AlGaAs nanowires

Superlattices and Microstructures 48 (2010) 114–125

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Laser-induced reshaping of the density of impurity states in GaAs/AlGaAs nanowires A. Radu ∗ Department of Physics, ‘‘Politehnica’’ University of Bucharest, RO-77206 Bucharest, Romania

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Article history: Received 9 March 2010 Received in revised form 30 March 2010 Accepted 5 April 2010 Available online 22 April 2010 Keywords: Quantum well wire Shallow donors Density of impurity states Laser radiation

abstract The binding energy of shallow-donor impurities in a cylindrical quantum well wire irradiated by an intense non-resonant laser field is calculated within the effective mass approximation by using a variational procedure. Accurate laser-dressing effects are considered for both the confinement potential of the wire and the Coulomb potential of the impurity. The computation of the ground state subband energy eigenfunctions for different laser field intensities is based on a bidimensional finite element method. Important changes of the electron probability density under intense laser field conditions are predicted. The study reveals that the laser field compete with the quantum confinement and breaks down the degeneracy of states for donors symmetrically positioned within the nanostructure. A proper analysis of the density of impurity states is found to be essential for controlling the optical emission related to shallow donors in semiconductor quantum wires. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction The permanent advances in nanostructure fabrication techniques and their applications justify the interest for the physics involved. The quantum theory plays a key role in the understanding of low-dimensional semiconductor structures: quantum wells (QWs), quantum well wires (QWWs) and quantum dots (QDs). The concept and design of new high-tech opto-electronic devices (OEDs) demand complex theoretical models which could describe and predict with accuracy the optical and transport properties of quantum structures. These properties rely on the energy levels of carriers in the semiconductor nanostructures and can be controlled by several factors: dimensionality, confinement,

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impurity doping and external fields. Reduction in dimensionality makes the carriers to be more localized, which enhance their energy levels. The confinement potential profile is defined by the chemical composition of the semiconductor heterostructures and has an important effect on their opto-electronic properties. In extrinsic semiconductors, the impurification with donors/acceptors increases the localization of the carriers by Coulombian interaction. Another interesting option for adjusting opto-electronics properties in low-dimensional systems is the application of external electromagnetic fields. The factors above are generally interdependent and, for designing efficient quantum devices, they must be understood together. The electron states of hydrogen-like impurities in low-dimensional semiconductor heterostructures placed in external electric and/or magnetic fields have attracted much interest due to the potential technological applications in the OEDs design. In quantum structures the binding energy, as well as other properties of the impurity states, depends on the shape and size of the confining potential, and also on the impurity center position. One may expect these characteristics to be more pronounced as the electronic confinement is increased while reducing the nanostructure dimensionality. The binding energy of a hydrogenic donor in a cylindrical QWW in the presence of a longitudinal magnetic field has been calculated using infinite [1,2] and finite [3] confining potential models. The influence of the electric field and potential shape on the impurity energy in rectangular and cylindrical QWWs has been presented in earlier studies [4–6]. The effect of the magnetic field on the ground and 2p− , 3p− -like impurity states in wires with different radius has also been investigated by Montes et al. [7]. In Ref. [8], the binding energy and the self-polarization have been calculated as functions of the electric and magnetic fields and the impurity position in a QWW of rectangular cross-section. Aktas et al. have calculated the ground state binding energy of a hydrogenic donor in a coaxial cylindrical quantum well wire (CQWW) subjected to an external electric field [9] and a uniform magnetic field parallel with the wire axis [10]. In Ref. [11] both the effects of the electric and of the magnetic field on the donor binding energy in a CQWW have been investigated for different impurity positions and barrier thicknesses. The dependence on electric field strength and magnetic field induction of the binding energy and the photoionization cross-section of a hydrogen-like donor impurity in a QWW has been obtained in Refs. [12,13]. It was shown that the electrostatic and magnetostatic fields modify the quantum states of carriers confined in semiconductor nanostructures. Such studies have been extended to dynamic fields, created by high-intensity THz lasers, as free electron lasers (FELs). The interaction of intense laser fields (ILFs) with carriers in semiconductor structures has been studied for various materials and nanostructure dimensionalities. Changes of transport and optical properties of low-dimensional systems in the presence of ILF have been intensively investigated. Studies have been reported on resonant absorption [14], THz assisted resonant tunneling [15], change of electronic states in nanowire superlattices [16], optical bistability with tunneling-induced interference [17]. The effects of a high-frequency ILF on the confinement potential of quantum nanostructures are significant for designing new tunable QW and QD lasers, opto-electronic modulators and ultra-fast infrared detectors. Some recent works focused on the laser-induced potential profile reshape in particular nanostructure configurations: square quantum wells (SQWs), parabolic quantum wells (PQWs) and V-shaped quantum wells (VQWs) [18]. There were also several attempts of describing the effects of a non-resonant THz ILF on the confinement potential of QWWs. The binding energy of an axial donor in a cylindrical QWW placed in intense, high-frequency laser fields has been investigated [19] by making use of a theory which ‘‘dresses’’ both the infinite confinement potential in the wire and the Coulombian potential of the impurity. The laser field dependencies of the binding energy and of the donor-related photoionization cross-section in graded quantum well wires (GQWWs) under an external static field have been calculated by a variational method, using the effective mass approximation [20]. Alternatively, the laser–heterostructure interaction can be treated within an extended dressed atom approach [21,22], so that the effect of this interaction corresponds to a renormalization of the semiconductor energy gap and of the conduction/valence effective mass. A study of THz laser-induced 1D → 0D transitions in the density of states for electrons in a cylindrical semiconductor QWW has been recently reported within a non-perturbative scheme based upon a Green’s function approach [23]. Note also Refs. [24,25] in which the ILF effect on the donor binding energy in a cylindrical QWW with and without electric field has been studied.

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Fig. 1. Schematic view of a cylindrical GaAs/Alx Ga1−x As QWW axially irradiated by an ILF.

There are only few studies [26] on the electronic states of an off-axis donor in QWWs under ILFs. Moreover, although the effects of the laser dressing on the QWW potential play an important role, in the previous works they have been neglected or treated within the approximation suggested by Ehlotzky [27]. In this paper, the effects of the ILF on the donor binding energy in a cylindrical QWW for different impurity positions and intensities of the laser beam are investigated. We take into account the precise laser-dressing effect on the finite confinement potential by numerical temporal averaging, a method that we have already used for various QW profiles [18]. The numerical calculations of the ground state subband energy levels for different laser field parameters are performed by a bidimensional finite element method (FEM). The problem of an off-axis impurity leads to a series of effects that do not exist in nanostructures with an impurity located on the axis. Thus, even in the absence of an ILF, in a strong confinement regime, a large spread of the ground state energy values is observed as the impurity position varies [4,28,29]. Therefore a proper consideration of the density of impurity states may be of relevance in the interpretation of experimental data on optical phenomena related to these structures. To the best of our knowledge, this is the first study of the density of impurity states in cylindrical QWWs under ILF, which consider accurate laser-dressing effects on both confinement and Coulomb potentials. 2. Theory 2.1. Model for donors in a QWW under THz ILF A QWW must be imagined as a potential well that confines carriers (electrons or holes) which were originally free to move in three dimensions, to a single dimension, forcing them to occupy a quasi-onedimensional volume of space and affecting their transport properties and the related opto-electronic processes. The effect of the quantum confinement in the transverse direction of the wire becomes visible when the QWW transverse dimensions become comparable to the de Broglie wavelength of the carrier. This effect consists in a quantization of the carrier’s transverse energy at discrete energy levels called ‘‘energy subbands’’. For given materials, the importance of this quantization depends on the transverse dimensions of the QWW which generally should be a nanoscale structure. There are several ways of constructing nanowires and one of them uses a couple of semiconductor materials with nearly the same lattice constant. Fig. 1 shows a circular cross-section QWW formed by having a quasi-infinite thin cylindrical volume of semiconductor material A (GaAs) with a radius R embedded within a bulk material B with a wider bandgap (Alx Ga1−x As). The confinement potential has a jump

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117

Fig. 2. Bidimensional profile of the confinement potential superposed on the transverse cross-section of the cylindrical QWW.

discontinuity at the interface between the (A) and (B) regions, corresponding to a net delimitation of the two semiconductor materials. A non-intentional doping with shallow hydrogenic donor impurities of the (A) region is considered. The z axis is chosen to be in the direction of the wire (i.e. perpendicular to the transverse plane of confinement, (x, y)). The quasi-monochromatic laser beam is considered to be parallel to the wire and linearly polarized along the radial direction of the wire. The method used in the following calculation is based upon a non-perturbative theoretical model that has been developed to describe and predict the atomic behavior in THz ILFs [30,31]. Its starting point is the space-translated version of the semi-classical Schrödinger equation for a particle moving under the combined action of a confinement potential and a radiation field. The quasimonochromatic laser beam (ω ∼ THz) is non-resonant with the semiconductor atomic structure and linearly polarized along the x axis. The time-dependent one-electron Schrödinger equation reads



(p + eA(t )) 2m∗

 ∂ Ψ (r, t ) + V (r) Ψ (r, t ) = ih¯ , ∂t

(1)

where A(t ) = A0 sin (ωt ) xˆ , e, and m∗ are the vector potential, the elementary charge, and the electron effective mass, respectively. xˆ is the unit vector along the polarization direction of the radiation. The potential energy for a hydrogenic donor impurity in the QWW is given by V (r) = V˜ (ρ) + V C (ρ, z ) ,

(2)

where ρ is the transverse component of the position vector r of the electron. V˜ is the confinement potential: V˜ (ρ) =



0, V0 ,

ρ ∈ [0, R) ρ ∈ [R, ∞) ,

(3)


1/2

where V0 is the conduction-band offset and ρ = |ρ| = x2 + y2 electron in the wire. V C is the Coulomb term of the potential energy: V C (ρ, z ) = −

e2 4π ε

q

ρ − ρi

is the radial position of the

(4)


2

+ z2

where ε is the semiconductor permittivity and ρi is the radial position vector of the donor in the QWW. The origin of the z axis has been chosen in the transverse plane containing the donor impurity. Fig. 2 presents the confinement potential of the cylindrical QWW as a function of the transverse coordinates (x, y) and also illustrates the axial sections, parallel with x and y axis, of the surface V = V˜ (x, y).

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By applying the time-dependent translation r → r + Kramers [30] into the form



eA0 m∗ ω

sin (ωt ) xˆ , Eq. (1) was transformed by

 ∂ Φ (r, t ) + V r Φ (r, t ) = ih¯ , ( ) ∗ 2m ∂t p2

(5)

where V (r) = V˜ (ρ) + V C (ρ, z ) = V r + α0 sin (ωt ) xˆ is called the ‘‘laser-dressed potential’’.




α0 =

denotes the laser parameter. At a given laser frequency ω, α0 can be modified by adjusting the radiation intensity which affects the amplitude of the vector potential, A0 . In the high-frequency regime (ωτ  1, where τ is the characteristic transit time of the electron in the well region), solutions of Eq. (5) can be obtained by noting that V (r) is an implicit periodic time function for any r location and oscillates very rapidly in time. Therefore, one may consider that the electron is in fact subjected to the time-averaged potential [18] eA0 m∗ ω

ω V a (r) = V˜ a (ρ) + V Ca (ρ, z ) = 2π

2π/ω

Z

V r + α0 sin (ωt ) xˆ dt .




(6)

0

2.2. Laser-dressed subband energies Within the context of an effective mass approximation, the laser-dressed subband levels are obtained from the time-independent Schrödinger equation,

 −

h¯ 2



2m∗

∂2 ∂2 + 2 2 ∂x ∂y



 + V˜ a (x, y) Φn (x, y) = En Φn (x, y),

(7)

where V˜ a (x, y) is the time-averaged laser-dressed confinement potential (LDCP) [18]: V˜ a (x, y) =

ω 2π

2π/ω

Z

V˜ (x + α0 sin (ωt )) xˆ + yyˆ dt ,




(8)

0

with yˆ denoting the unit vector along the y axis. Eq. (7) can be numerically solved by using a bidimensional FEM [32,33]. The normalized eigenfunctions Φn (x, y) (with n ≥ 1) and the corresponding eigenvalues En are found by transferring the equation in a discrete bidimensional spatial domain and solving the resulting generalized eigenvalue algebraic problem by the Arnoldi algorithm [34]. Fig. 3 qualitatively exemplifies the result of this computing method in the absence of the laser field, by superposing the electron localization probability density (LPD) kΦ1 (x, y)k2 related to the lowest subband energy level E1 on the bidimensional profile of the confinement potential V˜ (x, y). In addition, axial sections of the surface kΦ k2 = kΦ1 (x, y)k2 parallel with x and y axis are illustrated. 2.3. Binding energy calculation The energy of an electron bound to a donor impurity inside a QWW interacting with a laser field may be described by the Hamiltonian H = H0 + H1 ,

(9)

where H0 = −

h¯ 2 2m∗



∂2 ∂2 + 2 2 ∂x ∂y



+ V˜ a (x, y)

(10)

is the dressed subband Hamiltonian term and H1 = −

h¯ 2 2m∗

∂2 + V Ca (ρ, z ) . ∂ z2

(11)

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119

Fig. 3. First subband electronic probability density superposed on the bidimensional profile of the confinement potential.

For the time-averaged laser-dressed Coulomb (or impurity) potential (LDIP) we use the Ehlotzky [27] approximation V Ca

(ρ, z ) = −

e2 8π ε

"

1

1

#

+ , ρ + z zˆ − ρi + α0 xˆ ρ + z zˆ − ρi − α0 xˆ

(12)

where zˆ is the unit vector along the z axis. This approximation gives accurate results when compared to an exact numerical time averaging of the formula (4). In order to find the eigenstates of H, a variational procedure is applied. For the ground state of the impurity, the trial wave function is chosen as


Ψ1 (r, λ) = N Φ1 (x.y) exp −z 2 /λ2 ,

(13)

in which N denotes the renormalization constant and λ is the variational parameter. Previous works [20,35,36] making use of variational calculations for hydrogenic impurity binding energies in quantum structures suggest that this simple Gaussian-type function gives accurate results. The impurity binding energy Eb is given by Eb = E1 − min hΨ1 |H | Ψ1 i .

(14)

λ

Eb depends on the confinement potential V˜ (ρ), the impurity radial position vector ρi , and the laser parameter α0 . 2.4. Density of impurity states Assuming that the cylindrical QWW is not too thin, one may treat the impurity transverse coordinates xi and yi as continuous variables and, provided that the doping is homogeneous, may define a density of impurity states (DIS) per unit energy as [22]: g (Eb ) =

4

π

R2

Z

1

S

Lk (Eb )

|∇i (Eb )|

dl,

(15)

k

where ∇i means the gradient with respect to the impurity position and k Lk (Eb ) denotes the assembly of all fragments of the curve E = Eb lying within the irreducible (by symmetry operations) part of the circular cross-section of the QWW.

S

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A. Radu / Superlattices and Microstructures 48 (2010) 114–125

a

b

Fig. 4. (a) Juxtaposed pictures of the electron LPD function kΦ1 (x, y)k2 corresponding to the lowest subband energy level E1 and the confinement potential of the QWW in the absence of the laser field; (b) Related donor binding energy as a function of the impurity position (xi , yi ) within the transverse cross-section of the QWW.

The ‘‘center of gravity’’ of the impurity band is defined as [22,23] E¯ i (α0 ) =

Z

Ebmax Ebmin

Eb ρi , α0 g (Eb ) dEb .




(16)

The knowledge of the DIS profile as well as the impurity-band center of gravity may be relevant in the qualitative and quantitative understanding of the experimental data on shallow impurities in quantum heterostructures. 3. Numerical results and discussion In this work numerical calculations were performed for a GaAs/Alx Ga1−x As cylindrical QWW with x = 0.3 and R = 50 Å. A uniform effective mass m∗ = 0.0665 m0 of the electron throughout the nanostructure was assumed (m0 denotes the free electron mass). The conduction-band offset V0 = 228 meV was introduced by considering Miller’s rule (V0 = 60% 1Egap ≈ 0.7x + 0.2x2 in eV units). It was presumed that the dielectric permittivity ε is the same in both semiconductor materials, the static value εs = 12.6ε0 for α0 = 0, and εω = 10.9ε0 in the THz ILF (ε0 symbolizes the vacuum permittivity). Figs. 4–7(a) set together the computed time-averaged LDCP of the cylindrical QWW and the electronic LPD function kΦ1 (x, y)k2 corresponding to the first subband energy level E1 , for gradually increasing values of the laser parameter: α0 = 0 (Fig. 4); α0 = 30 Å (Fig. 5); α0 = 60 Å (Fig. 6); α0 = 90 Å (Fig. 7). The related binding isoenergy charts for shallow-donor impurities are presented in Figs. 4–7(b). These pictures are bidimensional visualizations of the binding energy as a function of the impurity position (xi , yi ) within the transverse cross-section of the QWW. Fig. 4(a) illustrates the localization symmetry of the electron in the nanostructure in the absence of external fields (α0 = 0). The degeneracy of the states for donors symmetrically positioned within the transverse cross-section of the QWW is evident from the Fig. 4(b). This picture reveals concentrically disposed circular binding isoenergy lines in the (xi , yi ) plane, as one should expect. On-axis position of the subband LPD maximum (Fig. 4(a)) is coincident for an on-axis impurity with the singularity of the undressed Coulomb potential given by Eq. (4) for z = 0 (denoted by S in Fig. 4(b)). As an outcome, the binding energy has an on-axis extreme value (26 meV approximately) and monotonically decreases with the rising of the impurity radial position. The near-(A/B) interface value of Eb is lower than its

A. Radu / Superlattices and Microstructures 48 (2010) 114–125

a

121

b

Fig. 5. Same as in Fig. 4 for α0 = 30 Å.

a

b

Fig. 6. Same as in Fig. 4 for α0 = 60 Å.

on-axis value with more than 10 meV. The obtained values of the donor binding energy in the absence of external fields are in good qualitative agreement with those reported in the literature for similar quantum structures [37–40]. Fig. 5(a) shows the localization of the electron in the cylindrical QWW for α0 = 30 Å. One may observe that for this relatively small value of the laser parameter (α0 < R) there is a slight increase of the on-axis maximum of the LPD kΦ1 (x, y)k2 when compared to the α0 = 0 case. The explanation lay in the behavior of the time-averaged LDCP, which is apparent from the same figure. Although the average LDCP bidimensional profile seems to expand on the laser polarization direction, the mean x axis width of the QWW within the y = 0 plane, which could be defined as

2 V0

R V0 0

−1

V˜ a (x+ , 0)dV ,

remains constant (equal with 2R) while α0 < 50 Å. On the other hand, as it is easily observable from

122

a

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b

Fig. 7. Same as in Fig. 4 for α0 = 90 Å.

the graphical profile of the function V˜ a (0, y), the mean y axis width within the x = 0 plane has a

RV

−1

diminished value with respect to the α0 = 0 case: V2 0 0 V˜ a (0, y+ )dV < 2R. These observations 0 suggest a laser-caused enhancement of the quantum confinement in the y direction, which increases the LPD extreme value described above. Fig. 5(b) reveals the laser-induced break down of the degeneracy of the states for donors equally distanced from the wire axis. The binding isoenergy contour lines in the transverse plane of the QWW expand more in the x direction, with an eccentricity which depends on the laser parameter. This behavior is due to the laser-dressing effect (Eq. (12)) on the Coulomb term V C of the potential energy. The binding energies are smaller than in the previous case (α0 = 0) primarily as a result of the spatial separation between the near-axial region with large values of the subband LPD (Fig. 5(a)) and the regions surrounding the singularity points of the time-averaged LDIP V Ca (ρ, 0). As an example, for an on-axis impurity, there are two singularity points: S− (−α0 , 0) and S+ (α0 , 0) (Fig. 5(b)). Further enhancement in α0 (Fig. 6(a)) leads to an additional transition on the x direction from a single to a double QWW confinement potential profile (for α0 > R). A symmetrical hill-like barrier appears in the vicinity of the x = 0 axis and inflates when the laser parameter increases (Fig. 7(a)). A similar behavior was predicted for a rectangular QW when α0 > L/2, where L is the well width [41]. The wave function of the electron begins to spread out in the polarization direction of the laser. The binding isoenergy contour lines change from a single-pole configuration (Figs. 4(b) and 5(b)) to a double-pole arrangement (Fig. 6(b)), with even smaller binding energy values. The presence of two symmetrical maxima in the binding energy diagram originates in an increase of the electron cloud near the laser-separated singularity positions of the time-averaged LDIP, since the laser field also disperses the electronic LPD function along the x axis. In very intense laser fields (α0 = 90 Å) the ground state LPD changes from a single radial symmetrical cloud (Figs. 4–6(a)) to a two-peaked function (Fig. 7(a)). This is due to the fact that, for large laser parameter values, the ‘‘leakage’’ of the electron wave function into the symmetrical ‘‘valleys’’ of the time-averaged LDCP becomes more important. In addition, the time-averaged LDIP given by Eq. (12) decreases with the increase of α0 and, as a consequence, the impurity binding energies significantly decrease (Fig. 7(b)). On the other hand, for large values of the laser intensity, the electron cloud is displaced along the polarization direction, from the wire axis towards the region (B) of the quantum structure. As a result, the binding energy is higher for impurities placed along the x axis. In Fig. 8 the ground state binding energy of donor impurities is presented as a function of the laser parameter for three impurity positions: xi = yi = 0 (on-axis impurity); xi = R; yi = 0 (on-interface

A. Radu / Superlattices and Microstructures 48 (2010) 114–125

123

Fig. 8. Binding energies for donor impurities in a R = 50 Å cylindrical QWW versus the laser field parameter, for three impurity positions. The dashed line represents the impurity-band center of gravity as defined in the theory section by Eq. (16).

impurity along the x axis); xi = 0; yi = R (on-interface impurity along the y axis). The presence of the ILF – which noticeably changes the confinement potential shape – breaks down the degeneracy of the impurity states. The distinct behavior of impurities positioned along or perpendicular to the polarization direction of the radiation may be understood by taking into account the laser field effect on the electronic cloud. One may notice that for α0 = 0 the binding energy is degenerate for identical positions on the transverse axes. As expected, the largest binding energy corresponds to the impurity located on the axis. It is very apparent from this figure that EB strongly decreases as the donor moves toward the interface of the QWW. The energy spreading δ Eb (α0 ) = Ebmax (α0 ) − Ebmin (α0 ) becomes smaller for increasing values of α0 (Fig. 8), as the electron subband energy levels E1 (α0 ) reaches the large upper part of the timeaveraged LDCP (Figs. 4–7(a)). For on-interface donors one may also notice a weaker dependence of Eb on the laser parameter, compared to the case xi = yi = 0, due to the three-dimensional character of the electron wave function as the impurity approaches the boundaries of the QWW. The dashed line in Fig. 8 represents the center of gravity of the impurity band, which may be relevant for the comparison of the calculated results with any experimental data for shallow donors in cylindrical QWWs. The DIS for a hydrogenic donor in a GaAs/Al0.3 Ga0.7 As cylindrical QWW with R = 50 Å is plotted in Fig. 9 for the selected values of the laser parameter. These results were obtained by using a histogram method for a mesh of points uniformly distributed in the transverse cross-section of the QWW. The number of points to be used in the mesh was methodically increased by bidimensional interpolation until the fluctuations in the DIS were stabilized. It should be noticed that for α0 = 0 the profile of g (Eb ) has a maximum at a relatively small binding energy (15.5 meV) associated to impurities placed near the interface. The DIS slowly decreases with the raise of the binding energy within the large interval δ Eb (0). For α0 = 30 Å the energy spreading δ Eb is smaller than in the first case and the medium height of the DIS profile augments. g (Eb ) has a maximum for the smallest binding energy (16.5 meV) for which the related isoenergetic contour line is still entirely contained in the transverse cross-section of the QWW (Fig. 5(b)). The DIS has a pronounced peak at a relatively large binding energy for α0 = 60 Å. This behavior can be explained by the large region of the domain (xi , yi ) with a quasi-constant binding energy (14 meV approximately) and consequently quasi-null values of the gradient ∇i (Eb ) (Fig. 6(b)). This feature persists for even larger values of the laser intensity (α0 = 90 Å), for which the DIS peak magnitude increases and the energy spreading diminishes. One may conclude that the intensity of the peak related to the on-interface impurities decreases with the increase of the laser parameter and disappears in strong laser fields (α0 > 60 Å), while g (Eb ) presents a maximum at a higher binding energy associated to

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A. Radu / Superlattices and Microstructures 48 (2010) 114–125

Fig. 9. Density of impurity states as a function of the donor binding energy for a R = 50 Å cylindrical QWW, for several values of the laser parameter.

impurities placed near the axis of the structure. As a consequence, an ILF should lead to an impurityrelated absorption spectrum that presents one main peak associated with on-axis impurities and, as the laser parameter increases, this spectrum must be red shifted. An analogous behavior was reported for QWs in the presence of the ILF [42]. Therefore, the optical properties associated with impurities in QWWs irradiated by ILFs should present some qualitative similarities with the corresponding properties in QWs. Nevertheless, the shape of the DIS and its laser-induced profile changes in QWWs are quite different from the results for QWs with similar sizes and consequently qualitative and quantitative differences in photoluminescence experiments should be assessable. 4. Conclusions In this paper we have studied the effects of the non-resonant THz ILF on the impurity binding energy and the DIS in a GaAs/Alx Ga1−x As cylindrical QWW. For the first time in literature, we take into account the precise high-frequency laser-dressing effect on both cylindrical QWW finite confinement potential and Coulomb potential. Within the effective mass approximation, the calculations were performed using a FEM and a variational procedure. We found that the laser field leads to a considerable decrease of the on-axis donor binding energy. The effect becomes less pronounced as the impurity ion approaches the interface of the structure. Our results prove that the experimental values of the binding energy of impurities in QWWs irradiated by an ILF could not be compared with the on-axis impurity values. Therefore the calculation of the center of gravity of the impurity band as well as the shape of the DIS may be important in the quantitative understanding of experimental data related to shallow impurities in QWWs under ILF. The laser field radiation strength, frequency, and polarization direction can all considerably modify the laser-dressing effects. Thus, by changing these parameters, one can obtain the tunability in the optical emission of the doped cylindrical QWWs. Such effects can be used for designing new laser-controlled OEDs. References [1] [2] [3] [4] [5] [6]

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