Fine structure of two-photon absorption in CdS

Solid State Communications, Vol. 21, pp. 471-473, 1977.

Pergamon Press.

Printed in Great Britain

FINE STRUCTURE OF TWO-PHOTON ABSORPTION IN CdS* J. Jackel t and H. Mahr Laboratory of Atomic and Solid State Physics and Materials Science Center, Corner University, Ithaca, NY 14853, U.S.A.

(Received 6 September 1976 by M. Cardona) We have observed the free structure of the P-exeitons (,4, n = 2) in Cds through two-photon absorption. The strengths of absorption peaks of P-excitons and their dependence on the polarization of the light agree with predictions of a four-band model of two-photon absorption. Additional two-photon absorption peaks were identified as phasematched two-step two-photon processes involving second harmonic polarizations. TWO-PHOTON absorption into P-exciton states has been reported for many substances. 1"z Resolution of the free structure of these states has previously been observed for ZnSe a only. This letter reports the first two-photon measurement in CdS of a free structure splitting of the A, n = 2 P-exciton state into its components Pz and Px,~, We also show that the results of two-photon absorption obtained for the A and B exciton series of CdS agree with polarization selection rules deduced from group theory and the symmetry assignments produced from linear measurements. We find that the relative strengths of absorption are consistent only with a fourband model of absorption. This conclusion agrees with the earlier two-photon absorption measurements of Sondergeld and Stafford. z Also reported are twophoton absorption peaks that are entirely due to a two~ step mechanism; unique identification of these features was obtained because of correlated second harmonic production measurements. A previously assigned n = 1 absorption peak 4 was thus identified as a phase-matched two-step peak. In the experiment reported, two-photon absorption was monitored by measuring luminescence following the absorption. Luminescence efficiences within the A and B bands of CdS are very nearly independent of exciting frequency 5 so absorption strengths in the frequency region measured are proportional to the observed luminescence. In the experiment a single dye laser pulse is focussed * Research supported by the Office of Naval Research, contract number N00014-75-C-0248, Technical Report No. 2 and the National Science Foundation under grant number DMR76-01281 through the Materials Science Center of Cornell University, Technical Report No. 2733. ~" Present address: Bell Laboratories, Crawford Hill, NJ 07733, U.S.A.

into the sample. Both input photons are therefore of the same frequency. The direction of propagation, k, is either along the c-axis of the crystal or perpendicular to it and along one of the other principal axes. The polarization of the laser pulse is either parallel to c, perpendicular to c, or at 45 ° to c. Slight misalignments (~< l0 °) make all orientations approximate. The sample, a bulk crystal of CdS with polished parallel sides, is held at 4.2 K in a helium bath. Two-photon induced luminescence is measured with a photomultiplier placed at 90 ° to the incident light. In addition second harmonic light generated in the sample was measured with a photomultiplier in the direction of the incident light. Figure 1 shows normalized two-photon induced luminescence intensities as a function of exciting frequency for input polarizations E m II c, Ein ± c and E~n at 45 ° to c, with the A, n = 2 and B, n = 2 exciton absorptions identifield. The additional peak at 2.573 eV for Ein II c (called "Phase-matched Absorption") is also seen in second harmonic generation experiments; it is due to phasematched two-step absorption, l'e In twostep absorption second harmonic light that is produced in the first step can generate a difference frequency wave at the fundamental frequency in a second step. The out-of-phase component of the fundamental wave produced leads to two-photon absorption. This effect is large only if second harmonic generation is phasematched; two-step absorption coincides therefore with peaks of second harmonic light at phase-matching. This indirect two-photon absorption is proportional to [Im (×C2))]2, where Xt2) is the second order nonlinear optical susceptibility, whereas direct two-photon absorption is proportional to Im (×o)), where ×o~ is the third order nonlinear optical susceptibility. 1 Relative exciton absorption strengths can be found from the spectrum of Fig. 1 if background absorption is subtracted.

471

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Vol. 21, Nol 5

FINE STRUCTURE OF TWO-PHOTON ABSORPTION IN CdS WAVELENGTH 4740 4760 I I

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Fig. 2. Luminescence intensity showing fine structure in two-photon absorption by A, n = 2 exciton. The Px.~, component is seen in all spectra; the Pz component appears only for mixed input polarization. (a) Eh, i c; (b) Een II c, slight misalignment; (c) Ee, II c; (d) El, II c , slight misalignment, best resolution. In Fig. 2, the region from 2.566 to 2.588 eV is shown in greater detail with the P~ and Px, y components of the A, n = 2 exciton identified. Absorption at the energy of the A, n = 3 exciton is also seen. Again the phasematched peak occurs at 2.573 eV. A small peak of luminescence intensity at 2.569 eV is situated at the

position of the B, n = 1 longitudinal exciton. No absorption is seen at the energy of the B, n = 1 transverse exciton. In Fig. 2 only the Px,y component appears for Ei. i c [Fig. 2(a)] or El. II c [Fig. 2(c)], but when a slight misali~rnent mixes the polarizations [Figs. 2(b) and (d)] peaks of luminescence are seen for both the Px, y and the Pz components. The separation of the two components ( ~ 0.9 meV) agrees well with the separation observed for absorption of a single photon. 7 Theoretical studies of the polarization dependence of two photon absorption have considered two different kinds of allowable transitions. In a two-band model, s involving one valence and one conduction band only, the only intermediate states allowed for absorption to P-states of a given exciton are the S-states of the same exciton series. In a four-band model z states of any exciton series may serve as the intermediate states for P-exciton absorption. For CdS that would involve the one conduction band and the A, B and C valence bands. The same general selection rules apply for two-photon absorption in either model, but relative strengths of absorption differ and some transitions allowed in the four-band model are absent in the two-band model. In models assuming an s-like conduction band and purely p-like valence bands, S-exciton states cannot be reached in two-photon absorption. In the two-band model no two-photon absorption is allowed for Ein II c for the A, n = 2 exciton. For the four-band model

Vol. 21, No. 5

FINE STRUCTURE OF TWO-PHOTON ABSORPTION IN CdS

absorption into the A, n = 2 Px, x state is allowed for Ein II c and gin I c and Ein II c simultaneously present. A more quantitative calculation using the angular dependence of valence and conduction band wavefunctions z,9 gives the following ratios of total strengths of A, n = 2 to B, n = 2 absorption for each model.

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The measured absorption strengths, derived from Fig. 1, confirm the four-band predictions. The most striking difference between the predictions of the two models is that absorption by the A, n = 2 exciton is entirely absent in the two-band model for Ein II c, while a four-band model predicts that a small absorption will take place. In a two-band model a misalignment of nearly 20 ° would be needed to create this much absorption for A, n = 2, and only the Pz, rather than the observed Px, y component would contribute to absorption. This is because in case of that much misalignment the Ein II c and Ein 45 ° to c components would produce a big enough effect. Alignment was much better in our experiments. Figure 2 confirms the selection rules. For good alignment [Figs. 2(a) and (c)] with Ein II c or gin I c alone, only a Px,~, peak is observed at 2.576 eV. For a slight admixture of the El, ± c polarization into an orientation which has Ein nearly parallel to c, both

473

components Pz and Px, y can be seen [Figs. 2(b) and (d)]. With good resolution [Fig. 2(d)] a splitting of ~ 0.9 meV is deduced. In agreement with the predictions no absorption was found at the position of the S-exciton states. We fred a small absorption peak at the position of the B, n = 1 longitudinal exciton, at about 2.569 eV in Fig. 2. We believe that this peak is due to a direct two-photon absorption process involving a slight misalignment between the direction of light propagation and crystal axis. In spectra taken with particular emphasis on alignment Ei,~ II c with CdS platelets no absorption peak was found at the B, n = 1 longitudinal exciton. In conclusion, we have resolved the Pz and Px,~ components of the A, n = 2 exciton of CdS and find the strengths and selection rules for absorption to agree with those predicted on the basis of previous linear measurements and of a four-band model for two-photon absorption. The presence of absorption at the A, n = 2 exciton when radiation is polarized parallel to the c-axis demonstrates that states in the B and C series serve as intermediate states for absorption by excitons in the A series. The ratios of absorption by A and B excitons confirm that the four-band model gives the best description of two-photon absorption by excitions in CdS for the incident photon energies used. By using second harmonic generation in addition to two-photon absorption measurements extra peaks due to two-step two-photon absorption could be separated from direct two-photon absorption peaks.

Acknowledgement - We thank R.F. Lehey for helpful discussions.

REFERENCES 1.

See, for example, review article by MAHR H., in Quantum Electronics: A Treatise. Vol. 1, Ch. 4; Two-Photon Absorption Spectroscopy (Edited by TANG C.L. & RABIN H.). Academic Press, New York (1975).

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