Abstract
In this work, we study the exciton states in a zincblende InGaN/GaN quantum well using a variational technique. The system is considered under the action of intense laser fields with the incorporation of a direct current electric field as an additional external probe. The effects of these external influences as well as of the changes in the geometry of the heterostructure on the exciton binding energy are discussed in detail.
Keywords:
Nitrides; Excitons; Intense laser field; Quantum wellsBackground
InGaNbased systems have revealed a high prospect for applications in optoelectronics. Although the hexagonal (wurtzite) allotropic form is the one most commonly considered, the zincblende (ZB) IIIV nitrides are also very promising materials that have been obtained with highquality crystal structure [14]. This is mostly due to the fact that the cubic symmetry avoids the presence of rather high spontaneous polarizations in the crystal, which are, in a greater extent, responsible for the presence of large builtin fields in wurtzitebased heterostructures, responsible for important reductions in the oscillator strength, and the optical recombination rates in that kind of systems [5,6]. However, the ZB structure in nitrides is provided with higher carrier mobilities, larger optical gain and lower threshold current density because of its smaller effective mass, and has mirror facets compatible with substrates such as GaAs [79]. In consequence, the ZB nitridebased heterostructures have drawn much attention in recent times [1013].
The knowledge of exciton states is important for the correct understanding of some optical properties in the semiconducting lowdimensional systems. Investigations on excitons and related optical properties in ZB nitride lowdimensional systems have been mostly performed in quantum dots [1418], but much less in quantum well (QW) heterostructures [19,20].
Research activities on the interaction of intense laser fields (ILF) with carriers in semiconductor nanostructures have revealed interesting physical phenomena. For instance, the presence of changes in the electron density of states in QWs and quantum well wires (QWWs) [21,22], the measurement of zeroresistance states in twodimensional electron gases under microwave radiation [23], terahertz resonant absorption in QWs [24], and FloquetBloch states in singlewalled carbon nanotubes [25], among others. A number of investigations on the effect of laser fields on low dimensional heterostructures have been published. The dressed atom approach was extended by Brandi et al. [26,27] to treat the influence of the laser field upon a semiconductor system. In the model, the interaction with the laser is taken into account through the renormalization of the semiconductor effective mass. The appearance of an unexpected transition from single to double QW potential induced by ILF was revealed in a theoretical study from Lima et al. [28]. Within the laserdressed potential model, it is found that the formation of a doublewell potential for values of the laser frequencies and intensities such that the socalled laserdressing parameter α_{0} is larger than L/2, where L is the QW width. This fact is associated with the possibility of generating resonant states into the system’s channel as well as of controlling the population inversion in QW lasers operating in the optical pumping scheme.
The present work is concerned with the theoretical study of the effects of ILF on exciton states in single ZB nitride QWs of the InGaNGaN prototype. The research is extended to include the additional influence of an applied direct (dc) electric field oriented along the growth direction of the system. The paper is organized as follows. In the ‘Theoretical framework’ subsection in the ‘Methods’ section, we describe the theoretical framework. The ‘Results and discussion’ section is dedicated to the results and discussion, and finally, our conclusions are given in the ‘Conclusions’ section.
Methods
Theoretical framework
Here, we are concerned with the effects of ILF on the binding energy of a heavyhole exciton in a single In_{x}Ga_{1−x}NGaN QW grown along the zaxis and in the presence of applied electric field. The envelopefunction and parabolicband approximations are assumed. The choice for the electric field orientation is . The Hamiltonian for the confined exciton is then given as follows:
where ( ) is the electron (hole) coordinate, ( ) is the spherically symmetric electron (hole) effective mass, εis the static dielectric constant, e is the absolute value of the electron charge, and V_{i} (z_{i}) (i = e,h) are the QW confining potential for the electron and hole. The functional form of the potential in the absence of the ILF is given as follows:
The electron and hole effective masses and the static dielectric constant have been considered to have the same value (the one in In_{x} Ga_{1−x}N) throughout the In_{x} Ga_{1−x}NGaN QW.
In order to find the eigenfunctions of the exciton Hamiltonian (Equation 1), it must be noticed that the total inplane exciton momentum is an exact integral of motion, and the exciton envelope wave function may be written as follows:
where S is the transverse area of the In_{x} Ga_{1−x}NGaN QW, , are the inplane center of mass and relative exciton coordinates, and is the eigenvalue of the operator . If (ground state), then is the eigenfunction of the Hamiltonian:
and
The method for the obtention of the electron and hole states is based on the work by Xia and Fan [29].
In order to consider the ILF effects (the polarization of the laser radiation is parallel to the zdirection), the socalled Floquet method is adopted [30,31]. According to this formalism, the second term at the right hand side in Equations 5 and 6 must be replaced by laserdressed potential 〈V〉( z_{i}α_{0i}), where for _{α0i} is the laserdressed parameter (from now on the ILFparameter) defined as follows [32]:
In Equation 7, I and ωare, respectively, the average intensity and the frequency of the laser, c is the velocity of the light, and _{A0} is the amplitude of the vector potential associated with the incident radiation. A detailed discussion on the derivation of 〈V〉( z_{i}α_{0i}) is provided in other studies [28,3337].
Under the laser effects, the last term of Equation 4—the onecenter electronhole Coulomb interaction—must be replaced by a twocenter Coulomb interaction as follows:
where z_{eh} = z_{e}− z_{h}and α_{0} = (eA_{0})/(μcω).
The procedure adopted for the variational evaluation of the exciton wave function in the In_{x} Ga_{1−x}NGaN QW under the ILF effects is the one proposed by Fox et al. [38] and Galbraith and Duggan [39]. The functional
must be minimized with the use of the variational wave function:
where λ is the variational parameter. Besides, and with .
The exciton binding energy is obtained from the following definition:
where E_{0} is the eigenvalue of the Hamiltonian in Equation 4 without the Coulomb interaction term—the last one at the right hand side—and λ_{min} is the value of the variational parameter in which the energy in Equation 11 reaches its minimum.
Results and discussion
Zincblende IIIV nitride heterostructures are strained ones, given the lattice mismatch between the constituent materials. Although we are considering here a (001)oriented In_{0.2} Ga_{0.8}NGaN QW configuration, the small indium content does not prevent from taking strain effects into account. In particular, there is a breaking of the degeneracy of heavy and light hole valence bands at the center of the twodimensional Brillouin zone. In this work, we are including strain effects in the most simple way, that is, by incorporating the straininduced shifts of the conduction and valence band edges in the unperturbed potential profile configuration for both electrons and holes (see, for instance, [40,41]). Data related with material properties and confining potential are taken from another work [42].
Considering the strain effects between the well and barrier materials, the electron and hole confinement potential have been obtained, respectively, by the following:
and , where Q = 0.7, , , and _{e11} = ( a^{w}− a^{b})/ a^{w}. The superindex w and b refer to the well (In_{x} Ga_{1−x}N) and barrier (GaN) materials.
In Table 1, the main used parameters are reported. Here, m_{0} is the free electron mass. The parameters of the In_{x} Ga_{1−x}N material have been obtained by linear interpolation between InN and GaN.
The potential responsible for the confinement of electrons and heavy holes in the QW is depicted in Figure 1 for several values of the ILF parameter (Figure 1a,b,c,d). The column at the lefthand side contains the graphics that correspond to the conduction band profile, while the corresponding valence band bendings are shown in the column at the right. It is possible to observe the evolution of the QW shape associated with the change in the laser intensity—without applied dc field—by going through rows one to four in the picture. The transition from a single to a double QW potential is detected in the figures of the fourth road. We consider, of interest, to highlight that the confining potential for holes in a In_{0.2} Ga_{0.8}NGaN QW also experiences that kind of singletodouble QW transition at the value of α_{0}reported in the current work. This is because such a feature is not present in the case, for instance, of a Ga_{0.7} Al_{0.3}AsGaAs QW, in which, for the same value of the ILF parameter, the shape of the conduction band profile is very similar with that of Figure 1b [43]. Despite the greater value of the hole effective mass in the present system compared with that of the arsenidebased one, the main reason of such a difference lies in the height of the valence band confining barrier, which in the latter case is almost three times larger than the one formed in the nitridebased heterostructure studied here.
Figure 1. Confinement potential andzdependent amplitude of probability for the first two electron and ground hole confined states in aIn_{0.2}Ga_{0.8}NGaN QW. The results are for L=200 Å and have been considered several values of the ILFparameter: α_{0} = 0(a), α_{0} = 50 Å (b), α_{0} = 100 Å (c), α_{0} = 150 Å (d). For the sake of illustration, the scale for the wave function amplitudes has been set to the same value. Graphics in row (e) correspond to the variation of the energies of the first two electron states (left panel) and the heavy hole ground state (right panel) as functions of the intense laser field parameter. In all cases, it is taken that F = 0 and P = 0.
In the fifth row (Figure 1e), the evolution of the confined electron and hole levels as functions of α_{0} clearly show the growth in the energy values that resulted from the laserinduced deformation of the conduction and valence band potential profiles. Such modification in the QW shape involves a significant rise of the well bottom which acts by pushing up the energy levels. In the valence band, the original depth of the QW is only enough to accommodate a single heavyhole level and, according to the basic properties of the confined onedimensional motion, there will always be one energy level in the hole subsystem. In the conduction band, for sufficiently large laser field intensities, the first excited state is expelled from the QW, and there only remains a single confined level (the ground state one).
Figure 2 contains our results for the heavyhole exciton binding energy as a function of the QW width, without the application of any dc electric field and taking several values of the α_{0} as a parameter. The shape of the curves is typical in the case of a zincblende QW. Independent of the laser intensity, there is initially a growth in E_{b}associated to the transition from a purely twodimensional exciton to a quasitwodimensional one, that is, for the lower values of the well width, it favored the overlap between the confined electron and hole densities of probability, making that the expected values of the intercarrier distance, 〈ϕ z_{e}− z_{h}ϕ〉 to be smaller, thus provoking the strengthening of the Coulombic interaction between them. As long as the QW widens, this expected value becomes larger, and the electrostatic interaction weakens, with the consequent reduction in the exciton binding energies. The decrease in E_{b}for a fixed well width, L, observed when going from a zero laser field to a more intense one is also due to a decrease in the Coulombic correlation between both types of carriers. In fact, as can be seen from Figure 1, augmenting the laser intensity makes the allowed confined energy states to shift upwards. Therefore, the corresponding wave functions will spread over a wider interval of the coordinate, and the values of 〈ϕ z_{e}− z_{h}ϕ〉 will be larger. The kind of convergence exhibited by the curves for larger L reflects the increasing effect of the rigid barriers located at ± L_{∞}/2 (withL_{∞} = 600Å). This means that in all cases, the curves are tending toward the the exciton binding energy of an infinite barrier QW of width Ł_{∞}, with or without a laser effect.
Figure 2. Binding energy of heavyhole exciton in a In_{0.2}Ga_{0.8}NGaN QW. As a function of the wellwidth, for several values of the ILFparameter with F = 0 and P = 0.
If an intense laser field is applied taking the QW geometry as a varying parameter, the results obtained for the heavyhole exciton binding energy as a function of α_{0} are those shown in the Figure 3. They are consistent with the explanation given above regarding the weakening in the strength of the electronhole interaction associated with the loss of confinement induced either by the increment in the laser intensity or by the enlargement of the QW size.
Figure 3. Binding energy of heavyhole exciton in a In_{0.2}Ga_{0.8}NGaN QW. As a function of the ILFparameter, for several values of the quantum wellwidth with F = 0 and P = 0.
If a dc electric field of increasing intensity is applied to the system, keeping fixed its dimension, the heavyhole exciton binding energy evolves as observed in the Figure 4. Once again, the value of the laser field strength appears parameterizing the different curves in the graphics. In the case of zero laser field, the variation of _{Eb}(F)corresponds to an all the way decreasing function, the dc electric field amplitude. It is known that the dc field effect is mainly that of augmenting the polarization by pushing apart, spatially speaking, the carriers of opposite sign. At the same time, the rectangular QW potential profile transforms in a way that reduced the degree of carrier localization inside the well region. All this has the consequence of increasing the value of 〈ϕ z_{e}− z_{h}ϕ〉 and the corresponding fall in the Coulomb interaction. However, this particular evolution of the binding energy seem to practically disappear for the two intermediate values of the ILF parameter considered. One notices from Figure 4 that a very slight decrease in E_{b} is obtained when the value of F goes from zero to 20 kV/cm, if α_{0} is a quarter of the QW width. At the same time, what we see when α_{0} is equal to the half of the well width is, even, a slight increase in E_{b}over almost the entire interval of F considered, though for the largest values of the dc field amplitude, that quantity starts showing a decreasing behavior. Hence, what is happening here is a phenomenon of compensation of the progressive augmenting of the electronhole expected distance via the deformation of the QW potential profile obtained when combining the effects of the two kinds of externally applied fields, that is, if the effect of the dc field is to push the electronic wave function towards the lefthand side of the QW, given that the height of the barrier for electrons is significantly bigger than the one corresponding to the valence band, the displacement of the electron wave function is counteracted by the barrier repulsion (one must keep in mind that the dc field strength values considered here are not very high). On the other hand, the electric field will induce a displacement of the heavy hole towards the right. However, the QW barrier height is so small here that, thanks to the ILFinduced pushingup effect of the energy level position, the hole density of probability can penetrate further to the left, with the consequent increment in the overlap between electron and hole wave functions. As a result of this, the expected electronhole distance diminishes. This is the cause of the compensating effect and the apparent insensitivity of E_{b}with respect to F for such modified QW shapes associated to such particular values of α_{0}. Once the laser field intensity is sufficiently high (lower curve in Figure 4), the heavyhole exciton binding energy recovers its decreasing variation as a function of the dc field strength (again due to the fall in the carrier localization), with the exception of a very slight increment noticed for very small values of F. Here, the combination of the slow linear change of eFzwith the ILFinduced double QW shape of the confining potential (Figure 1d) leads to the kind of compensating effect mentioned above. In this case, it leads to a small reduction in 〈ϕ z_{e}− z_{h}ϕ〉 and the observed little increase in E_{b}in that region.
Figure 4. Binding energy of heavyhole exciton in a In_{0.2}Ga_{0.8}NGaN QW. As a function of the applied electric field with L = 200Å and several values of the ILFparameter.
Finally, Figure 5 shows the variation of the heavyhole exciton binding energy as a consequence of the increment in the intensity of the zoriented applied dc electric field. In this situation, the width of the QW appears and is considered as the parameter that differentiates between the curves depicted.
Figure 5. Binding energy of heavyhole exciton in a In_{0.2}Ga_{0.8}NGaN QW. As a function of the applied electric field for several values of the quantum wellwidth (L) with α_{0} = 3L/4.
The configuration chosen includes an applied laser field with intensity given, in each case, by the parameter α_{0} = 3L/4. It is seen that for the two lowest values of the well width, E_{b}is a slight decreasing function of F until a certain critical value, F_{c}, of the dc field strength at which initiates an abrupt fall that leads to a constant, limit value, that remains for the rest of the increasing range of the amplitude F. The decrease occurring while F < F_{c} is justified along the same arguments expressed above with regard to the progressive enlargement of the intercarrier average distance that associates with the loss in electron and hole confinement. The abrupt descent in E_{b}has to do with the escape of one (electron or hole) of the wave functions away from the QW region, towards the infinite barrier on the side it was pushed to by the electric field. The value of the expected electronhole distance then suffers a sudden rise which reflects in the drop of E_{b} observed. Augmenting further the dc field strength will function to cause the same effect on the other wave function in such a way that the increase in F will not have any other influence on the polarization because the carriers will remain confined by the infinite barriers at ± L_{∞}/2. Therefore, one may see that E_{b}adopts a constant value when F becomes large enough.
It is worth mentioning that, for all the values of L taken into account, setting α_{0} = 3L/4implies a great modification of the confining potential profile which, as one of the main features, presents a significantly reduced effective well depth. At the same time, the effect of confinement reduction on the carrier wave functions is more pronounced for narrower QWs, for the allowed energy levels are, initially, placed at higher energy positions. Thus, the application of the not so intense dc fields readily leads to the mentioned wave function escape. This explains why the phenomenon of abrupt change in E_{b} is manifested for smaller dc field intensities.
The curves that correspond to the two highest values of L in Figure 5 show an increasing behavior for the smallest electric field amplitudes. This fact relates with the reduction in 〈ϕ z_{e}− z_{h}ϕ〉 obtained as a result of the combination of the laser and dc fields on the confinement of the carriers. A small F associates with a slight linear deformation of the already modified (by the laser effect) potential profile. The electron and hole densities of probability are pushed in opposite directions, but the potential well barriers, not so deformed, repel them away. This has the consequence of bringing the two particles a little bit closer and, therefore, of augmenting the strength of their Coulombic interaction. However, when the dc field is augmented, the dominant influence is that causing the spatial spreading of the carrier wave functions, which leads to the decrease in E_{b}. Notice that the pronounced fall is also present when L = 150Å, but for L = 200Å E_{b} is a rather smooth monotonically decreasing function of F, without any abrupt change. This is because the QW width is large enough to avoid the sudden escape of the wave functions and also because the limiting infinite barriers are much closer to the inner well ones.
Conclusions
The properties of heavyhole excitons in InGaNGaNbased quantum wells under intense laser and applied dc electric fields are studied for a set of different values of the fields intensities and the well spatial dimensions. In general, for a fixed geometry of the unperturbed system, the exciton binding energy is a decreasing function of the intense laser field parameter and of the dc electric field, although certain combinations of the two applied field intensities may lead to a rather insensitive behavior of the binding energy with respect to the application of a dc field. It is shown that the changes of the degree of carrier confinement and of the carrier polarization associated to the influence of the laser and the dc fields are mainly responsible for the exciton properties mentioned. To our knowledge, there seem to be no previous reports on exciton properties in zincblende nitride QW induced by intense laser fields. Thus, the results of the present work might be considered as a first approximation to the subject in this kind of systems.
Competing interests
The authors declare that they have no competing interests.
Author’s contributions
CMD carried out the numerical work. MEMR carried out the discussion of results and writing. CAD carried out the numerical work. All authors read and approved the final manuscript.
Acknowledgements
Carlos A Duque is grateful to the Colombian Agencies CODIUniversidad de Antioquia (project: E01535Efectos de la presión hidrostática y de los campos eléctrico y magnético sobre las propiedades ópticas no lineales de puntos, hilos y anillos cuánticos de GaAs(Ga,Al)As y Si/SiO_{2}) and Facultad de Ciencias Exactas y NaturalesUniversidad de Antioquia (CADexclusive dedication project 20122013). Miguel E MoraRamos thanks Mexican CONACYT for the support through 20112012 sabbatical grant no. 180636 and research grant CB2008101777. He is also grateful to the Escuela de Ingeniería de Antioquia and the Universidad de Antioquia for hospitality in his sabbatical stay.
References

Mizuta M, Fujieda S, Matsumoto Y, Kawamara T: Low temperature growth of GaN and AlN on GaAs utilizing metalorganics and hydrazine.
Jpn J Appl Phys 1986, 25:L945. Publisher Full Text

Yoshida S: Growth of cubic IIInitride semiconductors for electronics and optoelectronics application.
Physica E 2000, 7:907. Publisher Full Text

Hsiao CL, Liu TW, Wu CT, Hsu HC, Hsu GM, Chen LC, Shiao WY, Yang CC, Gällström A, Holtz PO, Chen CC, Chen KH: Highphasepurity zincblende InN on rplane sapphire substrate with controlled nitridation pretreatment.
Appl Phys Lett 2008, 92:111914. Publisher Full Text

Novikov SV, Stanton NM, Campion RP, Morris RD, Green HL, Foxon CT, Kent AJ: Growth and characterization of freestanding zincblende (cubic) GaN layers and substrates.
Semicond Sci Technol 2008, 23:015018. Publisher Full Text

Andreev AD, O’Reilly EP: Theory of the electronic structure of GaN/AlN hexagonal quantum dots.
Phys Rev B 2000, 62:15851. Publisher Full Text

Schulz S, Schumacher S, Czycholl G: Tightbinding model for semiconductor quantum dots with a wurtzite crystal structure: from oneparticle properties to Coulomb correlations and optical spectra.

Park SH, Chuang SL: Comparison of zincblende and wurtzite GaN semiconductors with spontaneous polarization and piezoelectric field effects.
J Appl Phys 2000, 87:353. Publisher Full Text

Lagarde D, Balocchi A, Carre H, Renucci P, Amand T, Maries X, Founta S, Mariettem H: Roomtemperature optical orientation of the exciton spin in cubic GaN/AlN quantum dots.

Marquardt O, Mourad D, Schulz S, Hickel T, Czycholl G, Neugeauer J: Comparison of atomistic and continuum theoretical approaches to determine electronic properties of GaN/AlN quantum dots.

Lemos V, Silveira E, Leite JR, Tabata A, Trentin R, Scolfaro LMR, Frey T, As DJ, Schikora D, Lischka K: Evidence for phaseseparated quantum dots in cubic InGaN layers from resonant Raman scattering.
Phys Rev Lett 2000, 84:3666. PubMed Abstract  Publisher Full Text

Li SF, Schörmann J, Jas DA, Lischka K: Room temperature green light emission from nonpolar cubic InGaN/GaN multiquantumwells.
Appl Phys Lett 2007, 90:071903. Publisher Full Text

Husberg O, Khartchenko A, As DJ, Vogelsang H, Frey T, Schikora D, Lischka K, Noriega OC, Tabata A, Leite JR: Photoluminescence from quantum dots in cubic GaN/InGaN/GaN double heterostructures.
Appl Phys Lett 2001, 79:1243. Publisher Full Text

Zhu JL, Yang N, Li BL: Exciton spectra and polarization fields modified by quantumdot confinements.

Xia CX, Wei SY: Quantum size effect on excitons in zincblende GaN/AlN quantum dot.

Schulz S, Mourad D, Czycholl G: Multiband description of the optical properties of zincblende nitride quantum dots.

Xia CX, Zeng ZP, Wei SY: Effects of applied electric field and hydrostatic pressure on donor impurity states in cylindrical GaN/AlN quantum dot.

Xia CX, Zeng ZP, Liu ZS, Wei SY: Exciton states in zincblende GaN/AlGaN quantum dot: effects of electric field and hydrostatic pressure.

Shi L, Yan ZE: Exciton in a strained (001)oriented zincblende GaN/Al_{x}Ga_{1−x}N ellipsoidal finitepotential quantum dot under hydrostatic pressure.
Phys Stat Sol C 2011, 8:42. Publisher Full Text

Chichibu SF, Azuhata T, Okumura H, Tackeuchi A, Sota T, Mukai T: Localized exciton dynamics in InGaN quantum well structures.
Appl Surf Sci 2002, 190:330. Publisher Full Text

Park SH, Ahn D, Lee YT, Chuang SL: Exciton binding energies in zincblende GaN/AlGaN quantum wells.
Japn J Appl Phys 2004, 43:140. Publisher Full Text

Jauho AP, Johnsen K: Dynamical FranzKeldysh effect.
Phys Rev Lett 1996, 76:4576. PubMed Abstract  Publisher Full Text

Enders BG, Lima FMS, Nunes OAC, Fonseca ALA, Agrello DA, Fanyao Q, Da Silva Jr. EF, Freire VN: Electronic properties of a quasitwodimensional electron gas in semiconductor quantum wells under intense laser fields.

Mani RG, Smet JH, von Klitzing K, Narayanamurti V, Johnson WB, Umansky V: Zeroresistance states induced by electromagneticwave excitation in GaAs/AlGaAs heterostructures.
Nature 2002, 420:646. PubMed Abstract  Publisher Full Text

Asmar NG, Markelz AG, Gwinn EG, Cerne J, Sherwin MS, Campman KL, Hopkins PF, Gossard AC: Resonantenergy relaxation of terahertzdriven twodimensional electron gases.
Phys Rev B 1995, 51:18041. Publisher Full Text

Hsu H, Reichl LE: FloquetBloch states, quasienergy bands, and highorder harmonic generation for singlewalled carbon nanotubes under intense laser fields.

Brandi HS, Latgé A, Oliveira LE: Interaction of a laser field with a semiconductor system: application to shallowimpurity levels of quantum wells.

Brandi HS, Latgé A, Oliveira LE: Laser effects on donor states in lowdimensional semiconductor heterostructures.

Lima FMS, Amato MA, Nunes OAC, Fonseca ALA, Enders BG, da Silva Jr EF: Unexpected transition from single to double quantum well potential induced by intense laser fields in a semiconductor quantum well.
J Appl Phys 2009, 105:123111. Publisher Full Text

Xia JB, Fan WJ: Electronic structures of superlattices under inplane magnetic field.
Phys Rev B 1989, 40:8508. Publisher Full Text

Gavrila M, Kaminski JZ: Freefree transitions in intense highfrequency laser fields.
Phys Rev Lett 1984, 52:613. Publisher Full Text

Pont M, Walet NR, Gavrila M, McCurdy CW: Dichotomy of the hydrogen atom in superintense, highfrequency laser fields.
Phys Rev Lett 1988, 61:939. PubMed Abstract  Publisher Full Text

Sari H, Kasapoglu E, Sökmen I: The effect of an intense laser field on magneto donors in semiconductors.
Phys Lett A 2003, 311:60. Publisher Full Text

Kasapoglu E, Sari H, Güneş M, Sökmen I: Magnetic field and intense laser radiation effects on the interband trasnsitions in quentum well wires.
Surface Rev Lett 2004, 11:403. Publisher Full Text

Kasapoglu E, Sökmen I: The effects of intense laser field and electric field on intersubband absorption in a doublegraded quantum well.
Physica B 2008, 403:3746. Publisher Full Text

Diniz Neto OO, Qu F: Effects of an intense laser field radiation on the optical properties of semiconductor quantum wells.
Superlatt Microstruct 2004, 35:1. Publisher Full Text

Niculescu EC, Eseanu N: Interband absorption in square and semiparabolic nearsurface quantum wells under intense laser field.
Eur Phys J B 2011, 79:313. Publisher Full Text

Eseanu N: Intense laser field effect on the interband absorption in differently shaped nearsurface quantum wells.
Phys Lett A 2011, 375:1036. Publisher Full Text

Fox AM, Miller DAB, Livescu G, Cunningham JE, Jan WY: Excitonic effects in coupled quantum wells.
Phys Rev B 1991, 44:6231. Publisher Full Text

Galbraith I, Duggan G: Exciton binding energy and externalfieldinduced blue shift in double quantum wells.
Phys Rev B 1989, 40:5515. Publisher Full Text

Yu P, Cardona M: Fundamentals of Semiconductors, 3rd ed. Springer, Berlin; 2003.

Sadowski J: Excitonic luminescence in strained quentum wells.

Baser P, Elagoz S, Baraz N: Hydrogenic impurity states in zincblende InxGa1−xN/GaN in cylindrical quantum well wires under hydrostatic pressure.
Physica E 2011, 44:356. Publisher Full Text

Duque CA, MoraRamos ME, Kasapoglu E, Sari H, Sökmen I: Combined effects of intense laser field and applied electric field on exciton states in GaAs quantum wells: transition from the single to double quantum well.
Phys Stat Sol B 2012, 249:118. Publisher Full Text