Zn(S, Se)-based quantum wells : band offsets, excitons and optical properties

The Wannier exciton properties in a single quantum well (SQW) of Zn(S,Se)/ZnS strained materials are reproduced by an accurate variational envelope function. A systematic study of binding energy and oscillator strength is performed as a function of well thicknesses and strain parameter values. Optical response and second harmonic generation effects (SHG) in asymmetric single quantum wells (ASQWs) is computed and briefly discussed. 1.Introduction: ZnSe-based materials are becoming an attractive prospect for utilization in green-blue light emission(*). In spite of the efforts in technological applications, compared to the case of GaAs-based materials, little background knowledge is available in the litterature for this case (2). The Z n S a n S system shows large strain (ZnSe lattice constant is a=5.667A respect to the lattice constant a=5.412A of the ZnS) this influences the gap-tayloring properties and removes the cubic symmetry of the sample. In Section 2 a systemic study of Zn(S,Se)/ZnS strained materials and their exciton properties are computed by a variational envelope function in asymmetric QWs. The role of the strain effects on linear and non-linear optical properties of the exciton will be discussed in Section 3. 2.Exciton Properties: Let us consider a quantum well of dimension L, growths along the z-axis,(L,/2 < Z < L,/2) and cladded between two barriers. In the effective mass approximation the exciton Hamiitonian (in atomic units) is: where &o; is the bulk dielectric constant, and Ve and Vh are the confinement potentials for electron and hole respectively. Now, we put all the system into a box of thickness: LBOX>>L. In this case the electron and hole subbands will have to fulfil1 the so-called "no-escape boundary conditions" at the box boundaries (3). For L B O ~ ->oo we have a continuum of exciton states outside the well, while for large, but finite LBOX value, we have a quasi-continuum of states that will take into account the effect of the finite spatial dimension of the barriers('$. The l S-state wavefunction solutions of eq. l are obtained as variational expansions in the basis set: $ijn(~,ze,zh)=Nijnci(ze)vj(zh)ex~(-%r), (2) Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1993588 414 JOURNAL DE PHYSIQUE IV where = re-rh with 1r1=$2+(zez h ) ~ , Niln are the normalization constants of the function and Ci(k) (Vj(Zh)) is the conduction (valence) subband state of quantum number i 0). Ci(*) is obtained by the complete set of the orthonormalized eigenfunctions of the Hamiltonian: 1 a2 H e = -2me aze2 + Ve(ze). (3) fulfilling the no-escape boundary conditions: I c~(z,= + LBox/2) 12= 0, for i=1,2,3 ,... (4) and the continuity conditions at the well edges (z.&L;/2). Analogously for the hole subbands Vj(Zh). The parameters an (n=1,2,3, ...) are chosen as variational parameters and are computed by minimizing the first momentum of the Harniltonian of eq.l for each product of subbands Ci(*)Vj(zh). The exciton levels are obtained by minimizing the trial function , @(P, ze,zh)= Pijn $ijn(P, zeyzh) (5) with respect to the variational expansion coefficients Pijn. Let us consider the strained system ZnSel-,S,/ZnSe/ZnS with parameter values: ZnSe: m,=0.34mO mhh=l .760m, Egap=2.72eV CI2/Cl 1d.605 a=-5.9eV b=1.2eV ZnS : ~ = 0 . 1 6 m , mM=0.775m, E ap=3.64eV C12/Cll=0.642 a=-4.OeV b=-0.7eV and thicknesses: 200.4Lw(A)/200A . thls case, we have different values of potential confinements for electron and hole on the left (ZnSel-,S,/ZnSe) and on the right (ZnSennS) interfaces. In fig.1 the exciton binding energies are reported for two values of alloy concentration x=10% and 20% as a function of well thickness L,. For the interface ZnSeIZnS (43) the confinement potentials for electron and hole are respectively: Ve=80meV , Vh=780meV. The characteristic exciton quasi-two-dimensional transitions, due to the finite localizing potential values$$, are clearly shown. In this range of thicknesses the electron jumps in the left-barrier and the exciton recoveres the 3D behaviour. The dipole moment of the exciton, calculated per unit of area of the sample, is: f = l L B r ~ Q ( p = O , z = z ~ = z ~ ) I 2 (6) 'LBox/~ ThelS-exciton dipole moments for the lowest (n=l) and the first excited state (n=2), computed as a function of h, are reported in fig.2. IS^....'^..^'...^'...^....^ 1'0 2'0 3'0 4'0 5'0 Lw (A) Fig. l Exciton binding energies Lw (A) Fig2 Exciton dipole moments Note that in symmetric QWs the dipole moment of the state n=2 is zero. In asymmetric QWs all the exciton states have not definite parity and, for the parameter values choosen, the n=2 dipole moment is 2.5times lower than the fundamental exciton state (n=l). Moreover, the dipole moment has non-negligible values only for a very narrow range of thicknesses (about 18A for x=20%), thus only in that range of thicknesses electron and hole subbands could show strong asymmetries. 3.0ptical Response: We choose a sample with large exciton asymmetric behaviour in order to obtain a large SHG susceptibility, namely: &=30A and x=20%, The reflection and absorption spectra are shown in fig.3 for n=1,2 exciton states; the optical parameters used for calculation are: E0=8.66 4xa=0.0039 E~0=2.802eV. The n=2 exciton peak in the absorption spectrum results enhanced for &=30A (see fig.2) . This interesting property could be used as a fingerprint of the exciton asymmetric behaviour. Since only heavy-hole is CO-mputed in the linear optical response, we consider the component xxz of the second order susceptibility (7) and adopt a two subbands model for the exciton. The susceptibility is, x(2lxxz(2E) = q(2lxXz(i, j ,E) [-] lI2 + C ~ ( ~ ) ~ ~ ~ ( i , i , j , j ' , E ) +C ~ ( ~ ) ~ ~ ~ ( i , i ' , j , j , E ) , ijj ' ii ' j where, Kexx Ei-Ei?+Ei-Ei. K(2)xxz( i , i ' , j ,~ '* E)=(hij+h.h I J ' )Z (Elsij-Elsi.j.)ElsijElsi.j.(E-Elsij+iT)oir) where i and j are respectively the electron and hole subbands and EISij is the corresponding exciton energy , while hij is the 2D exciton Bohr radius. The Kexx value is : KeX = -2e3 h2Ep/(.n&om;&,), where Ep is the Kane energy. The absorption spectra and the modulus of the second order susceptibility, computed by this simplified exciton model, is given in fig.4 . 0 . 0 . 1 2.85 2.9 2.95 3 energy [eV] energy [eV] Fig.3 ~bsorption and reflectivity spectra Fig.4 Absorption and SHG 416 JOURNAL D E PHYSIQUE IV Note that in fig.4 we take into account also the step-like effect dues to the e-h continuum. This effect seems to depress the excited peak at about 2.91eV. Comparing SHG and absorption, the peak El-HH3 at 3.14eV seems promising for device applications. In fact, in that range of energies, also the reflectivity values could be depressed, as shown in fig.3. 4.Conclusions: The asymmetric ZnSel-,S,/ZnSe/ZnS system seems very promising for photonic applications. A systematic study of binding energy and oscillator strength is performed as a function of well thicknesses and strain parameter values in order to obtain exciton asymmetric behaviour. Finally, optical linear response and second order susceptibility are computed for a particular system well suited to obtain large second harmonic generation. Acknowledgments: The authors are indebited to Prof.F.Bassani for useful1 discussions and for the critical reading of the manuscript. This work was partly supported by the European Community Research Project "EASY, action no 6878. REFERENCES: l-J.Ding,H.Jeon, T.Ishiara, M.Hagerott, A.V.Nurmikko, H.Luo, N.Samarthand, J.Furdyna, Phys.Rev.Lett.69 (1992),1707. 2-F.Minami,K.Yoshida,J.Gregus,K.Inoue and H.Fujiyasu, "Optics of Exciton in Confined Systems" ed.A.DIAndrea,R.Del Sole,R.Girlanda and A.Quattropani, 1nst.of Physics 123, Bristol (1991) p.249. 3A.D7Andrea and R.Del Sole,Phys.Rev.B 41,(1990) 1413 see also: Excitons in Confined Systems, ed. by R.Del Sole, A.D'Andrea and A.Lapiccirella, Springer, Berlin (1987); p.102 and Optical Switching in Low Dimensional Systems, ed. by H.Haug and L.Banyai,Plenum,London (1988);p.289. 4-T.Nakayama,J.Phys.Soc,Jpn.59,(1990), 1029 5-Y.Yamada,Y.Masumoto,T.Taguchi and S.Takeda, Proc. 20th Int. Conf.of The Physics of Semiconductors, Ed.E.M.Anastassakis and J.D.Joannopoulos, World Scientific , Singapore (1990) p.941 6-A.D'Andrea and N.Tomassini, Phys.Rev.B47 (1992),7176 7-F.Bassani and R.Atanasov, to be published.