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Materials Science in Semiconductor Processing 4 (2001) 51-53

Probe of the vicinal Sið111Þ surface by second harmonic phase spectroscopy
D. Schuhmachera,*, G. Marowskya, A.A. Fedyaninb, T.V. Dolgovab, O.A. Aktsipetrovb
a

Laser-Laboratorium Gottingen e.V., Hans-Adolf-Krebs Weg 1, 37077 Gottingen, Germany Å Å b Department of Physics, Moscow State University, 119899 Moscow, Russia

Abstract The intrinsic surface sensitive technique of optical second harmonic (SH) phase and intensity measurements is used to probe a slightly miscut natively oxidized Sið111Þ surface. The experiments have been performed in a spectral interval covering the E2 resonance of silicon band structure. The phase and intensity of the SH wave measured at several azimuthal angular positions allow to separate the vicinal contributions. # 2001 Elsevier Science Ltd. All rights reserved.
Keywords: Vicinal silicon (1 1 1); Second harmonic generation; Phase measurement; Spectroscopy

1. Introduction The high technological importance of silicon has stimulated the development of surface analytical tools. Second harmonic (SH) generation stands out among other techniques as a non-destructive tool with in situ capability and specific interface sensitivity. In the dipole approximation SH generation is symmetry forbidden in the bulk of centrosymmetric media and only the broken symmetry at surfaces and interfaces yields a SH signal. Since the initial works in the early 80s [1] the silicon surfaces and also the vicinal silicon surfaces [2-6] have been well investigated by SH intensity measurements [7]. Recently, the combined intensity and phase spectroscopy have been proposed for studying the resonant SH response of the Si-SiO2 interface [8]. In this paper, the phase differences between vicinal and non-vicinal contributions to the SH field generated

by a vicinal Sið111Þ surface are directly measured using SH single beam interferometry. 2. Experimental A standard SH setup as shown in Fig. 1 (left panel) with a nanosecond optical parametrical oscillator (OPO) as pump source advanced for phase measurements is used for the experiments. The p-polarized SH wave is separated from the p-polarized fundamental wave by proper sets of color filters and detected by a photomultiplier tube (PMT). To normalize the SH intensity over the laser fluence and the spectral function of the detection system a small split-off portion of the pump beam is directed in a SH intensity reference channel consisting of a wedged z-cut quartz plate and a detection system similar to the sample channel. The phase of the SH-wave is obtained by single beam interferometry, a method quite different from linear optical methods. This method makes use of the different refractive indices e.g. of air for fundamental and SH waves. A second movable SH source, a 30 nm thick indium thin oxide (ITO) film (reference) is inserted in the beam path [8]. The total SH intensity

*Corresponding author. Tel.: +49-551-5035-49; fax: +49551-5035-99. E-mail address: dschuhma@llg.gwdg.de (D. Schuhmacher).

1369-8001/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S 1369 -8001(00 )0 0112-8


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D. Schuhmacher et al. / Materials Science in Semiconductor Processing 4 (2001) 51-53

is produced by the coherent sum of the SH waves from reference and sample. Because of air dispersion the total SH signal depends on the distance between both SH sources. The detected SH intensity I 2o is given by [9] I
2o

?

c jE 8p
2o r

2o r

2 þ Es o j 2o s

2

?I

þI

qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4pDn þ 2a Ir2o Is2o cos l þ Frs ; lo

ð1Þ

where Dn ? n2o À no , describing the air dispersion, and a51 indicating the laser coherence. The additional position-independent phase shift Frs ðlo ; l2o Þ between 2 2 Er o and Es o is associated with the spectral properties of the quadratic susceptibilities wð2Þ of the reference and the sample and the Green's function corrections for the SH wave propagation and reflection. Measuring the SH intensity for different distances gives the possibility to extract the position-independent phase shift from the interferograms.

Fig. 1. Scheme of the experimental setup (left panel); principle of phase measurement (right panel).

Fig. 2. Angular dependence of the SH intensity (left panel); SH interferograms obtained at several angles (middle and down right panels); phases received from the SH interferograms and from the fits (top right panel).


D. Schuhmacher et al. / Materials Science in Semiconductor Processing 4 (2001) 51-53

53

The azimuthal angular dependence (anisotropy) of the SH field generated by a vicinal Sið11 1Þ surface is given by [2,4] E 2o ðcÞ ? a0 ei
j
0

phase of the SH field generated from the vicinal Sið11 1Þ surface makes the SH single beam interferometry a prospective probe of vicinal silicon surfaces.

þ a3 ei

j

3

cosð3cÞþ a1 e

ij1

cosðcÞ;

ð2Þ Acknowledgements This work is supported by the Russian Foundation for Basic Research (RFBR) and Deutsche Forschungsgemeinschaft (DFG): RFBR Grant 98-02-04092 and 00-02-16253, DFG Grants 436 RUS 113=439=0, 436 RUS 113=439=0-2(R), MA 610=20-1, and MA 610=20-2 and by the North Atlantic Treaty Organization (NATO): NATO collaborative linkage Grant PST.CLG 975264.

where the threefold and the isotropic terms come from the Sið11 1Þ surface and the onefold term comes from the vicinal contribution. The aj eijj coefficients describe the complex linear and nonlinear optical properties of the sample and the chosen symmetry. The non-zero phase shift ðj1 À j3 Þ and the different symmetry of the vicinal and the ð111Þ crystallographic contributions produce large changes of the relative phase of the total SH wave as a function of the azimuthal angle. Fig. 2 presents a set of interferograms measured at different azimuthal angles (middle and down right panels) for lo ? 571 nm. Without vicinal contributions the SH intensity and phase anisotropies show threefold symmetry (dashed fits) and the phase and intensity in all three maxima are the same. The presence of the vicinal contribution modifies both anisotropies, the more pronounced changes are seen in the phase anisotropy. The difference in phase between the 3008 and 1808 maxima is 0:68 rad. The biggest changes in phase are observed in the minima of intensity anisotropy (2408 and 3608), where the threefold and isotropic contributions destructively interfere. The spectra (490 nm4lo 4680 nm) of SH phase and intensity received at different angular positions show unambiguously a different behavior of the vicinal and ð11 1Þ crystallographic contributions in the vicinity of the E2 resonance of the silicon bandstructure. These spectral results will be discussed in detail in a forthcoming paper.

References
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3. Conclusions In summary, the experimentally observed strong modification of the azimuthal dependence of the relative