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Frequency-domain interferometric second-harmonic spectroscopy P. T. Wilson, Y. Jiang, O. A. Aktsipetrov,* E. D. Mishina,* and M. C. Downer Department of Physics, University of Texas at Austin, Austin, Texas 78712 Received December 1, 1998 We report a new spectroscopic technique to measure simultaneously the intensity and the phase of secondharmonic (SH) radiation over a broad spectral range without laser tuning. Temporally separated SH pulses from two sources, excited by the same broad-bandwidth 15-fs Ti:sapphire fundamental pulse, interfere in a spectrometer to yield frequency-domain interference fringes. We demonstrate the technique by measuring the strongly bias-dependent phase of SH radiation from a SiySiO2 yCr metal-oxide-semiconductor capacitor in the spectral range of the Si E1 critical point. 1999 Optical Society of America OCIS codes: 190.4350, 190.1990, 190.4720, 190.7110, 240.6490, 120.5050.
Because of their high peak intensity, femtosecond laser pulses generate second-harmonic (SH) radiation from weakly nonlinear interfaces such as Si(001) with unprecedented eff iciency.1 The ref lected SH radiation is sensitive to surface conditions, including microroughness,2 strain,3 and adsorption,4 and to nearsurface electric fields.5,6 For determination of the resonant structure of the surface nonlinear susceptis2d bility, xsurface , and for quantitative comparison with microscopic theories of surface SH generation,7 spectroscopic SH amplitude and phase measurements are essential. Existing techniques8 permit such measurements only one frequency at a time, obviating real-time spectroscopic observations, which have become routine in linear ref lectance spectroscopies. In this Letter we demonstrate a powerful new technique for measuring the spectral amplitude and phase of ref lected SH radiation without laser tuning by exploiting the broad bandwidth and coherence of 15-fs pulses. The spectra of such pulses are broader than solid-state critical-point features, thus allowing parallel acquisition of SH spectra by dispersion of the ref lected SH radiation in a spectrometer equipped with an array detector. Sum-frequency as well as SH processes contribute to each frequency of the detected harmonic field Es2vd, which is proportional to Z
` 2`
Gs2v, z, z 0 d
Z
` 2`
x s2d s2v, v 1 D, v 2 D, z0 d
3 Esv 1 D, z0 dEsv 2 D, z0 ddDdz0 > 3 x s2d s2v, zd
Z
normalization of the detected spectrum to the SH spectrum generated by an identical pulse in a spectrally f lat reference sample, yielding a chirp-insensitive measurement of jGs2vdx s2d s2vdj. Figure 1(a) shows SH spectral amplitudes of Si12x Gex alloys s0 # x # 0.125d normalized to GaAs generated with unamplif ied 15-fs pulses from a Kapteyn-Murnane Laboratories Model TS Ti:sapphire laser10 with nonresonant fundamental wavelengths (715–765 nm) and SH wavelengths that are resonant with the E1 critical point of Si12x Gex . The spectra, each acquired in only ,1 s, are consistent with spectra acquired by tuning of a narrow-bandwidth laser across the same range (requiring ,10 min each). The well-known redshift of the E1 resonance with increasing Ge content11 is clearly evident. Figure 1(b)
Z
`
Gs2v, zd 0
`
Esv 1 D, zdEsv 2 D, zddDdz ,
(1)
2`
where G is a Green’s function that includes the nonlinear Fresnel coeff icients of the interface and the propagation of the SH radiation.9 However, when resonances at the fundamental frequencies v 6 D are absent or weak —a common, important special case in SH spectroscopy—the spectral amplitude jGs2vdx s2d s2vdj separates from the autoconvolution of the laser fundamental spectrum. jGs2vdx s2d s2vdj is then isolated by 0146-9592/99/070496-03$15.00/0
Fig. 1. SH spectrum measured with a 15-fs laser from (a) Si12x Gex for varying composition, x. Note the redshift of the peak with increasing x. (b) Native oxidized Si in real time during a heating and cooling cycle. Note the redshift and the attenuation of the peak during heating and recovery on cooling. 1999 Optical Society of America
April 1, 1999 / Vol. 24, No. 7 / OPTICS LETTERS
shows real-time monitoring of the E1 resonance of pure silicon during a heating and cooling cycle. The wellknown broadening and redshift of the E1 resonance during heating12 can be clearly observed. The spectral phase of the sample’s SH signal can also be determined by propagation of the reference and the sample SH pulses collinearly and sequentially into the spectrometer, where they create frequency-domain interferograms.13 Fourier analysis of these interferograms yields the spectral phase, fSHsvd. We call this method frequency-domain interferometric secondharmonic (FDISH) spectroscopy. Figure 2 shows our FDISH setup. The SH reference signal is generated before the sample by focusing of the pulse at f y7 onto a submicrometer SnO2 film and then delayed by T , 1 ps from the 15-fs fundamental pulse in the dispersive glass substrate upon which the film is deposited. These p-polarized incident pulses then ref lect from a Sis001dySiO2 yCr metaloxide-semiconductor (MOS) capacitor at 45±, where the fundamental pulse generates the sample SH pulse. The MOS capacitor consist of a p-type (15 V cm) Si substrate, an 8.7-nm oxide, and a 3.0-nm semitransparent Cr gate electrode. Bias voltage V of 29 V $ V # 10 V is applied between the Cr gate and an ohmic Al backside contact. In the experiment the p-polarized sample and the reference SH pulses were spectrally and polarization filtered before they sequentially entered a spectrograph, where an interferogram with fringe spacing 2pyT (see Fig. 2) was detected by a cooled CCD array. We repeated the measurement with a crystalline quartz standard sample to correct for phase distortions introduced by the SnO2 film and its substrate. The interferograms were inverse Fourier transformed to the time domain, yielding three peaks at t 0, 6T . The peak corresponding to the signal pulse st 2T d was selected, translated to t 0, and Fourier transformed back to the spectral domain.13 The delay T was determined to within an uncertainty sT > 7.5 fs, the time-domain pixel size, and is the primary source of uncertainty in the spectral phase, sw svd sv 2 v0 dsT . We then normalized the resulting spectrum in both amplitude and phase to the result of the same analysis for the quartz standard to obtain x refl L 2wSilicon d2 the phase difference Df swSilicon 1wSilicon x refl L x swquartz 1 wquartz 2 wquartz d. w is the phase of the nonlinear susceptibility, w L results from the inf luence of linear optics on the nonlinear optical process,9 and w refl is the phase imparted to the reference SH pulse upon ref lection from the sample. Although we do not attempt here to separate Dfs2vd quantitatively into its components, we note that the dispersion of L s2vd is weak over the detected spectral range, and wSi that w L and w x are separable in the limit that the susceptibility is homogeneous and the absorption of the fundamental pulse is weak. Figure 3(a) shows the resulting SH phase spectra Dfs2vd for several biases. Corresponding SH spectral amplitudes for V 24 V and V 19.9 V, where minimum and maximum amplitudes, respectively, were observed, are shown in the inset. In Fig. 3(b), the SH phase is replotted as a function of applied bias DfsVd
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for several frequencies. The corresponding SH amplitude for 2hn 3.4 eV is plotted as a function of V in the inset. The bias dependence of these signals originates from the strong electric-field-induced s3d second-harmonic (EFISH) polarization xbulk EDC that is present in the space-charge region immediately beneath the SiySiO2 interface.6 The space-charge field, which extends over a Debye length LD , has magnitude EDC > sV 2 VFB d fs´Si y´ox ddox 1 LD g21 for a MOS capacitor with oxide thickness dox .14 Two features of the results presented in Fig. 3 warrant special comment. First, the general form of DfsVd in Fig. 3(b) approximates a step function that shifts by p at the bias corresponding to minimum SH amplitude. This bias is very close to f lat-band voltage
Fig. 2. Experimental setup for FDISH measurement. The graph shows an example of a raw interferogram.
Fig. 3. (a) FDISH spectral measurements for the Si MOS capacitor at several biases. Inset, spectral amplitude at 23.79 and 9.37 V. ( b) Bias dependence of SH phase for 2hn 3.25 eV to 2hn 3.45 eV in evenly spaced increments.
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VFB ,6 which occurs at 24 V in our sample. Charged interfacial and oxide states create a field that is present at V 0. The p-phase shift occurs because the spacecharge electric field EDC , and the corresponding efs3d fective EFISH susceptibility, xbulk EDC , switch sign at this bias. The clear evidence of this shift shown in Fig. 3(b) conf irms the basic validity of the FDISH technique. Second, additional spectral structure is superimposed upon the step function, as is evident in Fig. 3. This structure can be attributed to the inherent dispers3d s2d sion of xbulk and of the surface dipole xsurface and the s2d bulk quadrupole xquadrupole susceptibilities, which are responsible for field-independent contributions to the SH signal from the SiySiO2 interface and the Si bulk, respectively. Contributions from the Cr and the oxide layers are negligible.6 For V ø VFB , the surface dipole contribution has been shown to dominate6 based on the strong redshift of the spectral amplitude of the E1 resonance from the bulk value 2hn 3.4 eV to the surface-modified value 3.3 eV [inset of Fig. 3(a)]. The corresponding phase spectra for V ø VFB reveal a strong dispersive feature at 2hn 3.38 eV [see V 24.25 V and V 23.79 V curves in Fig. 3(a)]. This feature is almost certainly associated with the E1 resonance but is displaced by nearly 0.1 eV to higher energy from the E1 amplitude peak at these biases. A possible explanation is that strong two-photon resonances at higher energies such as the E2 resonance s2hn 4.3 eVd pull the phase resonance to higher energy. For jV j .. jVFB j, the EFISH contribution dominates, as evidenced by the bias-dependent SH amplitude [inset of Fig. 3(b)] and the strong bulklike E1 amplitude peak at 3.4 eV [inset of Fig. 3(a)]. The corresponding phase spectra for these biases are relatively featureless throughout the detected spectral range [see Fig. 3(a)]. A possible explanation is that the expected resonant feature in the phase spectrum, like those of the surfacelike spectra for V ø VFB , is pulled to higher energies, and thus beyond the currently detected spectral range. Extension of FDISH spectroscopy to higher photon energies and a microscopic theory of the SH susceptibilities will be necessary to clarify this point. In summary, we have measured the bias-dependent SH amplitude and phase spectra of a p-type SiySiO2 yCr MOS capacitor, using the new technique of FDISH spectroscopy. This technique exploits all the unique features of femtosecond pulses: high peak intensity to optimize SHG eff iciency, broad bandwidth for SH spectroscopy, and coherence for SH phase measurement. Pulses of ,10 fs (see Ref. 15) will permit these features to be exploited still more effectively. FDISH spectroscopy can reveal the inf luence of one-photon resonances if the phase structure of
the fundamental pulse is independently characterized by a technique such as frequency-resolved optical gating. This procedure then becomes a special case of temporal analysis by dispersion of a pair of light E-f ields (TADPOLE).16 This work was supported by Robert Welch Foundation grant F-1038, National Science Foundation Science and Technology Center Program grant CHE-890210, Texas Advanced Technology Program grant 003658-178, and a grant from Advanced Micro Devices, Inc. M.C. Downer’s e-mail address is
[email protected]. *Permanent address, Department of Physics, Moscow State University, Moscow 119899, Russia. References 1. J. I. Dadap, X. F. Hu, N. M. Russell, J. G. Ekerdt, M. C. Downer, and J. K. Lowell, IEEE J. Sel. Topics Quantum Electron. 1, 1145 (1995). 2. S. T. Cundif f, W. H. Knox, F. H. Baumann, K. W. Evans-Lutterodt, M.-T. Tang, M. L. Green, and H. M. van Driel, Appl. Phys. Lett. 70, 1414 (1997). 3. W. Daum, H.-J. Krause, U. Reichel, and H. Ibach, Phys. Rev. Lett. 71, 1234 (1993). 4. X. F. Hu, Z. Xu, D. Lim, M. C. Downer, P. S. Parkinson, B. Gong, G. Hess, and J. G. Ekerdt, Appl. Phys. Lett. 71, 1376 (1997). 5. G. Lupke, C. Meyer, C. Olhof f, H. Kurz, S. Lehmann, and G. Morowsky, Opt. Lett. 20, 1997 (1995). 6. J. I. Dadap, X. F. Hu, M. Anderson, M. C. Downer, J. K. Lowell, and O. A. Aktsipetrov, Phys. Rev. B 53, R7607 (1996); P. Godef roy, W. de Jong, C. van Hasselt, M. Devillers, and Th. Rasing, Appl. Phys. Lett. 68, 1981 (1996). 7. B. S. Mendoza, A. Gaggiotti, and R. del Sole, Phys. Rev. Lett. 81, 3781 (1998). 8. R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996); K. J. Veenstra, A. V. Petukhov, A. P. de Boer, and Th. Rasing, Phys. Rev. B 58, R16020 (1998). 9. P. Guyot-Sionnest, W. Chen, and Y. R. Shen, Phys. Rev. B 33, 8254 (1986). 10. M. T. Asaki, C.-P. Huang, D. Garvey, J. Zhou, H. C. Kapteyn, and M. M. Murnane, Opt. Lett. 18, 977 (1993). 11. G. E. Jellison, Jr. and F. A. Modine, Phys. Rev. B 27, 7466 (1983). 12. J. Humlicek, M. Garriga, M. I. Cardona, and M. Cardona, J. Appl. Phys. 65, 2827 (1988). 13. L. Lepetit, G. Ch´eriaux, and M. Jof f re, J. Opt. Soc. Am. B 12, 2467 (1995). 14. O. A. Aktsipetrov, A. A. Fedyanin, J. I. Dadap, and M. C. Downer, Laser Phys. 6, 1142 (1996). 15. J. Zhou, G. Taft, C.-P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, Opt. Lett. 19, 1149 (1994). 16. D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbugel, K. W. DeLong, R. Trebino, and I. A. Walmsley, Opt. Lett. 21, 884 (1996).
