength. We propose a way for preparation of qubit by using the strong quantum conﬁnement to the impurity in the quantum dot. Also we calculate the wave functions of some low-lying states to discuss the oscillator strength which is related to the electronic dipoleallowed transitions from 0s state to 0p state. The results shows that the electronic dipole-allowed transitions mostly happen between the 0s state and 0p state, especially for the quantum conﬁnement large enough. In Section 2, we introduce the model and method for our calculation. In Section 3, the numerical analysis to our important analytical issues are reported. Finally, a brief summary is given in Section 4. 2. Model and method Within the framework of effective-mass approximation, the Hamiltonian of an center hydrogenic donor conﬁned by a spherical QD with a parabolic potential in the presence of electric ﬁeld along the z axis under the inﬂuence of hydrostatic pressure and the temperature can be written by

H¼

p2 e2s þ qF r þ VðrÞ 2me ðP; TÞ eðP; TÞr

ð1Þ

where the hydrogenic impurity locates at the center of the QD, es is the reduced charge of the electron, pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ namely, es ¼ e= 4pe0 and q is the absolute value of the electron charge e. rðpÞ is the position vector (the momentum vector) of the electron originating from the center of the dot, me ðP; TÞ is the effective mass of an electron and VðrÞ is the conﬁning potential in the form of

VðrÞ ¼

1 m ðP; TÞx20 r 2 2 e

ð2Þ

where x0 is the strength of the conﬁnement potential frequency. In our model, the Hamiltonian of single hydrogenic impurity in a spherical QD can be expressed as the sum of the original harmonic oscillator Hamiltonian term H0 , a Coulomb interaction term H1 and a electric potential term H2 , i.e.,

H ¼ H0 þ H1 þ H2

ð3Þ

where

H0 ¼

p2 1 þ m ðP; TÞx20 r2 2me ðP; TÞ 2 e

e2s eðP; TÞr H1 ¼ qF r H1 ¼

ð4Þ ð5Þ ð6Þ

In order to obtain the eigenfunction and eigenenergy associated with the hydrogenic donor in a spherical QD, let us consider a linear function of the form

Wm ¼

X

cj wj ðr; h; uÞ

ð7Þ

j

In there, wj ðrÞ is a 3D harmonic oscillator state with the frequency x0 and an energy hx0 . The principal, orbital, and magnetic quantum numbers of wj ðr; h; uÞ are nj ; lj , ð2nj þ lj þ 3=2Þ and mj , respectively. In the presence of the electric ﬁeld, only the magnetic quantum number is a good one. The summation in Eq. (7) includes only the terms with a ﬁxed magnetic quantum numbers m, (i.e., m1 ¼ m2 ¼ . . . ¼ m). Here, so j denotes the whole set quantum number nj ; lj in brevity. Let N j ¼ 2nj þ lj and obviously the accuracy of solutions depends on how large the model space is. The dimension of the model space is constrained by 0 6 N j 6 30. The matrix elements of H are then given by the following expressions

hWm jHjWm i ¼

o X n ci cj 2nj þ lj þ 3=2 hx0 di;j þ uIi;j þ uIIi;j i;j

ð8Þ

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with

Z 1 e2s R R rdr eðP; TÞ 0 ni ;li ;r nj ;lj ;r Z 1 uIIi;j ¼ qF Rni ;li ;r Rnj ;lj ;r r 3 dr hY li ;m j cos hjY lj ;m i

uIi;j ¼

ð9Þ ð10Þ

0

Here, we introduce a recurrence formula with the form as

cos hY l;m ¼ al;m Y lþ1;m þ al1;m Y l1;m

ð11Þ

where

al;m

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 ðl þ 1Þ m2 ¼ ð2l þ 1Þð2l þ 3Þ

The application of hydrostatic pressure modiﬁes lattice constants, dot size, effective masses and dielectric constants. We present the explicit expressions for these quantities as a function of pressure and temperature, where the pressure is expressed in kbar and the temperature is 300 K [19]. For the electron effective masses,we have [15–20]

me ðP; TÞ ¼

C

1 þ EP

m0

2 EC g ðP;TÞ

1 þ EC ðP;TÞþ D g

ð12Þ

0

where m0 is the single electron bare mass, ECP is an energy related to the momentum matrix element corresponding to the temperature T ? 0 K and the hydrostatic pressure P ? 0 kbar, namely, ECP ¼ 7510 meV and the spin-orbit splitting D0 ¼ 341 meV, ECg ðP; TÞ is the energy gap for the GaAs QD, 2

ECg ðP; TÞ ¼ E0g þ aP þ bP 2

bT T þc

ð13Þ

where E0g ¼ 1519 meV is the energy gap for the GaAs QD related to T ¼ 0 K and P ¼ 0 bar, a ¼ 12:6 meV=kbar, b ¼ 0:0377 meV=kbar2 , b ¼ 0:5405 meV=K and c ¼ 204 K [19]. The static dielectric constants can be written as

eðP; TÞ ¼ eð0; TÞ expðd1 ðT T 0 ÞÞ expðd2 PÞ þ c0 5

ð14Þ 3

where eð0; 300 KÞ ¼ 13:18, d1 ¼ 20:4 10 =K, d2 ¼ 1:73 10 =K, T 0 ¼ 300 K. In view of the value of the band-edge density of states effective mass m0e ¼ 0:067m0 related to the temperature 0 K and the hydrostatic pressure 0 kbar [19], the corresponding static dielectric e is chosen as 12.4, then the parameter c0 is about zero. In order to investigate the binding energy of the impurity for the ground state and some low-lying states, We need to diagonalize the matrix in Eq. (8) to obtain the energy corresponding to the ground state and some excited state and to obtain the corresponding wavefunction by using Schmidt orthogonal algorithm. The donor binding energy EB of the hydrogenic impurity can be given as follows

EB ðDÞ ¼ E0 ðP; TÞ EðP; TÞ

ð15Þ

where EðP; TÞ) and E0 ðP; TÞ are, respectively, the low-lying levels of an electron in the spherical QDs with and without the Coulomb potential in the presence of the electric ﬁeld with taking into account both the temperature and the pressure effect. In spectroscopy, oscillator strength is a dimensionless quantity which can express the probability of absorption or emission of electromagnetic radiation in transitions between energy levels of an atom or molecule. Thus, the oscillator strength is a very important physical quantity in the study of the optical properties which are related to the electronic dipole-allowed transitions. Generally, the oscillator strength Pfi of the impurity is deﬁned as [21,22]

Pji ¼

2me ðP; TÞ 2 h

Eji jhjjr cos hjiij2

ð16Þ

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But there is a prerequisite that optical vector is along the z-axis. The oscillator strength can offer addiP tional information on the ﬁne structure and selection rules of the optical absorption and j Pji ¼ 1 associated to the sum for all of j state [22]. Using Eq. (11), the dipole-allowed optical transitions are always from the states M‘ ¼ 1. Here we focus our attention on the 0s state to 0p state. So Eji denotes difference of the energy between 0s and 0p. 3. Results and discussion For typical GaAs QDs in the temperature 0 K and the hydrostatic pressure 0 kbar, e ¼ 12:4, and 2 m0e ¼ 0:067m0 . In the following, the effective Rydberg Ry ¼ m0e e4s =2h e2 ¼ 5:93 meV and nm are taken to be the energy and length units, respectively. In Fig. 1, we investigate the binding energy of the ground state as the function of the electric ﬁeld F hx0 ¼ 50; 100 and 200 meV associated to the temperature in three different quantum conﬁnements 0 K and the hydrostatic pressure 0 kbar using the CI method (solid line) and the perturbation method (dash line). It is easily seen that the binding energy decreases monotonously with increasing of the strength of the applied electric ﬁeld for the three quantum conﬁnements. The reason is that the emergence of the electric ﬁeld can destroy the symmetry of potential ﬁeld applied to the center hydrogen impurity, which can cause the change of the distribution the electronic probability density. In order to pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ clear our viewpoint, here we can deﬁne the conﬁned potential radius R ¼ h=m0e x0 as the characteristic length associated with the conﬁning potential. Electron is bound by the electric ﬁeld which can weaken the interaction between impurity and electron, thus we can easy to understand that the overlap integral of wave function of ground state induced by the Coulomb interaction is decreasing with increasing of the strength of the electric ﬁeld. Also, the binding energy of the ground state increases with increasing of the quantum conﬁnement for ﬁxed the applied electric ﬁeld. The reason is that the conﬁned potential radius is decreasing with increasing of the quantum conﬁnement, which can cause the enhancement of the interaction between impurity and electron. It is important to observe that in the regime of very strong conﬁnement ð hx0 ¼ 200 meVÞ, the binding energy of the ground state is almost not inﬂuenced by the change of the strength of the electric ﬁeld. This behavior of binding energy with increasing F is related to the fact that, when the conﬁnement strength is predominant, the variation is very small in the proper range of F, and the effect of electric ﬁeld is seen to be appreciable for weak conﬁnement. Obviously, the electric ﬁeld effect will become more and more weak with the increasing of the conﬁnement strength. This result is similar to the result of Ref. [7,23]. That is to says, the Coulomb interaction term can be ignored or viewed as perturbation term in the large enough

Fig. 1. The binding energy of the ground state as the function of the electric ﬁeld F in three different quantum conﬁnement x0 ¼ 50; 100 and 200 meV associated to the temperature 0 K and the hydrostatic pressure 0 kbar using the CI method (solid h line) and the perturbation method (dash line).

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quantum conﬁnement. There is a comparison of the results reported by the perturbation method and by CI method. It is clear seen in Fig. 1 that the binding energies obtained by the CI method are larger than those obtained by the perturbation method. Factually, the perturbation method can be viewed as an approximate of the CI method under the strong quantum conﬁnement. In Fig. 2, we investigate the binding energies of the ground state and some low-lying excited state as the function of the electric ﬁeld F in the quantum conﬁnement hx0 ¼ 100 meV associated to the temperature 0 K and the hydrostatic pressure 0 kbar using the CI method. In Fig. 2(a), the binding energy of 0s, 1s, 2s, 0p, 1p, 0d, 1d, 0f, 0g states with m = 0 as the function of the electric ﬁeld are investigated in detailed. we ﬁnd that the binding energy decreases with the increase of the principle quantum number n for ﬁxed l under the electric ﬁeld F = 0 kV/cm. It is because that the energy of the electron with the bigger n has a high value, which leads to weaken the ability of electron trapped by the impurity. Furthermore, we ﬁnd that the binding energies of these low-lying states for the impurity change dramatically in the presence of the electric ﬁeld. In principle, the binding energy decreases monotonically with decreasing of the strength of the electric ﬁeld for the s-states (i.e. s states), but for p-, d-, f- and g-states, the binding energy increase to a maximum, then decrease with increasing the strength of the electric ﬁeld. The reason is that the competition between the rotational energy and the Coulomb interaction energy ﬁnally determines the binding energy of the low-lying states of the impurity in QDs, and the electric ﬁeld effect on the probability distribution of these low-lying state for impurity results in the reduction of the interaction between a donor impurity and an electron. However, here are some seem disappointing. We note that the some levels of the binding energy overturn and a gap appears between the two turnover energy levels. such as 1s and 0d states. Factually, it is very interesting for us to produce the QD qubit for these impurity states. When the quantum conﬁnement is large enough, the spacing of the energy is too large between different N states (all of the state satisfying N ¼ 2n þ ‘), which leads to hardly transmit for electron from the different N states. Thus the electron is locked into a small space state satisfying N ¼ 2n þ ‘. For Example, the states of the impurity associated with N ¼ 4 includes 2s, 1d and 0g states. These states of impurity for N ¼ 4 can be obtain by using three-level quantum states with a ﬁtting strong quantum conﬁnement, i.e. jwi ¼ c1 j2ai þ c2 j1di þ c3 j0gi. Indeed, it is the fact that the Coulomb interaction energy can be view as a perturbation term in the strong quantum conﬁnement, but here we must take into account the degeneracy of the energy level of impurity in comparison

Fig. 2. The binding energy of the ground state and some low-lying excited state as the function of the electric ﬁeld F in the quantum conﬁnement hx0 ¼ 100 meV associated to the temperature 0 K and the hydrostatic pressure 0 kbar using the CI method.

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with the results in Ref. [7]. It is easily seen that these qubits can be controlled by the electric ﬁeld, and the occupation states can be easily transited from 2s to 1d and 1d to 0g with increasing of the strength of electric ﬁeld. In Fig. 2(b), we ﬁnd that the splitting of the level of the binding energy appears in the presence of the electric ﬁeld (the well-known stark effect) because the symmetry of the system of impurity associated with shape of the potential is destroyed and then the degeneracy of energy level of the impurity is partially removed. In addition, the binding energies for the low-lying states always decrease as the increase of m for ﬁxed n; l. According to angular distribution of wave function, the states with m ¼ 0 mainly distribute along the z axis, but the angular distribution of wave function deviate too far from the z axis with increasing m. So, the donor impurity inﬂuences the state with smaller m and ,then, a larger binding energy is obtained [23]. It is worth noting that the state of 1s and 0d for ﬁxed the m ¼ 0 associated with N ¼ 2. In the strong quantum conﬁnement, 1s and 0d for the impurity states can be view as two level qubit, namely jwi ¼ c1 j1si þ c2 j2di, which can be adjusted by the electric ﬁeld to realize the transition from 1s to 0d state. In Fig. 3, we discuss the binding energy of the ground state (a) and the ﬁrst excited state (b) as the hx0 ¼ 100 meV associated to the temperfunction of the electric ﬁeld F in the quantum conﬁnement ature 300 K using the CI method, where the hydrostatic pressure are both chosen as 0, 20, 50, 100 kbar. It is easily seen that the binding energy of the ground state and the ﬁrst excited state of the impurity depend sensitively on both the hydrostatic pressure and the electric ﬁeld. We ﬁnd that the binding energy of both the ground state 0s and the ﬁrst excited state 0p are increasing with increasing of the hydrostatic pressure P. The reason is that the appearance of the hydrostatic pressure can be change the energy gap, static dielectric constants and effective mass for GaAs [24]. In the ﬁtting hydrostatic pressure range, both the energy gap and effective mass for GaAs are increases monotonically but static dielectric constant is decreasing monotonically with increasing of the hydrostatic pressure (see in Fig. 4). The characteristic length associated with the conﬁning potential is rewritten pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ as R ¼ h=me ðP; TÞx0 . In the temperature 300 K, thus the characteristic length associated with the conﬁning potential is to become more and more smaller with increasing of the hydrostatic pressure, which increases the interaction between the impurity ion and the electron. Another, the static dielectric constant for GaAs is decreasing with increasing of the hydrostatic pressure, which strength the

Fig. 3. The binding energy of the ground state (a) and the ﬁrst excited state (b) as the function of the electric ﬁeld F in the quantum conﬁnement hx0 ¼ 100 meV associated to the temperature 300 K using the CI method, where the hydrostatic pressure are both chosen as 0, 20, 50, 100 kbar.

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Fig. 4. The energy gap, static dielectric constants and effective mass for GaAs as the function of the hydrostatic pressure P under the temperature T = 300 K.

Fig. 5. The radial wave function of ground state and some low-lying excited state for the magnetic quantum number m ¼ 0 as the function of the reduced distance 1R in the quantum conﬁnement hx0 ¼ 100 meV and the electric ﬁeld F = 100 kV/cm associated to the temperature 300 K and the hydrostatic pressure 50 kbar .

Coulomb interaction between the impurity ion and the electron. Thus we can easily understand that both the binding energy of the 0s and 0p states for impurity are increasing with the increase of the hydrostatic pressure. The oscillator strength is a very important physical quantity in the study of the optical properties which are related to the electronic dipole-allowed transitions. However, for the quantities of the oscillator strength which depends on the wave function of the impurity state. So we investigate the radial wave function of ground state and some low-lying excited states in Fig. 5 for the magnetic quantum

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number m ¼ 0 as the function of the reduced distance 1R (the dimensionless 1R ¼ r=R) in the quantum conﬁnement hx0 ¼ 100 meV and the electric ﬁeld F = 100 kV/cm associated to the temperature 300 K and the hydrostatic pressure 50 kbar. It is easily seen that as the same with the 3D harmonic oscillator state, there are no node in the 0s, 0p, 1d states, but in principle there is a node in the 1s state. It is because that these impurity states are very complex which consists of different the 3D harmonic oscillator state with the ﬁxed l and m. Further research in Fig. 6, we investigate the oscillator strength for the magnetic quantum number m ¼ 0 associated to optical transitions from 0s state to 0p state as the x0 ¼ 50 meV under function of the electric ﬁeld F in the quantum conﬁnement (a) hx0 ¼ 100 and (b) h four different hydrostatic pressure P = 0, 20, 50, 100 kbar and the temperature T = 300 K. In both two cases, the oscillator strength for the magnetic quantum number m ¼ 0 associated to optical transitions from 0s state to 0p state are bigger than 0.95. In other word, the electronic dipole-allowed transitions mostly happen between the 0s state and 0p state, especially for the larger quantum conﬁnement. The reason is that the spacing of energy level from the ground state to the other excited state is very large so that only the transition from 0s to 0p state is allowed to happen. It is easily seen that the hydrostatic pressure suppresses the electron transition from 0s to 0p state. This is precisely the result of the increase of the binding energy with increasing of hydrostatic pressure in Fig. 3. From Fig. 3, it is easily seen that the energy spacing between 0s and 0p state is increasing with increasing of hydrostatic pressure. It is because that the spacing of energy level between 0s state and 0p state is proportional to the spacing of binding energy between 0s and 0p state (see From Eq. (15)). Also, the electric ﬁeld affects dramatically the oscillator strength. It is easily seen that the oscillator strengths decrease with an increasing of the electric ﬁeld, then attain to its minimum at a certain electric ﬁeld and ﬁnally increase with increasing of the electric ﬁeld. It is still the result of the difference between the two energy levels. We can easily see that the spacing of the two energy level decreases ﬁrstly, then attains to its minimum, ﬁnally increases with increasing of the electric ﬁeld. In addition, the minimum of the oscillator strength shifts to the high electric ﬁeld with increasing of the hydrostatic pressure. When the strength of the electric ﬁeld is large enough, we note that only the electron transition happen between 0s to 0p state (the oscillator strength f 1), especially for the small quantum conﬁnement.

Fig. 6. Oscillator strength for the magnetic quantum number m ¼ 0 associated to optical transitions from 0s state to 0p state as the function of the electric ﬁeld F in the quantum conﬁnement (a) hx0 ¼ 100 and (b) hx0 ¼ 50 meV under four different hydrostatic pressure P = 0, 20, 50, 100 kbar and the temperature T = 300 K.

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4. Conclusion In this paper, impurity binding energy associated with the ground state and some low-lying states in a GaAs spherical parabolic quantum dot with taking into account hydrostatic pressure and electric ﬁeld are theoretically studied by using the conﬁguration–integration methods (CI). The binding energies of these low-lying states of the impurity depend sensitively on the hydrostatic pressure, electric ﬁeld and the parabolic conﬁnement strength. Based on the analysis of these impurity states, we propose a way for the preparation of the QD qubit by using the strong quantum conﬁnement to the impurity for the quantum dot. Also we calculate the wave functions of some low-lying states to discuss the oscillator strength which is related to the electronic dipole-allowed transitions from 0s state to 0p state. The results show that the electronic dipole-allowed transitions mostly happen between the 0s state and 0p state, especially for the quantum conﬁnement large enough. Acknowledgments This work was supported by Guangxi Natural Science Foundation in China under Grant No. 0991109 and Guangxi Department of Education Research Projects in China under Grant No. 200911LX37. References [1] [2] [3] [4] [5] [6] [7]

[8] [9] [10] [11] [12] [13] [14] [15]

[16] [17]

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